Automatic transaction quotation method and system based on deep learning

Abstract

The invention discloses an automatic transaction quotation method and system based on deep learning. The method comprises the following steps: acquiring an underlying asset price at an initial moment; based on Brownian motion, sampling is carried out between the initial moment and the terminal moment, and Brownian motion increments of the target asset price at a plurality of sampling moments are obtained; performing forward recursion to obtain an underlying asset price at a terminal moment based on the underlying asset price at the initial moment and the Brownian motion increments and fluctuations corresponding to the plurality of sampling moments; based on the target asset price at the terminal moment, the corresponding value of the generation element function and the corresponding value of the hedging strategy function, the derivative price at the initial moment, the fluctuation ratio corresponding to each sampling moment, the corresponding value of the generation element function and the corresponding value of the hedging strategy function are obtained through reverse recursion; the price is obtained by fitting at least based on the underlying asset price corresponding to the sampling moment.

Description

Technical Field

[0001] The present application belongs to the field of automated trading technology, and in particular, relates to an automated trading quotation method and system based on deep learning. Background Art

[0002] An option contract, as a type of derivative contract, refers to a standardized or non-standardized contract that stipulates that the buyer has the right to buy or sell the agreed subject matter (including futures contracts) at a specific price at a certain time in the future. Trading activities with option contracts as the trading subject are an important part of derivative trading and have risk management functions such as hedging. The pricing of option contracts and the design of trading strategies provide traders with standardized trading and risk management support. The present invention provides an option pricing method and a trading system. Traditional option pricing methods, such as the Black-Scholes model and the binomial tree model, are widely used in financial markets, but these methods are usually based on certain assumptions (such as constant volatility, risk-free interest rates, etc.), and fail to fully consider the nonlinear characteristics of the market, volatility changes and other influencing factors. Therefore, these classic models have certain limitations in the actual market, especially in the context of drastic market fluctuations or emergencies, traditional pricing methods may not accurately reflect the value of option contracts.

[0003] In order to cope with these limitations, in recent years, option pricing methods based on deep learning have gradually become a research hotspot in the field of financial technology. Deep learning can extract complex patterns and relationships from market transaction data by analyzing them, without relying on the assumptions of traditional models. This makes the application of deep learning in financial markets have great potential, especially in option pricing and trading execution strategy optimization.

[0004] With the electronicization and automation of market transactions, automated trading systems have become an important part of modern financial markets. Traditional options trading relies on manual decision-making and market experience, while modern automated trading systems can perform real-time option pricing and generate option quotes by utilizing deep learning algorithms combined with real-time market data. These systems can use historical data, market volatility and other information to quickly execute quotation functions, thereby achieving low-latency and high-efficiency transactions. At the same time, through deep learning methods, the system can dynamically evaluate the risks of transactions based on real-time market data and automatically adjust trading strategies, thereby reducing potential losses for traders. Summary of the invention

[0005] The embodiments of the present application provide a deep learning-based automated trading quotation method and system that can accurately calculate the price of derivatives.

[0006] In a first aspect, an embodiment of the present application provides an automated trading quotation method based on deep learning, including: obtaining the price of the underlying asset at the initial moment; based on Brownian motion, sampling between the initial moment and the terminal moment to obtain the Brownian motion increments of the underlying asset price at multiple sampling moments; based on the underlying asset price at the initial moment, the Brownian motion increments corresponding to multiple sampling moments, and the volatility, forward recursion is used to obtain the underlying asset price at the terminal moment; based on the underlying asset price at the terminal moment, the corresponding values ​​of the generator function, and the corresponding values ​​of the hedging strategy function, reverse recursion is used to obtain the derivative price at the initial moment, and the volatility, the corresponding values ​​of the generator function, and the corresponding values ​​of the hedging strategy function corresponding to each sampling moment are obtained by fitting a neural network model based at least on the underlying asset price corresponding to the sampling moment.

[0007] In an optional embodiment of the first aspect, based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion, including: based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the initial derivative price at the initial moment is reversely recursively derived; based on the measurability auxiliary amount, the measurability of the initial derivative price at the initial moment is calibrated to obtain the derivative price at the initial moment, and the measurability auxiliary amount is determined based on the Brownian motion increments at multiple sampling moments.

[0008] In an optional embodiment of the first aspect, the process of training a neural network model includes: obtaining multiple underlying asset price samples; for the multiple underlying asset price samples, based on Brownian motion, obtaining multiple Brownian motion paths corresponding to the underlying asset price samples; based on the neural network model, fitting the derivative prices at the initial moment corresponding to the multiple Brownian motion paths to obtain multiple derivative price fitting values; based on the loss function of the neural network model, the multiple derivative price fitting values ​​corresponding to the multiple Brownian motion paths and the multiple derivative price true values, determining the loss value of the neural network model, the multiple derivative price true values ​​being the true derivative prices at the initial moment; based on the loss value, training the neural network model to obtain a trained neural network model.

[0009] In an optional embodiment of the first aspect, the loss function is: ,in, Used to represent the derivative price fitting value, Used to indicate the true value of derivative prices. It is used to indicate the derivative price corresponding to the nth sampling moment, N is used to indicate the target number of steps, n=0, 1, ..., N-1, It is used to represent the measurability auxiliary quantity at the nth sampling moment. The measurability auxiliary quantity is determined based on the Brownian motion increment. and It is used to indicate the penalty coefficient, K is used to indicate the execution price, and i is used to indicate the bullish derivative price or bearish derivative price. Used to indicate the time division between the initial moment and the terminal moment, Used to represent the corresponding value of the hedging strategy function at the nth sampling moment, Used to represent the gradient operator, Used to indicate the nth sampling moment, Used to indicate the price of the underlying asset corresponding to the nth sampling moment, Used to represent the volatility function corresponding to the nth sampling moment.

[0010] In an optional embodiment of the first aspect, based on Brownian motion, sampling is performed between an initial moment and a terminal moment to obtain Brownian motion increments of the underlying asset price at multiple sampling moments, including: based on a target number of steps, random sampling is performed between an initial moment and a terminal moment to obtain multiple sampling moments; based on Brownian motion, the Brownian motion increments of the underlying asset price corresponding to each sampling moment are obtained.

[0011] In an optional embodiment of the first aspect, based on the underlying asset price at the initial moment, the Brownian motion increments and the volatility corresponding to multiple sampling moments, the underlying asset price at the terminal moment is obtained by forward recursion, including: substituting the underlying asset price at the initial moment, the Brownian motion increments and the volatility at multiple sampling moments into a forward stochastic differential equation for forward recursion to obtain the underlying asset price at the terminal moment.

[0012] In an optional embodiment of the first aspect, based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion, including: substituting the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function into the backward stochastic differential equation for reverse recursion to obtain the derivative price at the initial moment.

[0013] In an optional embodiment of the first aspect, obtaining the price of the underlying asset at an initial moment includes: obtaining the price of the underlying asset at an initial moment in response to an input operation of a user in a trading system interface; the method also includes: displaying the price of the derivative at the initial moment on the trading system interface.

[0014] In the second aspect, an embodiment of the present application provides a trading system, including: an acquisition module, used to acquire the price of the underlying asset at the initial moment; a sampling module, used to perform sampling between the initial moment and the terminal moment based on Brownian motion, and obtain the Brownian motion increments of the underlying asset price at multiple sampling moments; a forward recursion module, used to forward recursively obtain the underlying asset price at the terminal moment based on the underlying asset price at the initial moment, the Brownian motion increments corresponding to multiple sampling moments, and the volatility; a reverse recursion module, used to reversely recursively obtain the derivative price at the initial moment based on the underlying asset price at the terminal moment, the corresponding values ​​of the generator function, and the corresponding values ​​of the hedging strategy function, and the volatility corresponding to each sampling moment is obtained by fitting the neural network model based on at least the underlying asset price corresponding to the sampling moment.

[0015] In a third aspect, an embodiment of the present application provides a computer-readable storage medium having computer program instructions stored thereon. When the computer program instructions are executed by a processor, an automated trading quotation method based on deep learning as in the first aspect is implemented.

[0016] The automatic transaction quotation method based on deep learning of the embodiment of the present application uses Brownian motion to sample between the initial moment and the terminal moment, and can obtain the Brownian motion increment of the underlying asset price at multiple sampling moments. Using the Brownian motion increments at multiple sampling moments, the randomness of the underlying asset price changing over time can be well simulated. Using the underlying asset price at the initial moment, the Brownian motion increments and volatility corresponding to multiple sampling moments, the underlying asset price at the terminal moment can be forwarded, and the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be reversed. The derivative price at the initial moment can be reversed. Since the neural network model can quickly process a large amount of data and can better capture nonlinear relationships, the volatility corresponding to each sampling moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be fitted more accurately by using the neural network model, so that the derivative price at the initial moment can be accurately calculated, thereby realizing low-latency and high-efficiency transactions, and can also help users make corresponding decisions based on the derivative price at the initial moment, reducing the potential losses of traders. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solution of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0018] Figure 1It is a flowchart of an automated transaction quotation method based on deep learning provided by an embodiment of the present application; Figure 2 This is a schematic diagram of an interface of a trading system provided by an embodiment of the present application; Figure 3 is a schematic diagram of an interface of a trading system provided by another embodiment of the present application; Figure 4 is a schematic diagram of a price curve of an underlying asset provided by another embodiment of the present application; Figure 5 is a schematic diagram of a derivative price curve provided by another embodiment of the present application; Figure 6 It is a flowchart of an automated transaction quotation method based on deep learning in an option pricing scenario provided by another embodiment of the present application; Figure 7 It is a structural diagram of a trading system provided by an embodiment of the present application; Figure 8 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present application.

[0019] The above drawings include the following reference numerals: 700, trading system; 710, acquisition module; 720, sampling module; 730, forward recursion module; 740, reverse recursion module; 801, processor; 802, memory; 803, communication interface; 810, bus. DETAILED DESCRIPTION

[0020] The features and exemplary embodiments of various aspects of the present application will be described in detail below. In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present application, rather than to limit the present application. For those skilled in the art, the present application can be implemented without the need for some of these specific details. The following description of the embodiments is only to provide a better understanding of the present application by illustrating the examples of the present application.

[0021] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "include..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0022] Traditional deep learning-based automated trading quotation methods, such as the Black-Scholes model and the binomial tree model, usually require assumptions about constant volatility, risk-free interest rates, etc., and traditional deep learning-based automated trading quotation methods cannot fully consider the market's nonlinear characteristics, volatility changes and other influencing factors. As a result, traditional deep learning-based automated trading quotation methods have certain limitations in the actual market.

[0023] In addition, in the context of drastic market fluctuations or unexpected events, traditional pricing methods cannot accurately reflect the prices of derivatives.

[0024] For example, an option contract is a standardized or non-standardized contract that stipulates that the buyer has the right to buy or sell the agreed subject matter (including futures contracts) at a specific price at a certain time in the future. Trading activities with option contracts as the trading subject are an important part of derivatives trading and have risk management functions such as hedging. The pricing of option contracts and the design of trading strategies provide traders with standardized trading and risk management support.

[0025] In order to accurately price options, in recent years, option pricing methods based on deep learning have gradually become a research hotspot in the field of financial technology. Deep learning can extract complex patterns and relationships from market transaction data without relying on the assumptions of traditional models. This makes the application of deep learning in financial markets have great potential, especially in option pricing and trading execution strategy optimization.

[0026] With the electronicization and automation of market transactions, automated trading systems have become an important part of the modern financial market. Traditional option trading relies on manual decision-making and market experience, while automated trading systems can perform real-time option pricing and generate option quotes by utilizing deep learning algorithms combined with real-time market data. Automated trading systems can use historical data, market volatility and other information to quickly execute quotation functions, thereby achieving low-latency and high-efficiency transactions. At the same time, through deep learning methods, automated trading systems can dynamically evaluate the risks of transactions based on real-time market data and automatically adjust trading strategies, thereby reducing potential losses for traders.

[0027] In view of this, the automatic transaction quotation method and system based on deep learning of the embodiment of the present application. By using Brownian motion to sample between the initial moment and the terminal moment, the Brownian motion increment of the underlying asset price at multiple sampling moments can be obtained. By using the Brownian motion increments at multiple sampling moments, the randomness of the underlying asset price changing over time can be well simulated. By using the underlying asset price at the initial moment, the Brownian motion increments and volatility corresponding to multiple sampling moments, the underlying asset price at the terminal moment can be forwarded, and the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be reversed. The derivative price at the initial moment can be reversed. Since the neural network model can quickly process a large amount of data and can better capture nonlinear relationships, the volatility corresponding to each sampling moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be obtained more accurately by using the neural network model, so that the derivative price at the initial moment can be accurately calculated, thereby realizing low-latency and high-efficiency transactions, and can also help users make corresponding decisions based on the derivative price at the initial moment, reducing the potential losses of traders.

[0028] In practical applications, in an embodiment of the present application, the deep learning-based automated transaction quotation method provided in the embodiment of the present application can be implemented when a processor of an electronic device executes a program or instruction.

[0029] It should be noted that the application scenarios described in the above embodiments of the present application are intended to more clearly illustrate the technical solutions of the embodiments of the present application, and do not constitute a limitation on the technical solutions provided in the embodiments of the present application. A person of ordinary skill in the art will know that with the emergence of new application scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems. The deep learning-based automated transaction quotation method provided in the embodiments of the present application can be applied to various application scenarios that require accurate quotation of the underlying assets.

[0030] The following first introduces the deep learning-based automated transaction quotation method provided in the embodiment of the present application.

[0031] Figure 1 FIG. 1 is a flow chart of an automated transaction quotation method based on deep learning provided by an embodiment of the present application. Figure 1 As shown, the automated transaction quotation method based on deep learning in the embodiment of the present application includes steps S101 to S104.

[0032] In step S101, the price of the underlying asset at the initial moment is obtained.

[0033] Optionally, the initial time can be recorded as 0, that is, t=0, where t represents the initial time.

[0034] Optionally, the underlying asset price may be the price of a stock. In the case where the underlying asset price is the price of a stock, the derivative price may be the price of an option.

[0035] In practical applications, there are many ways to obtain the price of the underlying asset at the initial moment.

[0036] In one embodiment, the price of the underlying asset at the initial moment is obtained in response to the user's input operation in the trading system interface. By responding to the user's input operation, the price of the underlying asset at the initial moment can be obtained simply and quickly, and the user's personalized needs can also be met.

[0037] For example, when using a trading system to price options, a user can input the option contract information to be quoted into the trading system through the trading system interface. The option contract information includes but is not limited to parameters such as the underlying asset price, exercise price, and expiration date.

[0038] In another embodiment, the price of the underlying asset at the initial moment may be obtained through a third-party data platform.

[0039] In step S102, based on Brownian motion, sampling is performed between the initial moment and the terminal moment to obtain the Brownian motion increments of the underlying asset price at multiple sampling moments.

[0040] Brownian motion: It is a continuous-time random process used to characterize the random fluctuations of the underlying asset price over time.

[0041] Brownian motion increment: refers to the change in Brownian motion between two different sampling moments. In an optional embodiment, the Brownian motion increment It obeys normal distribution, that is, . Among them, 0 is recorded as the initial time, T is recorded as the terminal time, N is recorded as the target number of steps, Denote the time division between 0 and T and Recorded as the time interval, , n=0, 1,…, N-1.

[0042] Based on Brownian motion, sampling is performed between the initial moment and the terminal moment to obtain the Brownian motion increments of the underlying asset price at multiple sampling moments. There are many ways to implement this.

[0043] In one embodiment, based on the target number of steps, random sampling is performed between the initial moment and the terminal moment to obtain multiple sampling moments; based on the Brownian motion, the Brownian motion increment of the underlying asset price corresponding to each sampling moment is obtained.

[0044] In this embodiment, based on the target number of steps, the time interval between the initial moment and the terminal moment is discretized to obtain multiple sampling moments, which can make the calculation process easy to implement and process, and facilitate the computer to execute the corresponding program. Based on Brownian motion, the Brownian motion increment of the underlying asset price corresponding to each sampling moment can be quickly obtained, and the use of Brownian motion can also better characterize the random fluctuation of the underlying asset price over time.

[0045] For example, for a given terminal time T, the target number of steps is introduced, and the time interval between 0 and T is divided equally to obtain the time interval Starting from the initial moment, every time interval , we can get a sampling moment. Then after the last time interval The sampling moment obtained is the terminal moment. Based on Brownian motion, the Brownian motion increment corresponding to the underlying asset price at each sampling moment can be obtained. ,in, , n=0, 1,…, N-1.

[0046] In another embodiment, the Monte Carlo simulation method may be used to obtain the Brownian motion increment of the underlying asset price corresponding to each sampling moment.

[0047] In step S103, based on the price of the underlying asset at the initial moment, the Brownian motion increments and the volatility corresponding to multiple sampling moments, the price of the underlying asset at the terminal moment is obtained by forward recursion.

[0048] Volatility: It is used to measure the fluctuation degree of the price of the underlying asset, reflecting the uncertainty and risk level of the price changes of the underlying asset.

[0049] For example, when the underlying asset price is a stock price, volatility can be used to measure the volatility of the stock price to reflect the uncertainty and risk level of stock price changes.

[0050] It should be noted that each sampling moment corresponds to a volatility. In the actual calculation process, the volatility at the current sampling moment can be calculated from the corresponding underlying asset price at the previous sampling moment.

[0051] In one embodiment, based on the underlying asset price at the initial moment, the Brownian motion increments and volatility corresponding to multiple sampling moments, the underlying asset price at the terminal moment is obtained by forward recursion, including: substituting the underlying asset price at the initial moment, the Brownian motion increments and volatility at multiple sampling moments into a forward stochastic differential equation for forward recursion to obtain the underlying asset price at the terminal moment.

[0052] In the forward stochastic differential equation, by introducing random terms (i.e. volatility and Brownian motion increment), the random factors between two sampling moments can be accurately captured, so the dynamic changes of the underlying asset price at different sampling moments can be more accurately described.

[0053] In an optional embodiment, assuming that represents the price of the underlying asset at the initial moment. Then, the price of the underlying asset at the initial moment, the Brownian motion increment and volatility at each sampling moment are substituted into the forward stochastic differential equation In , forward recursion can get the price of the underlying asset at each sampling moment. Through this recursive process, the price of the underlying asset at the terminal moment can be obtained. Among them, Used to indicate the price of the underlying asset corresponding to the n+1th sampling moment, Used to represent the price of the underlying asset corresponding to the nth sampling moment, n=0, 1, ..., N-1, It is used to represent the risk-free interest rate. Used to indicate time intervals. It is used to represent the Brownian increment corresponding to the nth sampling moment. Used to represent the volatility function corresponding to the n+1th sampling moment.

[0054] Optionally, after obtaining the underlying asset price corresponding to each sampling moment, the underlying asset price trajectory is composed of the underlying asset prices corresponding to the initial moment and multiple sampling moments. For example, the underlying asset price trajectory can be expressed as ( , , …, ).

[0055] In step S104, based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion. The volatility, the corresponding value of the generator function and the corresponding value of the hedging strategy function corresponding to each sampling moment are obtained by fitting the neural network model based on at least the underlying asset price corresponding to the sampling moment.

[0056] Optionally, generator functions can be used to describe the dynamic behavior of the random process.

[0057] Exemplarily, the hedging strategy function may be used to represent the amount of underlying assets held at time t. In the case where the hedging strategy is Delta hedging, the risk may be eliminated by adjusting the appropriate amount of underlying assets held.

[0058] In one embodiment, based on the underlying asset price at the terminal moment, the corresponding value of the generator function, and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion, including: substituting the underlying asset price at the terminal moment, the corresponding value of the generator function, and the corresponding value of the hedging strategy function into the backward stochastic differential equation for reverse recursion to obtain the derivative price at the initial moment.

[0059] In the backward stochastic differential equation, by introducing random terms (i.e., Brownian motion increments) and dynamically changing parameters (corresponding values ​​of the generator function and the corresponding values ​​of the hedging strategy function), the uncertainty and market dynamics between the two sampling moments can be well captured, thereby accurately describing the dynamic process of how derivative prices change over time and market factors.

[0060] In an optional embodiment, the price of the underlying asset at the terminal time Substitution In the terminal moment, the derivative price can be obtained , where K is used to represent the execution price, Used to represent the derivative price at the terminal moment. Substitute the derivative price at the terminal moment, the corresponding value of the generator function, and the corresponding value of the hedging strategy function into In the above example, we can reversely recursively obtain the derivative price at the initial moment, where: Used to indicate the derivative price corresponding to the nth sampling moment, Used to indicate the derivative price corresponding to the n+1th sampling moment, It is used to represent the value of the generator function corresponding to the nth sampling moment. It is used to represent the corresponding value of the hedging strategy function corresponding to the nth sampling moment. It is used to represent the Brownian increment corresponding to the nth sampling moment. , c is used to represent the bullish derivative price, and p is used to represent the bearish derivative price.

[0061] In an optional embodiment, the price process of the underlying asset at the terminal moment obtained by forward recursion and the price process of the derivative product at the initial moment obtained by reverse recursion can also be expressed in the following continuous form, that is,:

[0062]

[0063] in, It is used to represent the forward recursive process of the underlying asset price. s is used to represent the time. The value range of s is [0, T]. Used to represent the price of the underlying asset at time s, Used to represent Brownian motion at time s, Used to represent the price of the underlying asset at time t, It is used to represent the price process of bullish / bearish derivatives with any expiration date (terminal time) T>0 and execution price K>0. Used to represent the volatility function, Used to represent generator functions, Used to represent the price of derivatives at time t, Used to represent the corresponding value of the hedging strategy function at time s.

[0064] In an optional embodiment of the present application, the underlying asset price at the initial moment Starting from, forward recursion the price path of the underlying asset at the terminal time T From the terminal moment At the beginning, reverse recursion is used to obtain the derivative price path, thereby obtaining the derivative price at the initial moment Among them, the volatility function in the forward recursion process and the backward recursion process is , Generator function The hedging strategy function Z is an unknown number, and its specific value can be fitted by the neural network model. Through the neural network model, the volatility function is fitted , Generator function And the hedging strategy function Z, the derivative price at the initial moment can be obtained.

[0065] In one embodiment, based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion, including: based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is reversely recursively derived; based on the measurability auxiliary quantity, the measurability of the derivative price at the initial moment is calibrated to obtain the derivative price at the initial moment, and the measurability auxiliary quantity is determined based on the Brownian motion increments at multiple sampling moments.

[0066] Measurability is used to indicate that the price of derivatives depends on random information up to now, but not on random information in the future. It is a function related to the sampling moment and the underlying asset price corresponding to the sampling moment. Since the underlying asset price at each sampling moment is obtained based on forward recursion, the measurability auxiliary quantity is naturally measurable. Since the initial derivative price at the initial moment is obtained by reverse recursion, that is, the initial derivative price at the initial moment is naturally dependent on future information. Using the measurability auxiliary quantity to calibrate the measurability of the initial derivative price at the initial moment is to use the measurability auxiliary quantity to filter future information, thereby ensuring that the derivative price at the initial moment is measurable and accurate.

[0067] Optional, measurability aid It can be obtained by neural network fitting.

[0068] In an optional embodiment, the process of training a neural network model includes: obtaining multiple underlying asset price samples; for the multiple underlying asset price samples, based on Brownian motion, obtaining multiple Brownian motion paths corresponding to the underlying asset price samples; based on the neural network model, fitting the derivative prices at the initial moment corresponding to the multiple Brownian motion paths to obtain multiple derivative price fitting values; based on the loss function of the neural network model, the multiple derivative price fitting values ​​corresponding to the multiple Brownian motion paths and the multiple derivative price true values, determining the loss value of the neural network model, the multiple derivative price true values ​​being the true derivative prices at the initial moment; based on the loss value, training the neural network model to obtain a trained neural network model.

[0069] Using the loss value obtained based on the loss function to measure the difference between the fitted value of the derivative price and the true value of the derivative price can intuitively reflect the fitting error of the neural network model. By minimizing the loss value to train the neural network model, the parameters of the neural network model can be continuously adjusted, so that the fitting result of the neural network model is closer and closer to the true value of the derivative price, so that a more accurate derivative price at the initial moment can be obtained later.

[0070] In an optional embodiment, the loss value of each Brownian motion path can be obtained by using the loss function: , i=1,…,M, M is used to represent the total number of Brownian motion paths. , we can get the average loss of M Brownian motion paths. We use the average loss to train the neural network model and get the trained neural network model.

[0071] Optionally, the network parameters of each neural network model can be optimized and adjusted based on the loss average and the gradient method, so as to find the volatility function driven by market data. and the appropriate structure of the generator function g, while adjusting Y and Z at any time to satisfy and the driving equation for g.

[0072] In one embodiment, the loss function is: ,in, Used to represent the derivative price fitting value, Used to indicate the true value of derivative prices. It is used to indicate the derivative price corresponding to the nth sampling moment, N is used to indicate the target number of steps, n=0, 1, ..., N-1, It is used to represent the measurability auxiliary quantity at the nth sampling moment. The measurability auxiliary quantity is determined based on the Brownian motion increment. and It is used to indicate the penalty coefficient, K is used to indicate the execution price, and i is used to indicate the bullish derivative price or bearish derivative price. Used to indicate the time division between the initial moment and the terminal moment, Used to represent the corresponding value of the hedging strategy function at the nth sampling moment, Used to represent the gradient operator, Used to indicate the nth sampling moment, Used to indicate the price of the underlying asset corresponding to the nth sampling moment, Used to represent the volatility function corresponding to the nth sampling moment.

[0073] In the loss function, the true value of the derivative price is used Fitting value with derivative price The difference between the two values ​​is used to calibrate the output of the neural network model, so that the obtained derivative price fitting value is closer to the true value of the derivative price. , it can be guaranteed that the solution set output by the neural network model is a measurable solution. The specific reason is that the derivative price at the initial moment is obtained by reverse recursion, that is, the derivative price at the initial moment is naturally dependent on future information, so it is difficult to ensure that the derivative price at the initial moment is about Measurable. yes Measurable, add in the loss function and The equal constraint can not only satisfy the BSE, but also obtain a measurable solution. In the loss function, Y is used to represent the constraint of Z. Compared with finding a numerical solution to a given equation, since the generator function of the BSE can be changed during optimization, Z can play an important role in the optimization process as a hedging strategy function, and can effectively avoid the optimization process from staying at the local optimum. In summary, based on the loss function of this embodiment, the derivative price at the initial moment is measurable.

[0074] There are many ways to implement the neural network model based on the underlying asset price corresponding to each sampling moment, fitting the volatility corresponding to each sampling moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function.

[0075] In one embodiment, a neural network model can be used to perform different tasks to fit the volatility corresponding to each sampling moment, the corresponding value of the generator function, and the corresponding value of the hedging strategy function.

[0076] In another embodiment, multiple neural network models can be used to fit volatility, corresponding values ​​of generator functions, and corresponding values ​​of hedging strategy functions based on the underlying asset price corresponding to the sampling moment. For example, the multiple neural network models can be a first neural network model, a second neural network model, and a third neural network model. Among them, the first neural network model fits volatility based on the underlying asset price corresponding to the sampling moment. The second neural network model fits the corresponding value of the generator function based on the underlying asset price corresponding to the sampling moment. The third neural network model fits the corresponding value of the hedging strategy function based on the underlying asset price corresponding to the sampling moment.

[0077] For example, for the volatility function to be determined obtained by forward recursion of the forward stochastic differential equation , and the hedging strategy function obtained by reverse recursion of the backward stochastic differential equation And the generator function , respectively introduce the first neural network , the second neural network And the third neural network Replace the recursive formula , and . At the same time, the fourth neural network model is introduced , fitting measurability auxiliary quantity , and through the measurability auxiliary quantity To calibrate The first neural network model corresponds to the network parameters , the second neural network model corresponds to the network parameters , the third neural network model corresponds to the network parameters And the corresponding network parameters of the fourth neural network model The first neural network model , the second neural network model , the third neural network model And the fourth neural network model Can be expressed as:

[0078]

[0079]

[0080]

[0081] It is worth noting that since T is not fixed, each neural network model explicitly depends on the time .

[0082] In one embodiment, the deep learning-based automated trading quotation method of the present application also includes: displaying the derivative price at the initial moment on the trading system interface.

[0083] In this embodiment, the price process of the underlying asset is characterized by a forward stochastic differential equation, in which the volatility function is a function to be estimated; the price process of the derivatives is characterized by a backward stochastic differential equation, in which the generator function and the hedging strategy function are functions to be estimated. At the same time, the discrete formats of the forward stochastic differential equation and the backward stochastic differential equation are given, and the volatility, the corresponding values ​​of the generator function and the corresponding values ​​of the hedging strategy function are fitted using a neural network model, so as to obtain the derivative price at the initial moment and display it on the trading system interface, so that the user can obtain the derivative price at the initial moment more intuitively.

[0084] In an optional embodiment, in order to simplify the user's input operation and improve the interactivity of the trading system, an image or video can be displayed on the interface of the trading system to guide the user to use the trading system. Figure 2 As shown, “Please enter the corresponding setting parameters and click the button below to obtain the derivative price at the initial moment” can be displayed on the interface of the trading system. In this way, users can operate the trading system in a timely and convenient manner according to the guidance on the interface of the trading system.

[0085] For example, Figure 2 As shown, after the user enters the underlying asset price, risk-free interest rate, terminal time and other information at the corresponding position on the interface of the trading system, the trading system determines the derivative price at the initial moment through the built-in deep learning-based automated trading quotation method and trained neural network model of the present application, and displays the derivative price at the initial moment on the interface of the trading system.

[0086] like Figure 3 As shown, in order to make the interface of the trading system tidy and enable users to quickly and efficiently obtain valid information, the trading system also has a second interface, so as to avoid placing too much information on the same trading interface, making the interface of the trading system messy. For example, the price of the underlying asset, that is, the first curve formed over time (such as Figure 4 As shown, the derivatives price obtained by the deep learning-based automated trading quotation method and the trained neural network model of the present application forms a second curve over time (as shown in FIG. Figure 5 The first curve and the second curve are both displayed on the second interface of the trading system, so that the user can more intuitively obtain the underlying asset price and the derivative price at each sampling moment.

[0087] It should be noted that as time goes by and the price of the underlying asset changes, Figure 3 The "first curve" and "second curve" in the graph will also change continuously, so Figure 3 The "first curve" and "second curve" in the figure can be curves of various shapes, and the present application does not limit this. Figure 3 More intuitive, this application Figure 3 The words "first curve" and "second curve" are used to represent them, but in actual applications, Figure 3 The areas corresponding to the “first curve” and the “second curve” are used to present the actual first curve and the second curve.

[0088] The automated transaction quotation method based on deep learning of the embodiment of the present application uses Brownian motion to sample between the initial moment and the terminal moment, and can obtain the Brownian motion increment of the underlying asset price at multiple sampling moments. Using the Brownian motion increments at multiple sampling moments, the randomness of the underlying asset price changing over time can be better simulated. Using the underlying asset price at the initial moment, the Brownian motion increments and volatility corresponding to multiple sampling moments, the underlying asset price at the terminal moment can be forwarded, and the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be reversed. The derivative price at the initial moment can be reversed. Since the neural network model can quickly process a large amount of data and can better capture nonlinear relationships, the volatility corresponding to each sampling moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function can be fitted more accurately by using the neural network model, so that the derivative price at the initial moment can be accurately calculated, thereby achieving low-latency and high-efficiency transactions.

[0089] on the other hand, It is used to represent the corresponding value of the hedging strategy function at the nth sampling moment, and the function contains risk information about the underlying price and the underlying volatility. By receiving the underlying asset price in real time, it can realize the synchronous generation of derivative prices and dynamic hedging instructions, dynamically evaluate the transaction risk, and achieve the function of automatically adjusting the transaction strategy to reduce the potential loss of traders.

[0090] The deep learning-based automated trading quotation method of this application jointly models the underlying asset price and the derivative price, and uses a data-driven approach to find a volatility function that fits the actual situation. And the generator function , avoiding deviations in model settings.

[0091] The deep learning-based automated trading quotation method of this application combines the neural network model and the backward stochastic differential equation, and introduces the representation The neural network control term is used to find the generator function that is more suitable for the actual situation in a data-driven way, making the search for the generator function easier and more accurate.

[0092] The automatic transaction quotation method based on deep learning in this application introduces The constraints ensure that the adaptive solution that satisfies the equation is obtained, and has Measurability, so that corresponding hedging strategies are feasible.

[0093] The automatic transaction quotation method based on deep learning in this application introduces The constraints reduce the optimization difficulty caused by the changes of the generator function during the optimization process, and effectively avoid the situation where the optimization process stays at the local optimum.

[0094] The deep learning-based automated trading quotation method of the present application displays the derivative price at the initial moment on the trading system interface, thereby realizing the automated determination of the derivative price at the initial moment.

[0095] To facilitate understanding, the processing of the deep learning-based automated trading quotation method provided in the embodiment of the present application is described below using an option pricing scenario as an example. Figure 6 The flowchart of the automatic transaction quotation method based on deep learning in the option pricing scenario is as follows. The automatic transaction quotation method based on deep learning includes steps S601 to S605.

[0096] In step S601, data collection: historical data is collected from the market, including but not limited to key indicators such as historical option prices and volatility.

[0097] In step S602, data processing: preprocessing the collected historical data, including but not limited to normalization, noise removal, etc., to ensure the quality and consistency of the data.

[0098] In step S603, model training and fitting: using the preprocessed historical data to train the neural network model.

[0099] Specifically: using a neural network model to fit the derivative price fitting value corresponding to the preprocessed data; determining the loss value of the neural network model based on the loss function of the neural network model, multiple derivative price fitting values ​​and multiple derivative price true values; and training the neural network model based on the loss value to obtain a trained neural network model.

[0100] In step S604, the trading system inputs: the user inputs the option contract information to be quoted through the trading system interface, including but not limited to parameters such as stock price, exercise price and expiration date.

[0101] In step S605, the trading system outputs: the trading system generates a fitting result of the option price based on the trained neural network model, and provides the final option price and corresponding hedging strategy for traders to make decisions.

[0102] The trading system has a built-in neural network model, and the trading system performs option pricing through the following steps.

[0103] Specifically: Based on Brownian motion, sampling is performed between the initial moment and the terminal moment (i.e., the expiration date input by the user through the interface of the trading system) to obtain the Brownian motion increments of the stock price at multiple sampling moments.

[0104] Based on the stock price at the initial moment, the Brownian motion increments and volatility corresponding to multiple sampling moments, the stock price at the terminal moment is obtained by forward recursion.

[0105] Based on the stock price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the option price at the initial moment is obtained by reverse recursion.

[0106] Among them, the trained neural network model is used to fit the volatility, corresponding value of the generator function and corresponding value of the hedging strategy function corresponding to the current sampling moment based on at least the stock price corresponding to the previous sampling moment, thereby obtaining the volatility, corresponding value of the generator function and corresponding value of the hedging strategy function corresponding to each sampling moment.

[0107] Based on the volatility corresponding to each sampling moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the option price at the initial moment is obtained.

[0108] Based on the same inventive concept, the present application embodiment also provides a trading system. Figure 5 The deep learning-based automated transaction quotation method provided in the embodiments of the present application is described in detail.

[0109] It should be noted that the trading system is a device corresponding to the above-mentioned automated trading quotation method based on deep learning. All implementation methods in the above-mentioned method embodiment are applicable to the embodiment of the device and can achieve the same technical effect, which will not be repeated here.

[0110] Figure 7 Schematic diagram of a trading system provided in an embodiment of the present application. Figure 7 As shown, the trading system 700 includes an acquisition module 710 , a sampling module 720 , a forward recursion module 730 , and a reverse recursion module 740 .

[0111] The acquisition module 710 may be used to acquire the price of the underlying asset at an initial moment.

[0112] The sampling module 720 may be used to perform sampling between an initial time and a terminal time based on Brownian motion, and obtain Brownian motion increments of the underlying asset price at multiple sampling times.

[0113] The forward recursion module 730 can be used to obtain the price of the underlying asset at the terminal moment by forward recursion based on the price of the underlying asset at the initial moment, the Brownian motion increments and the volatility corresponding to multiple sampling moments.

[0114] The reverse recursion module 740 can be used to reversely recursively obtain the derivative price at the initial moment based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function. The volatility, the corresponding value of the generator function and the corresponding value of the hedging strategy function corresponding to each sampling moment are obtained by fitting the neural network model based on at least the underlying asset price corresponding to the sampling moment.

[0115] In one embodiment, the reverse recursion module can also be used to reversely recurse the initial derivative price at the initial moment based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function; based on the measurability auxiliary quantity, the measurability of the initial derivative price at the initial moment is calibrated to obtain the derivative price at the initial moment, and the measurability auxiliary quantity is determined based on the Brownian motion increments at multiple sampling moments.

[0116] In one embodiment, the reverse recursion module can also be used to obtain multiple underlying asset price samples; for the multiple underlying asset price samples, based on Brownian motion, multiple Brownian motion paths corresponding to the underlying asset price samples are obtained; based on the neural network model, the derivative prices at the initial moment corresponding to the multiple Brownian motion paths are fitted to obtain multiple derivative price fitting values; based on the loss function of the neural network model, the multiple derivative price fitting values ​​corresponding to the multiple Brownian motion paths and the multiple derivative price true values, the loss value of the neural network model is determined, and the multiple derivative price true values ​​are the true derivative prices at the initial moment; based on the loss value, the neural network model is trained to obtain a trained neural network model.

[0117] In one embodiment, the loss function is: ,in, Used to represent the derivative price fitting value, Used to indicate the true value of derivative prices. It is used to indicate the derivative price corresponding to the nth sampling moment, N is used to indicate the target number of steps, n=0, 1, ..., N-1, It is used to represent the measurability auxiliary quantity at the nth sampling moment. The measurability auxiliary quantity is determined based on the Brownian motion increment. and It is used to indicate the penalty coefficient, K is used to indicate the execution price, and i is used to indicate the bullish derivative price or bearish derivative price. Used to indicate the time interval between the initial time and the terminal time. Used to represent the corresponding value of the hedging strategy function at the nth sampling moment, Used to represent the gradient operator, Used to indicate the nth sampling moment, Used to indicate the price of the underlying asset corresponding to the nth sampling moment, Used to represent the volatility function corresponding to the nth sampling moment.

[0118] In one embodiment, the sampling module can also be used to perform random sampling between the initial moment and the terminal moment based on the target number of steps to obtain multiple sampling moments; based on Brownian motion, obtain the Brownian motion increment of the underlying asset price corresponding to each sampling moment.

[0119] In one embodiment, the forward recursion module can also be used to substitute the underlying asset price at the initial moment, the Brownian motion increment and volatility at multiple sampling moments into the forward stochastic differential equation for forward recursion to obtain the underlying asset price at the terminal moment.

[0120] In one embodiment, the reverse recursion module can also be used to substitute the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function into the backward stochastic differential equation for reverse recursion to obtain the derivative price at the initial moment.

[0121] In one embodiment, the acquisition module can also be used to respond to the user's input operation in the trading system interface to obtain the price of the underlying asset at the initial moment. The trading system of the present application also includes a display module. The display module can be used to display the derivative price at the initial moment on the trading system interface.

[0122] Figure 8 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application is shown.

[0123] The electronic device may include a processor 801 and a memory 802 storing computer program instructions.

[0124] Specifically, the processor 801 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0125] The memory 802 may include a large capacity memory for data or instructions. By way of example and not limitation, the memory 802 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive or a combination of two or more of these. In appropriate cases, the memory 802 may include a removable or non-removable (or fixed) medium. In appropriate cases, the memory 802 may be inside or outside the integrated gateway disaster recovery device. In a specific embodiment, the memory 802 is a non-volatile solid-state memory.

[0126] The memory may include a read-only memory (ROM), a random access memory (RAM), a magnetic disk storage medium device, an optical storage medium device, a flash memory device, an electrical, optical or other physical / tangible memory storage device. Therefore, generally, the memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., a memory device) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the deep learning-based automated trading quotation method according to the first aspect of the present application.

[0127] The processor 801 reads and executes computer program instructions stored in the memory 802 to implement any one of the deep learning-based automated trading quotation methods in the above embodiments.

[0128] In one example, the electronic device may further include a communication interface 803 and a bus 810. Figure 8 As shown, the processor 801, the memory 802, and the communication interface 803 are connected via a bus 810 and communicate with each other.

[0129] The communication interface 803 is mainly used to implement communication between various modules, devices, units and / or equipment in the embodiments of the present application.

[0130] Bus 810 includes hardware, software or both components coupled to each other. For example and not limitation, the bus may include accelerated graphics port (AGP) or other graphics bus, enhanced industry standard architecture (EISA) bus, front side bus (FSB), hypertransport (HT) interconnection, industry standard architecture (ISA) bus, infinite bandwidth interconnection, low pin count (LPC) bus, memory bus, micro channel architecture (MCA) bus, peripheral component interconnect (PCI) bus, PCI-Express (PCI-X) bus, serial advanced technology attachment (SATA) bus, video electronics standard association local (VLB) bus or other suitable bus or two or more of these combinations. Where appropriate, bus 810 may include one or more buses. Although the present application embodiment describes and shows a specific bus, the present application considers any suitable bus or interconnection.

[0131] The electronic device can execute the automatic transaction quotation method based on deep learning in the embodiment of the present application, thereby realizing the combination of Figures 1 to 3 Described is a deep learning-based automated trading quotation method.

[0132] In addition, in combination with the automated transaction quotation method based on deep learning in the above embodiments, the present application embodiment can provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when the computer program instructions are executed by the processor, any one of the automated transaction quotation methods based on deep learning in the above embodiments is implemented.

[0133] An embodiment of the present application also provides a computer program product, including a computer program, which, when processed and executed, implements any one of the deep learning-based automated trading quotation methods in the above-mentioned embodiments.

[0134] It should be clear that the present application is not limited to the specific configuration and processing described above and shown in the figures. For the sake of simplicity, a detailed description of the known method is omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present application is not limited to the specific steps described and shown, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps after understanding the spirit of the present application.

[0135] The functional blocks shown in the structural block diagram described above can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present application are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier. "Machine-readable medium" may include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROMs, flash memories, erasable ROMs (EROMs), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0136] It should also be noted that the exemplary embodiments mentioned in this application describe some methods or systems based on a series of steps or devices. However, this application is not limited to the order of the above steps, that is, the steps can be performed in the order mentioned in the embodiment, or in a different order from the embodiment, or several steps can be performed simultaneously.

[0137] The above describes various aspects of the present application with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present application. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine so that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the functions / actions specified in one or more boxes of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit. It can also be understood that each box in the block diagram and / or flowchart and the combination of boxes in the block diagram and / or flowchart can also be implemented by dedicated hardware that performs a specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0138] The above is only a specific implementation of the present application. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, modules and units described above can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. It should be understood that the protection scope of the present application is not limited to this. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in this application, and these modifications or replacements should be included in the protection scope of this application.

Claims

1. An automated trading quotation method based on deep learning, characterized in that: include: Get the underlying asset price at the initial moment; Based on Brownian motion, sampling is performed between the initial moment and the terminal moment to obtain the Brownian motion increment of the underlying asset price at multiple sampling moments; Based on the underlying asset price at the initial moment, the Brownian motion increments and the volatility corresponding to the multiple sampling moments, forward recursion is used to obtain the underlying asset price at the terminal moment; Based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial moment is obtained by reverse recursion. The volatility, the corresponding value of the generator function and the corresponding value of the hedging strategy function corresponding to each sampling moment are obtained by fitting a neural network model based on at least the underlying asset price corresponding to the sampling moment.

2. The method according to claim 1, characterized in that Based on the underlying asset price at the terminal time, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial time is obtained by reverse recursion, including: Based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function, reversely recursively deduce the initial derivative price at the initial moment; Based on the measurability auxiliary quantity, the measurability of the initial derivative price at the initial moment is calibrated to obtain the derivative price at the initial moment, and the measurability auxiliary quantity is determined based on the Brownian motion increments of the multiple sampling moments.

3. The method according to claim 1, characterized in that: The process of training the neural network model includes: Get multiple underlying asset price samples; For the plurality of the underlying asset price samples, based on the Brownian motion, obtaining a plurality of Brownian motion paths corresponding to the underlying asset price samples; Based on the neural network model, fitting the derivative prices at the initial moment corresponding to the multiple Brownian motion paths to obtain multiple derivative price fitting values; Determine the loss value of the neural network model based on the loss function of the neural network model, a plurality of derivative price fitting values ​​corresponding to the plurality of Brownian motion paths, and a plurality of derivative price true values, wherein the plurality of derivative price true values ​​are the true derivative prices at the initial moment; Based on the loss value, the neural network model is trained to obtain the trained neural network model.

4. The method according to claim 3, characterized in that The loss function is: in, It is used to represent the fitted value of the derivative price. Used to represent the true value of the derivative price. It is used to indicate the derivative price corresponding to the nth sampling moment, N is used to indicate the target number of steps, n=0, 1, ..., N-1, is used to represent the measurability auxiliary quantity at the nth sampling moment, wherein the measurability auxiliary quantity is determined based on the Brownian motion increment, and It is used to indicate the penalty coefficient, K is used to indicate the execution price, and i is used to indicate the bullish derivative price or bearish derivative price. used to indicate the time division between the initial time and the terminal time, It is used to represent the corresponding value of the hedging strategy function at the nth sampling moment, Used to represent the gradient operator, is used to indicate the nth sampling moment, It is used to indicate the price of the underlying asset corresponding to the nth sampling moment. Used to represent the volatility function corresponding to the nth sampling moment.

5. The method according to claim 1, characterized in that Based on the Brownian motion, sampling is performed between the initial moment and the terminal moment to obtain the Brownian motion increment of the underlying asset price at multiple sampling moments, including: Based on the target number of steps, random sampling is performed between the initial moment and the terminal moment to obtain a plurality of sampling moments; Based on the Brownian motion, the Brownian motion increment of the underlying asset price corresponding to each sampling moment is obtained.

6. The method according to claim 1, characterized in that Based on the underlying asset price at the initial moment, the Brownian motion increments and volatility corresponding to the multiple sampling moments, the underlying asset price at the terminal moment is obtained by forward recursion, including: Substitute the underlying asset price at the initial moment, the Brownian motion increments at multiple sampling moments, and the volatility into a forward stochastic differential equation for forward recursion to obtain the underlying asset price at the terminal moment.

7. The method according to claim 1, characterized in that Based on the underlying asset price at the terminal time, the corresponding value of the generator function and the corresponding value of the hedging strategy function, the derivative price at the initial time is obtained by reverse recursion, including: Substitute the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function into the backward stochastic differential equation for reverse recursion to obtain the derivative price at the initial moment.

8. The method according to any one of claims 1 to 7, characterized in that Get the underlying asset price at the initial moment, including: In response to an input operation of a user on a trading system interface, obtaining the price of the underlying asset at the initial moment; The method further comprises: The derivative price at the initial moment is displayed on the trading system interface.

9. A trading system, characterized in that: include: The acquisition module is used to obtain the underlying asset price at the initial moment; A sampling module, configured to perform sampling between the initial moment and the terminal moment based on Brownian motion, and obtain the Brownian motion increment of the underlying asset price at multiple sampling moments; A forward recursion module, used to forward recursively obtain the price of the underlying asset at the terminal moment based on the price of the underlying asset at the initial moment, the Brownian motion increments and the volatility corresponding to the multiple sampling moments; A reverse recursion module is used to reversely recursively obtain the derivative price at the initial moment based on the underlying asset price at the terminal moment, the corresponding value of the generator function and the corresponding value of the hedging strategy function. The volatility, the corresponding value of the generator function and the corresponding value of the hedging strategy function corresponding to each sampling moment are obtained by fitting a neural network model based on at least the underlying asset price corresponding to the sampling moment.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer program instructions, which, when executed by a processor, implement the deep learning-based automated trading quotation method as described in any one of claims 1 to 8.

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