Method and device for evaluating options, electronic equipment and storage medium

Abstract

The embodiment of the invention discloses a method and device for evaluating options, electronic equipment and a storage medium. The method comprises the following steps: loading an accumulation profit and loss function of an option in a quantum system; the cumulative profit-loss function is obtained through the product of the profit-loss value of the option and the first auxiliary quantum bit; measuring the amplitude of the first auxiliary quantum bit in the first target quantum state for multiple times, and constructing a maximum likelihood function based on a measurement result; determining the amplitude of the first auxiliary qubit based on a maximum likelihood function; and obtaining a risk value of the option based on the amplitude and the cumulative profit-loss function. Thus, the risk value is obtained based on the amplitude, calculation of the risk value of the option in the quantum system is achieved, the accuracy of risk value calculation is improved, and then the accuracy of option risk assessment is improved.

Description

Technical Field

[0001] This application relates to the field of quantum finance technology, and particularly relates to a method and device for evaluating options, an electronic device, and a storage medium. Background Art

[0002] Currently, as a leveraged financial instrument, options themselves have great risks. Therefore, when conducting option trading, it is usually necessary to calculate the risk measure of options. However, due to the asymmetric risks and information between the two parties of option trading, compared with other financial assets, the risk measure of options is more difficult. Therefore, how to accurately measure option risks in order to manage such risks has become one of the main research issues in financial risk management.

[0003] Currently, there are two types of widely used indicators for option risk measures: one is the Greek letters, and the other is the VaR (Value at Risk) method. Among them, the Greek letters are similar to the sensitivity analysis in risk management, which only considers the impact of a single factor on the option price, and is simple to calculate and convenient to use. However, in reality, there are many factors affecting option risks, and only referring to the Greek letters cannot accurately measure option risks; the VaR method calculates the maximum possible loss of an asset or assets at a specified confidence level. Currently, the VaR method is widely used in the supervision of financial institutions.

[0004] However, in related technologies, the historical simulation method, the parametric method, or the Monte Carlo simulation method is usually used to calculate the maximum possible loss of an asset or assets at a specified confidence level. However, the above methods have high requirements for computing performance, and basic computing devices cannot meet their computing requirements, resulting in low accuracy in option risk assessment. Summary of the Invention

[0005] To solve the above technical problems, embodiments of the present application provide a method and device for evaluating options, an electronic device, and a storage medium, which can improve the accuracy of option evaluation.

[0006] According to one aspect of the embodiments of the present application, a method for evaluating options is provided, including: loading the cumulative profit and loss function of an option in a quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by a first auxiliary qubit;

[0007] Performing multiple measurements on the amplitude of the first auxiliary qubit in the first target quantum state, and constructing a maximum likelihood function based on the measurement results;

[0008] Determining the amplitude of the first auxiliary qubit based on the maximum likelihood function;

[0009] Obtain the risk value of the option based on the amplitude and the cumulative profit and loss function.

[0010] In some embodiments, loading the cumulative profit and loss function of the option in the quantum system includes: loading the price distribution of the option in the quantum system; and loading the cumulative profit and loss function of the option based on the price distribution.

[0011] In some embodiments, loading the price distribution of the option in the quantum system includes: characterizing the option price of each option using a plurality of qubits; determining the probability corresponding to each option price; determining the probability distribution corresponding to each option price based on each of the probabilities, and loading the probability distribution into the quantum system.

[0012] In some embodiments, loading the cumulative profit and loss function of the option based on the price distribution includes: comparing the option price of each option with a preset exercise price; multiplying the probability distribution corresponding to each option price by the second auxiliary qubit respectively; in the case where the option price is less than or equal to the exercise price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to a zero profit and loss value; in the case where the option price is greater than the exercise price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price; and loading the cumulative profit and loss function according to each profit and loss value.

[0013] In some embodiments, loading the cumulative profit and loss function according to each profit and loss value includes: in the case where the quantum state of the second auxiliary qubit is in the second target quantum state, comparing the profit and loss value corresponding to the second auxiliary qubit with a preset profit and loss parameter to obtain a comparison result; and determining the cumulative profit and loss distribution with the profit and loss value less than the profit and loss parameter based on the comparison result and the quantum state of the second auxiliary qubit to obtain the cumulative profit and loss function.

[0014] In some embodiments, measuring the amplitude of the first auxiliary qubit in the first target quantum state multiple times and constructing a maximum likelihood function based on the measurement results includes: amplifying the first auxiliary qubit in the first target quantum state; measuring the amplitude of the amplified first auxiliary qubit multiple times to obtain measurement results; and constructing a maximum likelihood function based on the measurement results.

[0015] In some embodiments, determining the amplitude value corresponding to the first auxiliary qubit based on the maximum likelihood function includes: obtaining the likelihood parameter when the maximum likelihood function is at its maximum value; the maximum likelihood function is constructed through the likelihood parameter; obtaining the amplitude estimate value corresponding to the likelihood parameter; and determining the amplitude estimate value as the amplitude value.

[0016] According to one aspect of the embodiments of the present application, there is provided an apparatus for evaluating options, including: a loading module configured to load the cumulative profit and loss function of an option in a quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by a first auxiliary qubit; a construction module configured to perform multiple measurements on the amplitude of the first auxiliary qubit in a first target quantum state and construct a maximum likelihood function based on the measurement results; a determination module configured to determine the amplitude of the first auxiliary qubit based on the maximum likelihood function; and an acquisition module configured to obtain the risk value of the option based on the amplitude and the cumulative profit and loss function.

[0017] According to one aspect of the embodiments of the present application, there is provided an electronic device, including: one or more processors; a storage device for storing one or more programs, which, when executed by the one or more processors, cause the electronic device to implement the above-mentioned method for evaluating options.

[0018] According to one aspect of the embodiments of the present application, there is provided a computer-readable storage medium having computer-readable instructions stored thereon, which, when executed by a processor of a computer, cause the computer to execute the above-mentioned method for evaluating options.

[0019] In the technical solution provided by the embodiments of the present application, by loading the cumulative profit and loss function of an option in a quantum system, then performing multiple measurements on the amplitude of the first auxiliary qubit in a first target quantum state, constructing a maximum likelihood function based on the measurement results, determining the amplitude of the first auxiliary qubit based on the maximum likelihood function, and then obtaining the risk value of the option based on the amplitude and the cumulative profit and loss function. In this way, this solution loads the cumulative profit and loss function of the option in the quantum system to perform amplitude estimation using the maximum likelihood estimation algorithm in the quantum system, and obtains the risk value based on this amplitude, realizing the calculation of the risk value of the option in the quantum system. Compared with the prior art, the basic computing device cannot meet the computing requirements of the historical simulation method, the parametric method or the Monte Carlo simulation method, resulting in low accuracy of option risk assessment. The quantum system of the present application can meet the computing requirements of calculating the risk value of the present application, improving the accuracy of risk value calculation, and thus improving the accuracy of option risk assessment.

[0020] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. Description of the Drawings

[0021] The accompanying drawings herein are incorporated into and form a part of the specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. In the drawings:

[0022] Figure 1 is a flowchart of a method for evaluating options shown in an exemplary embodiment of the present application;

[0023] Figure 2 is a price distribution diagram of an option when it is a call option shown in an exemplary embodiment of the present application.

[0024] Figure 3 is a profit and loss curve diagram of the buyer when it is a call option shown in an exemplary embodiment of the present application;

[0025] Figure 4 is a profit and loss curve diagram of the seller when it is a call option shown in an exemplary embodiment of the present application;

[0026] Figure 5 is a flowchart of a method for evaluating options shown in another exemplary embodiment of the present application;

[0027] Figure 6 is a block diagram of a device for evaluating options shown in an exemplary embodiment of the present application;

[0028] Figure 7 shows a schematic structural diagram of an electronic device suitable for implementing the embodiments of the present application. Detailed Embodiments

[0029] Here, the exemplary embodiments will be described in detail, and the examples are shown in the accompanying drawings. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are only examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0030] The block diagrams shown in the accompanying drawings are only functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0031] The flowcharts shown in the accompanying drawings are merely illustrative and not necessarily include all content and operations / steps, nor are they necessarily executed in the described order. For example, some operations / steps can be decomposed, while some operations / steps can be combined or partially combined, so the actual execution order may change according to the actual situation.

[0032] As used in this application, "a plurality of" means two or more. "And / or" describes the association relationship of associated objects and indicates that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after.

[0033] See Figure 1 , Figure 1 is a flowchart of a method for evaluating options shown in an exemplary embodiment of this application.

[0034] As Figure 1 shown, in an exemplary embodiment, the method for evaluating options at least includes steps S110 to S140, which are introduced in detail as follows:

[0035] Step S110, loading the cumulative profit and loss function of the option in the quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by the first auxiliary qubit.

[0036] It should be noted that the quantum system is a comprehensive system involving multiple fields such as quantum computing, quantum communication, and quantum measurement, and it uses the principles of quantum mechanics to achieve specific functions.

[0037] The quantum system is constructed based on the principles of quantum mechanics and is essentially different from the classical system. In the classical system, information is stored and processed in binary form, that is, represented by 0 and 1. While the quantum system uses qubits, that is, quantum bits, as the basic computing unit, and quantum bits can be in a superposition state of 0 and 1, or even any superposition state of the two. This superposition state allows the quantum system to represent and process multiple states at the same time, thus possessing powerful parallel computing capabilities.

[0038] Furthermore, loading the cumulative profit and loss function of the option in the quantum system includes: loading the price distribution of the option in the quantum system; loading the cumulative profit and loss function of the option based on the price distribution. In this way, by loading the price distribution of the option in the quantum system and then loading the cumulative profit and loss function of the option based on the price distribution in the quantum system, it is convenient to obtain the risk value of the option based on the cumulative profit and loss function in the quantum system, which improves the efficiency of risk value calculation compared to calculating the risk value in a classical computer.

[0039] Furthermore, loading the price distribution of options in a quantum system includes: representing the option prices of each option using multiple qubits; determining the probabilities corresponding to each option price; determining the probability distribution corresponding to each option price based on each probability, and loading this probability distribution into the quantum system. In this way, by representing the option prices of each option using multiple qubits, determining the probability distribution corresponding to each option price based on the probabilities corresponding to each option price, and then loading this probability distribution into the quantum system, the loading of the probability distribution of options into the quantum system is achieved. Compared with calculating the risk value in a classical computer, using the quantum system to load the probability distribution of options facilitates the subsequent calculation of the risk value and improves the efficiency of risk value calculation.

[0040] It should be noted that representing the option prices of each option using multiple qubits means that by setting the quantum states of each qubit, the quantum data composed of multiple qubits are made different so as to be able to represent different option prices.

[0041] Among them, the option prices of each option follow a normal distribution as the expiration date changes. Among them, the expiration date of an option refers to the last date specified in the option contract for the option buyer to exercise the right, also known as the expiration date, execution date or last trading day of the option contract. On this day, the option buyer has the right to decide whether to execute the purchase or sale of the underlying asset according to the provisions of the option contract.

[0042] It can be seen that the option price is initially a continuous value. In order to facilitate representing the option prices of each option using multiple qubits, it is necessary to sample the option prices within a preset range at equal step lengths to obtain multiple discrete option prices. For example, sampling the option prices within [S Tmin , S Tmax at equal step lengths to obtain multiple discrete option prices; among them, the preset range [S Tmin , S Tmax is the interval of 3 times the standard deviation on both the left and right sides of the mathematical expectation of the continuous option price, that is, the middle value of the preset range [S Tmin , S Tmax is the mathematical expectation of the continuous option price; S Tmax is the upper limit value of the preset range, and the difference between S Tmax and this mathematical expectation is 3 times the standard deviation; S Tmin is the lower limit value of the preset range, and the difference between the mathematical expectation S Tmin and it is 3 times the standard deviation.

[0043] In some embodiments, three qubits can be used to represent eight option prices. For example, when the quantum data composed of three qubits is |000>, the first option price can be represented; when the quantum data composed of three qubits is |001>, the second option price can be represented; when the quantum data composed of three qubits is |010>, the third option price can be represented; when the quantum data composed of three qubits is |011>, the fourth option price can be represented; when the quantum data composed of three qubits is |100>, the fifth option price can be represented; when the quantum data composed of three qubits is |101>, the sixth option price can be represented; when the quantum data composed of three qubits is |110>, the seventh option price can be represented; when the quantum data composed of three qubits is |111>, the eighth option price can be represented.

[0044] It should be noted that since each option price satisfies a normal distribution, the probability of each option price can be calculated through the normal distribution formula.

[0045] Furthermore, based on each probability, the probability distribution corresponding to each option price is determined, and this probability distribution is loaded into the quantum system, including: by Determine the probability distribution corresponding to each option price and load this probability distribution into the quantum system. Among them, |0> n Represents n qubits with a ground state of 0; Represents that n qubits with a ground state of 0 evolve into n qubits with quantum states of through the operator L; the operator L represents the process of using multiple qubits to represent the option prices of each option; is the probability distribution function corresponding to each option price in the quantum system; Represents the quantum state of a qubit, which can be 1 or 0; n is the number of qubits; i is used to represent the i-th option price; pi is the probability of the i-th option price.

[0046] It should be noted that the operator L is used to act on the X register of the quantum system to load the price distribution of the option in the quantum system.

[0047] Specifically, please refer to Figure 2 Figure 2 is the price distribution diagram of the option when it is a call option.

[0048] Such as Figure 2As shown, 3 qubits are used to represent 8 option prices. For example: when the quantum data composed of 3 qubits is |000>, the first option price 1.209 can be represented; when the quantum data composed of 3 qubits is |001>, the second option price 1.438 can be represented; when the quantum data composed of 3 qubits is |010>, the third option price 1.667 can be represented; when the quantum data composed of 3 qubits is |011>, the fourth option price 1.896 can be represented; when the quantum data composed of 3 qubits is |100>, the fifth option price 2.126 can be represented; when the quantum data composed of 3 qubits is |101>, the sixth option price 2.355 can be represented; when the quantum data composed of 3 qubits is |110>, the seventh option price 2.584 can be represented; when the quantum data composed of 3 qubits is |111>, the eighth option price 2.813 can be represented.

[0049] Figure 2 In it, the x-axis is the option price; the y1-axis represents the probability corresponding to the option price. The y2-axis represents the profit and loss of the option. Figure 2 The bar chart in it represents the probability of the option price. Figure 2 The dotted line in it is the distribution chart of the option price. It can be seen that the option price shows a normal distribution. Figure 2 The line chart in it is the profit and loss of the option price when the strike price K = 1.896.

[0050] Furthermore, based on the price distribution, the cumulative profit and loss function of the option is loaded, including: comparing the option price of each option with a preset strike price; multiplying the probability distribution corresponding to each option price by the second auxiliary qubit respectively; when the option price is less than or equal to the strike price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to the zero profit and loss value; when the option price is greater than the strike price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price; loading the cumulative profit and loss function according to each profit and loss value. In this way, by introducing the second auxiliary qubit, it is convenient to use the second auxiliary qubit to indicate the mapping of the profit and loss value, so that the cumulative profit and loss function of the option can be loaded through the probability distribution of the option price in the quantum system. It is convenient to calculate the risk value based on this cumulative profit and loss function using the quantum system. Compared with calculating the risk value in a classical computer, calculating the risk value using the quantum system meets the high requirements for risk value calculation and improves the efficiency of risk value calculation.

[0051] It should be noted that the exercise price, also known as the strike price or the exercise price, refers to the price at which the two parties to an option transaction agree to execute the call option and put option contracts within a specified future period. The exercise price is stored in the Z register of the quantum system.

[0052] By comparing the option price of each option with the preset exercise price, a built-in quantum comparator in the quantum system can be used to compare the option price of each option with the preset exercise price.

[0053] In some embodiments, in the classical algorithm, for a call option, the profit and loss value of the option can be expressed as P T = max(S T - K, 0), where P T is the profit and loss value of the option; S T is the option price of the option; K is the preset exercise price; max(S T - K, 0) represents taking the maximum value between S T - K and 0. For a put option, the profit and loss value of the option can be expressed as P T = max(K - S T , 0), where P T is the profit and loss value of the option; S T is the option price of the option; K is the preset exercise price; max(K - S T , 0) represents taking the maximum value between K - S T and 0.

[0054] Exemplarily, for a call option, if S T < K, the buyer of the option will not conduct the transaction. Therefore, the profit and loss value is 0; if S T = K, whether or not to conduct the transaction, the profit and loss value of the option will not change and remains 0; if S T > K, the buyer of the option will conduct the transaction. Therefore, the profit and loss value is S T - K. It can be seen that for a call option, the profit and loss value of the option conforms to the formula P T = max(S T - K, 0).

[0055] Exemplarily, as Figure 3 and Figure 4 , Figure 3 is the profit and loss curve graph of the buyer for a call option. Figure 4 is the profit and loss curve graph of the seller for a call option.

[0056] Combined with Figure 3 and Figure 4 shown, the x-axis is the option price S T of the option, and K is the preset exercise price. Figure 3 The y-axis ofFigure 4 The y-axis represents the profit and loss value of the seller.

[0057] In Figure 3 , the profit and loss value of the buyer shows an upward trend after S T = K, and the buyer has a gain after exercising the option. On the contrary, the profit and loss value of the seller shows a downward trend after S T = K, and the seller incurs a loss after exercising the option. It can be seen that the gain of the option buyer is equal to the loss of the seller. When the option price of the option continues to increase, theoretically, the maximum loss of the option buyer is limited while the profit is infinite, which means that the risk that the option seller needs to bear may be infinite.

[0058] When applying the above classical algorithm to a quantum system, the option prices of each option are compared with a preset exercise price through a quantum comparator; then, through operation P, when the option price is less than or equal to the exercise price, the profit and loss value corresponding to the option price is mapped to a zero profit and loss value; and when the option price is greater than the exercise price, the profit and loss value corresponding to the option price is mapped to the profit and loss value corresponding to the option price.

[0059] Specifically, when the quantum system executes operation P, a second auxiliary qubit is introduced, and this second auxiliary qubit is used to assist the quantum system in mapping the profit and loss.

[0060] Exemplarily, the definition of operation P is where represents multiplying the probability distribution corresponding to each option price by the second auxiliary qubit respectively, and |0> among them is the second auxiliary qubit. After comparing the option prices of each option with the preset exercise price through a quantum comparator, if S T < K, the second auxiliary qubit is flipped from the |0> state to the |1> state. If S T > K, the second auxiliary qubit is controlled to remain in the |0> state.

[0061] Then the quantum system can map the profit and loss value according to the quantum state of the second auxiliary qubit. For example: when the second auxiliary qubit is in the |0> state, the profit and loss value corresponding to this option price is mapped to a zero profit and loss value. On the contrary, when the second auxiliary qubit is flipped from the |0> state to the |1> state, the profit and loss value corresponding to the option price is mapped to its corresponding profit and loss value P T .

[0062] Further, loading the cumulative profit and loss function according to each profit and loss value includes: when the quantum state of the second auxiliary qubit is in the second target quantum state, comparing the profit and loss value corresponding to the second auxiliary qubit with a preset profit and loss parameter to obtain a comparison result; determining the cumulative profit and loss distribution where the profit and loss value is less than the profit and loss parameter based on the comparison result and the quantum state of the second auxiliary qubit, and obtaining the cumulative profit and loss function. In this way, it is possible to determine the cumulative profit and loss distribution where the profit and loss value is less than the profit and loss parameter by combining the quantum state of the second auxiliary qubit and the comparison result between the profit and loss value corresponding to the second auxiliary qubit and the preset profit and loss parameter, and obtain the cumulative profit and loss function, realizing the loading of the cumulative profit and loss function in the quantum system, so as to calculate the risk value based on this cumulative profit and loss function using the quantum system. Compared with calculating the risk value in a classical computer, calculating the risk value using the quantum system meets the high requirements for risk value calculation and improves the efficiency of risk value calculation.

[0063] It should be noted that the second target quantum state is the |0> quantum state.

[0064] If the first auxiliary qubit corresponding to the profit and loss value is in the |1> state, it means that the profit and loss value is 0, which must be less than the preset profit and loss parameter. Then, it is not necessary to compare the profit and loss value with the preset profit and loss parameter, and it can be directly determined that the profit and loss value is less than the profit and loss parameter. When the second auxiliary qubit corresponding to the profit and loss value is in the |0> state, it is necessary to compare the profit and loss value corresponding to the second auxiliary qubit with the preset profit and loss parameter to obtain a comparison result.

[0065] Specifically, the preset profit and loss parameter is stored in the S register of the quantum system.

[0066] Comparing each profit and loss value with the preset profit and loss parameter to obtain a comparison result, that is, using a controlled comparator to compare each profit and loss value with the profit and loss parameter stored in the S register.

[0067] Exemplarily, the comparison result includes that the profit and loss value is greater than or equal to the profit and loss parameter or the profit and loss value is less than the profit and loss parameter.

[0068] It should be noted that when determining the cumulative profit and loss distribution, the first auxiliary qubit is introduced; the first auxiliary qubit is used to assist the quantum system in determining the cumulative profit and loss distribution.

[0069] Further, based on the comparison result and the quantum state of the second auxiliary qubit, determine the cumulative profit and loss distribution with the profit and loss value less than the profit and loss parameter, and obtain the cumulative profit and loss function, including: multiplying each profit and loss value by the first auxiliary qubit respectively; the initial quantum state of the first auxiliary qubit is the |0> quantum state; when the second auxiliary qubit is in the |1> quantum state, flip the first auxiliary qubit to the |1> quantum state. When the first auxiliary qubit is in the |0> quantum state, if the comparison result is that the profit and loss value is less than the profit and loss parameter, flip the first auxiliary qubit to |1>; if the comparison result is that the profit and loss value is greater than or equal to the profit and loss parameter, keep the first auxiliary qubit in the |0> quantum state.

[0070] Specifically, the definition of operation V is: where l is the profit and loss parameter. is the cumulative profit and loss function described above. in the second the |1> in and the second |0> in

[0071] Step S120, perform multiple measurements on the amplitude of the first auxiliary qubit in the first target quantum state, and construct a maximum likelihood function based on the measurement results.

[0072] where the first target quantum state is the |1> quantum state.

[0073] Further, perform multiple measurements on the amplitude of the first auxiliary qubit in the first target quantum state, and construct a maximum likelihood function based on the measurement results, including: amplifying the first auxiliary qubit in the first target quantum state; performing multiple measurements on the amplitude of the amplified first auxiliary qubit to obtain measurement results; constructing a maximum likelihood function based on the measurement results. In this way, by amplifying the first auxiliary qubit in the first target quantum state, then performing multiple measurements on the amplitude of the amplified first auxiliary qubit, and constructing a maximum likelihood function based on the measurement results, it is convenient to use the maximum likelihood function for amplitude estimation. Compared with the prior art that uses the phase estimation algorithm for amplitude estimation in a quantum system, the present application uses the maximum likelihood function for amplitude estimation, which does not require the exponential circuit depth required by the Fourier transform, has lower resource requirements for the quantum system, and has a wider range of applications.

[0074] It should be noted that after operation V, the first auxiliary qubit is in a quantum superposition state. Therefore, the amplitudes of each qubit cannot be directly obtained. At the same time, quantum measurement itself will cause the collapse of the wave function, so that only the probabilities of each qubit in different basis states can be obtained, and the amplitude cannot be directly obtained. In order to estimate the probability that the target qubit is in the |1> state, it is necessary to continuously estimate each amplitude in the quantum state.

[0075] Specifically, the amplitude estimation requires mapping it to a quantum operator A acting on n+1 qubits such that Where |ψ> is the measured qubit; a∈[0,1], a is the amplitude to be estimated; |ψ 0 > n Characterizes the normalized good state of n qubits; |ψ 1 > n Characterize the normalized bad state of n qubits. By repeatedly measuring |ψ>, we can get the probability that the last qubit is in |1>, and then we can get the value of a. However, the efficiency of this method is the same as that in the classical algorithm, and it cannot reflect the fast and efficient performance of quantum systems.

[0076] In this embodiment, the first auxiliary qubit in the first target quantum state can be amplified to increase the probability that the target qubit is in a good state, that is, the probability that the target qubit is in the |1> state.

[0077] Specifically, the first auxiliary qubit in the first target quantum state is amplified, that is, the target qubit is amplified according to a preset set of amplification times.

[0078] The preset zoom times set includes multiple zoom times, for example: in, is the number of magnifications; k 0 Represents the 0th amplification number; k 1 Characterizes the first amplification number; k R Represents the Rth amplification number.

[0079] For ease of explanation, the number of amplifications is represented by k below. When amplifying the first auxiliary qubit in the first target quantum state, k in the formula can be replaced by the number of amplifications in the amplification number set, for example: 0 , k 1 , …, k R wait.

[0080] Specifically, by calculating Q k ψ>=sin((2k+1)θ a )ψ 1 > n |1>+cos((2k+1)θ a )ψ 0 > n |0> to obtain the first auxiliary qubit after amplification. Among them, Q k ψ> is the first auxiliary qubit after amplification. a is the amplitude; θ a is a custom parameter, θ a ∈[0,π / 2], sin 2 θa = a; Q is the preset amplification operator, and k is the number of executions of the Q operator, i.e., the amplification times.

[0081] Exemplarily, the operator Q = -AS 0 A -1 S f ; where S f is used to multiply the good state by -1 and does not perform any operation on the bad state; S 0 is then used to multiply the amplitudes of n - 1 qubits in the |0> state by -1 and does not perform any operation on other states.

[0082] By defining a as sin 2 θ a , where θ a ∈[0, π / 2]. Substituting θ a into the measurement formula of the qubit |ψ>, we get |ψ> = A|0> n+1 = sinθ a |ψ 1 > n |1> + cosθ a |ψ 0 > n |0>.

[0083] Then, perform the Q operation on the qubit |ψ> k times, and the amplified first auxiliary qubit Q k |ψ> = sin((2k + 1)θ a )|ψ 1 > n |1> + cos((2k + 1)θ a )|ψ 0 > n |0>. It can be seen that after performing the Q operation k times, for a sufficiently small parameter a, the probability of obtaining the good state becomes at least 4k 2 times the original probability, thus achieving the purpose of amplification.

[0084] Furthermore, perform multiple measurements on the amplitudes of the amplified first auxiliary qubit to obtain measurement results, that is, perform a preset number of measurements on the amplified first auxiliary qubit to obtain the set of the number of times the first auxiliary qubit is |1> in the preset number of measurements under different amplification times where is the set of times; h 0 represents the number of times the first auxiliary qubit is |1> within the preset number of measurements when the amplification times is k 0 ; h 1 represents the number of times the first auxiliary qubit is |1> within the preset number of measurements when the amplification times is k 1 ; hR Characterize the amplification times as k R When, within a preset number of measurements, measure the number of times the first auxiliary qubit is |1>.

[0085] Further, construct a maximum likelihood function based on the measurement results, including: obtaining the maximum likelihood function through Obtain the maximum likelihood function. Wherein, L(h; θ a ) represents the maximum likelihood function; k q is the q-th amplification times in the set of amplification times; N q is the number of measurements for the q-th amplification; h q is the number of times the first auxiliary qubit is |1> within a preset number of measurements when the amplification times is k q When.

[0086] Step S130, determine the amplitude of the first auxiliary qubit based on the maximum likelihood function.

[0087] Specifically, determining the amplitude value corresponding to the first auxiliary qubit based on the maximum likelihood function includes: obtaining the likelihood parameter when the maximum likelihood function is at its maximum; the maximum likelihood function is constructed through the likelihood parameter; obtaining the amplitude estimate value corresponding to the likelihood parameter; and determining the amplitude estimate value as the amplitude value. In this way, the amplitude estimate value corresponding to the likelihood parameter is obtained through the likelihood parameter when the maximum likelihood function is at its maximum, realizing amplitude estimation in the quantum system. Compared with the prior art that uses the phase estimation algorithm for amplitude estimation in the quantum system, the present application adopts the maximum likelihood function for amplitude estimation, which does not require the exponential circuit depth required by the Fourier transform, has lower resource requirements for the quantum system, and has a wider range of use

[0088] Specifically, the likelihood parameter is θ a .

[0089] Exemplarily, obtain the likelihood parameter when the maximum likelihood function is at its maximum, that is, obtain the likelihood parameter when the maximum likelihood function is at its maximum through maximum likelihood estimation.

[0090] Specifically, obtain the likelihood parameter when the maximum likelihood function is at its maximum by calculating . Wherein, is the likelihood parameter when the maximum likelihood function is at its maximum; arg is the angular calculation function; max represents taking the maximum value; ln represents calculating the natural logarithm.

[0091] Further, obtaining the amplitude estimate value corresponding to the likelihood parameter includes: obtaining the amplitude estimate value corresponding to the likelihood parameter by calculating a = sin 2 θ a . Wherein, a is the amplitude estimate value corresponding to the likelihood parameter.

[0092] It should be noted that the amplitude estimation value is the probability that the first auxiliary qubit is in the |1> quantum state, that is, the sum of probabilities where the profit and loss value is less than the profit and loss parameter, that is where l is the profit and loss parameter.

[0093] Step S140, obtain the risk value of the option based on the amplitude and the cumulative profit and loss function.

[0094] In this embodiment, by loading the cumulative profit and loss function of the option in the quantum system, then measuring the amplitude of the first auxiliary qubit in the first target quantum state multiple times, constructing a maximum likelihood function based on the measurement results, determining the amplitude of the first auxiliary qubit based on the maximum likelihood function, and then obtaining the risk value of the option based on the amplitude and the cumulative profit and loss function. In this way, this solution loads the cumulative profit and loss function of the option in the quantum system to perform amplitude estimation using the maximum likelihood estimation algorithm in the quantum system, and obtains the risk value based on this amplitude, realizing the calculation of the risk value of the option in the quantum system. Compared with the prior art, the basic computing device cannot meet the computing requirements of the historical simulation method, the parametric method, or the Monte Carlo simulation method, resulting in low accuracy of option risk assessment. The quantum system of this application can meet the computing requirements of calculating the risk value of this application, improve the accuracy of risk value calculation, and thus improve the accuracy of option risk assessment.

[0095] Further, obtaining the risk value of the option based on the amplitude and the cumulative profit and loss function includes: determining the target amplitude based on the amplitude and a preset confidence interval; determining the profit and loss parameter corresponding to the target amplitude as the risk value of the option.

[0096] It should be noted that the risk value of the option is the minimum loss value of the option within the preset confidence interval. Since the amplitude estimation value a is calculated under the preset profit and loss parameter, it can be regarded as there is a corresponding relationship between the amplitude estimation value a and the profit and loss parameter. Specifically, determining the target amplitude based on the amplitude and the preset confidence interval includes: when the amplitude is less than the confidence interval, adjusting the preset profit and loss parameter and calculating the amplitude corresponding to the adjusted profit and loss parameter until the smallest profit and loss parameter is found such that the amplitude corresponding to this profit and loss parameter is greater than or equal to the confidence interval. In this way, it is possible to combine the binary search method to determine the smallest profit and loss parameter for which the amplitude corresponding to the profit and loss parameter is greater than or equal to the confidence interval.

[0097]

[0098] Please refer to Figure 5 Figure 5 , which is a flowchart of a method for evaluating an option.

[0099] Figure 5 As shown, the method for evaluating an option at least includes steps S501 to S513, which are introduced in detail as follows:

[0100] Step S501: Represent the option prices of each option using multiple qubits.

[0101] Step S502: Determine the probabilities corresponding to each option price.

[0102] Step S503: Determine the probability distribution corresponding to each option price based on each probability, and load this probability distribution into the quantum system.

[0103] Step S504: Compare the option prices of each option with a preset strike price.

[0104] Step S505: Multiply the probability distribution corresponding to each option price by a second auxiliary qubit respectively.

[0105] Step S506: In the case where the option price is less than or equal to the strike price, adjust the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to a zero profit and loss value.

[0106] Step S507: In the case where the option price is greater than the strike price, adjust the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price.

[0107] Step S508: Load the cumulative profit and loss function according to each profit and loss value. Among them, the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by a first auxiliary qubit.

[0108] Step S509: Measure the amplitude of the first auxiliary qubit in the first target quantum state multiple times, and construct a maximum likelihood function based on the measurement results.

[0109] Step S510: Obtain the likelihood parameter when the maximum likelihood function is at its maximum value. The maximum likelihood function is constructed through the likelihood parameter.

[0110] Step S511: Determine the amplitude of the first auxiliary qubit based on the maximum likelihood function.

[0111] Step S512: In the case where the amplitude is less than the confidence interval, adjust the preset profit and loss parameter, and calculate the amplitude corresponding to the adjusted profit and loss parameter until the smallest profit and loss parameter is found such that the amplitude corresponding to this profit and loss parameter is greater than or equal to the confidence interval.

[0112] Step S513: Determine the profit and loss parameter corresponding to the target amplitude as the risk value of the option.

[0113] In this embodiment, the option prices are characterized by multiple qubits, so as to load the probability distribution into the quantum system based on the probability distribution corresponding to each option price. Then, the option profit and loss are divided into two mapping cases by the second auxiliary qubit, so as to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price. The quantum amplitude estimation algorithm based on maximum likelihood estimation is used to perform amplitude estimation by using the first auxiliary qubit. In this way, the present application introduces a quantum algorithm into the risk measurement problem of options. Compared with the classical Monte Carlo sampling, the quantum amplitude estimation algorithm can provide quadratic acceleration and improve the efficiency of risk value calculation.

[0114] At the same time, the present application performs amplitude estimation through maximum likelihood estimation, reduces the number of required qubits and the number of controlled operations, thereby reducing the hardware requirements and potential error rates. In this way, the accuracy and stability of practical realizable quantum computing are improved. At the same time, the present application can better adapt to the current level of quantum technology development and improve the universality of the present application.

[0115] In some embodiments, please refer to Figure 6 , Figure 6 which is a block diagram of a device for evaluating options shown in an exemplary embodiment of the present application.

[0116] As Figure 6 shown, the exemplary device for evaluating options includes:

[0117] A loading module 601, configured to load the cumulative profit and loss function of an option into a quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by the first auxiliary qubit;

[0118] A construction module 602, configured to measure the amplitude of the first auxiliary qubit in the first target quantum state multiple times and construct a maximum likelihood function based on the measurement results;

[0119] A determination module 603, configured to determine the amplitude of the first auxiliary qubit based on the maximum likelihood function;

[0120] An acquisition module 604, configured to obtain the risk value of the option based on the amplitude and the cumulative profit and loss function.

[0121] In an exemplary embodiment, the loading module 601 includes:

[0122] A first loading sub-module, configured to load the price distribution of an option into a quantum system;

[0123] A second loading sub-module, configured to load the cumulative profit and loss function of the option based on the price distribution.

[0124] In an exemplary embodiment, the first loading sub-module includes:

[0125] A characterization sub-module, configured to characterize the option price of each option by using multiple qubits;

[0126] A first determination sub-module, configured to determine the probability corresponding to each option price;

[0127] A third loading sub-module, configured to determine the probability distribution corresponding to each option price based on each probability and load the probability distribution into the quantum system.

[0128] In an exemplary embodiment, the second loading sub-module includes:

[0129] A first comparison sub-module, configured to compare the option price of each option with a preset exercise price;

[0130] A multiplication sub-module, configured to multiply the probability distribution corresponding to each option price by a second auxiliary qubit respectively;

[0131] A first mapping sub-module, configured to adjust the quantum state of the second auxiliary qubit when the option price is less than or equal to the exercise price, so as to map the profit and loss value corresponding to the option price to a zero profit and loss value;

[0132] A second mapping sub-module, configured to adjust the quantum state of the second auxiliary qubit when the option price is greater than the exercise price, so as to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price;

[0133] A fourth loading sub-module, configured to load the cumulative profit and loss function according to each profit and loss value.

[0134] In an exemplary embodiment, the fourth loading sub-module includes:

[0135] A second comparison sub-module, configured to compare the profit and loss value corresponding to the second auxiliary qubit with a preset profit and loss parameter when the quantum state of the second auxiliary qubit is in a second target quantum state, and obtain a comparison result;

[0136] A second determination sub-module, configured to determine the cumulative profit and loss distribution with the profit and loss value less than the profit and loss parameter based on the comparison result and the quantum state of the second auxiliary qubit, and obtain the cumulative profit and loss function.

[0137] In an exemplary embodiment, the construction module 602 includes:

[0138] An amplification sub-module, configured to amplify the first auxiliary qubit in the first target quantum state;

[0139] A measurement sub-module, configured to measure the amplitude of the amplified first auxiliary qubit multiple times to obtain a measurement result;

[0140] A constructor sub-module configured to construct a maximum likelihood function based on measurement results.

[0141] In one exemplary embodiment, the determination module 603 includes:

[0142] A first acquisition sub-module configured to acquire likelihood parameters when the maximum likelihood function is at its maximum value; the maximum likelihood function is constructed through the likelihood parameters;

[0143] A second acquisition sub-module configured to acquire an amplitude estimation value corresponding to the likelihood parameters;

[0144] A third determination sub-module configured to determine the amplitude estimation value as the amplitude value.

[0145] It should be noted that the device for evaluating options provided in the above embodiments belongs to the same concept as the method for evaluating options provided in the above embodiments. The specific manners in which each module and unit perform operations have been described in detail in the method embodiments and will not be elaborated here. In practical applications, the device for evaluating options provided in the above embodiments can, as needed, allocate the above functions to different functional modules, that is, divide the internal structure of the device into different functional modules to complete all or part of the functions described above. This is not limited here either.

[0146] An embodiment of the present application also provides an electronic device, including: one or more processors; a storage device for storing one or more programs, and when the one or more programs are executed by the one or more processors, the electronic device implements the method for evaluating options provided in each of the above embodiments.

[0147] Figure 7 The structural diagram of a computer system of an electronic device suitable for implementing the embodiments of the present application is shown. It should be noted that Figure 7 The computer system 700 of the electronic device shown is only an example and should not impose any limitations on the functions and usage scope of the embodiments of the present application.

[0148] Such as Figure 7As shown, the computer system 700 includes a Central Processing Unit (CPU) 701, which can perform various appropriate actions and processes according to a program stored in a Read-Only Memory (ROM) 702 or a program loaded from a storage section 707 into a Random Access Memory (RAM) 703, such as executing the methods described in the above embodiments. In the RAM 703, various programs and data required for system operations are also stored. The CPU 701, ROM 702, and RAM 703 are connected to each other via a bus 704. An Input / Output (I / O) interface 705 is also connected to the bus 704.

[0149] The following components are connected to the I / O interface 705: an input section 706 including a keyboard, a mouse, etc.; an output section 707 including, for example, a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), etc. and a speaker, etc.; a storage section 708 including a hard disk, etc.; and a communication section 709 including a network interface card such as a LAN (Local Area Network) card, a modem, etc. The communication section 709 performs communication processing via a network such as the Internet. A drive 710 is also connected to the I / O interface 705 as needed. A removable medium 711, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 710 as needed so that a computer program read from it can be installed into the storage section 708 as needed.

[0150] Specifically, according to an embodiment of the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a computer program for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 709, and / or installed from the removable medium 711. When the computer program is executed by a Central Processing Unit (CPU) 701, various functions defined in the system of the present application are executed.

[0151] It should be noted that the computer-readable medium shown in the embodiments of the present application may be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two. A computer-readable storage medium may be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable computer program. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The computer program contained on the computer-readable medium may be transmitted by any appropriate medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0152] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present application. Among them, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the above module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order from that marked in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram or flowchart, as well as the combination of blocks in the block diagram or flowchart, may be implemented by a dedicated hardware-based system for performing the specified functions or operations, or may be implemented by a combination of dedicated hardware and computer instructions.

[0153] The units involved in the embodiments described in this application can be implemented in software or in hardware, and the described units can also be provided in a processor. Among them, the names of these units do not constitute a limitation on the units themselves in some cases.

[0154] Another aspect of this application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the method for evaluating options as described above. The computer-readable storage medium can be included in the electronic device described in the above embodiments, or can exist alone without being assembled into the electronic device.

[0155] Another aspect of this application also provides a computer program product or a computer program. The computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method for evaluating options provided in the above various embodiments.

[0156] The above content is only a preferred exemplary embodiment of this application and is not used to limit the implementation of this application. Those of ordinary skill in the art can easily make corresponding changes or modifications according to the main concept and spirit of this application. Therefore, the protection scope of this application should be subject to the protection scope required by the claims.

Claims

1. A method for evaluating an option, characterized in that include: Loading the cumulative profit and loss function of the option in the quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by the first auxiliary quantum bit; Measuring the amplitude of a first auxiliary qubit in a first target quantum state multiple times, and constructing a maximum likelihood function based on the measurement results; determining an amplitude of the first auxiliary qubit based on the maximum likelihood function; The risk value of the option is obtained based on the amplitude and the cumulative profit and loss function.

2. The method according to claim 1, characterized in that The cumulative profit and loss function of loading options in the quantum system includes: Loading price distribution of options in quantum systems; A cumulative profit and loss function for the option is loaded based on the price distribution.

3. The method according to claim 2, characterized in that The price distribution of options loaded in the quantum system includes: Using multiple qubits to represent the option price of each option; Determine the probability corresponding to each option price; The probability distribution corresponding to each option price is determined based on each of the probabilities, and the probability distribution is loaded into the quantum system.

4. The method according to claim 3, characterized in that The step of loading the cumulative profit and loss function of the option based on the price distribution comprises: Compare the option price of each option with the preset strike price; Multiplying the probability distribution corresponding to each option price by the second auxiliary qubit respectively; When the option price is less than or equal to the strike price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to a zero profit and loss value; In a case where the option price is greater than the exercise price, adjusting the quantum state of the second auxiliary qubit to map the profit and loss value corresponding to the option price to the profit and loss value corresponding to the option price; The cumulative profit and loss function is loaded according to each profit and loss value.

5. The method according to claim 4, characterized in that The cumulative profit and loss function is loaded according to each profit and loss value, including: When the quantum state of the second auxiliary qubit is in the second target quantum state, comparing the profit and loss value corresponding to the second auxiliary qubit with a preset profit and loss parameter to obtain a comparison result; Based on the comparison result and the quantum state of the second auxiliary qubit, a cumulative profit and loss distribution whose profit and loss value is less than a profit and loss parameter is determined to obtain the cumulative profit and loss function.

6. The method according to claim 1, characterized in that The step of measuring the amplitude of the first auxiliary qubit in the first target quantum state for multiple times and constructing a maximum likelihood function based on the measurement results includes: amplifying the first auxiliary qubit in the first target quantum state; Measuring the amplitude of the amplified first auxiliary qubit multiple times to obtain measurement results; A maximum likelihood function is constructed based on the measurement results.

7. The method according to claim 1, characterized in that The determining, based on the maximum likelihood function, an amplitude value corresponding to the first auxiliary qubit comprises: Obtaining a likelihood parameter when the maximum likelihood function is at a maximum value; the maximum likelihood function is obtained by constructing the likelihood parameter; Obtaining an amplitude estimate corresponding to the likelihood parameter; The amplitude estimate is determined as the amplitude value.

8. A device for evaluating options, characterized in that: include: A loading module configured to load a cumulative profit and loss function of an option into the quantum system; the cumulative profit and loss function is obtained by multiplying the profit and loss value of the option by the first auxiliary qubit; A construction module configured to measure the amplitude of the first auxiliary qubit in the first target quantum state multiple times and construct a maximum likelihood function based on the measurement results; a determination module configured to determine an amplitude of the first auxiliary qubit based on the maximum likelihood function; An acquisition module is configured to acquire the risk value of the option based on the amplitude and the cumulative profit and loss function.

9. An electronic device, characterized in that: include: one or more processors; A storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, enables the electronic device to implement the method for evaluating options as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: Computer readable instructions are stored thereon, and when the computer readable instructions are executed by a processor of a computer, the computer is caused to execute the method for evaluating options according to any one of claims 1 to 7.

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