Asset pricing method based on deep interactive learning

Abstract

The invention discloses an asset pricing method based on deep interactive learning, and belongs to the technical field of data processing. The FCDIN specifically comprises the following steps: carrying out embedded representation learning on company characteristics; performing high-order feature interaction based on a graph neural network; and carrying out multi-order feature aggregation based on an attention mechanism and outputting a final estimation result of the excess income. According to the asset pricing method based on deep interactive learning provided by the invention, the stock market operation law is taken as the basis, the existing financial theory is taken as the guidance, and economic explanation is emphasized; by adopting the modeling method based on the graph neural network, the problem of redundancy generated by factor interaction constructed by a traditional method is effectively avoided, and the modeling efficiency is improved. The FCDIN enhances the capability of capturing potential pricing information, shows the powerful advantage of coping with a complex market, and plays a key auxiliary role in investor decision making and financial department supervision.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to an asset pricing method based on deep interactive learning. Background Art

[0002] Predicting asset returns is an important topic in asset pricing research and investment management, and various methods have been developed to understand the determinants of stock returns. At present, it is a well-established fact that asset returns are usually correlated with various company characteristics, which represent exposure to systematic and non-diversifiable risk factors. With in-depth research, it is found that capital markets seem to be more efficient, which leads to the risk of failure and low pricing power of many company characteristics. In addition, there is evidence that complex nonlinear interactions between high-dimensional company characteristics are the main determinants of asset returns.

[0003] However, as a pricing information that cannot be directly observed, interaction effects are difficult to be captured by popular factors and simple machine learning (ML) models. Although ML models have great potential in asset pricing research, their performance and credibility seem unstable. On the one hand, most off-the-shelf ML models are general in different fields and lack economic principles in the model building process. On the other hand, interpretability challenges are prevalent. Investors and regulators prefer to understand how the model makes decisions and which variables or interactions drive the effectiveness of the model.

[0004] To this end, the present invention introduces the Company Feature Deep Interaction Network (FCDIN), which focuses on capturing the rich interactive information between high-dimensional company features and mining potential pricing information that is not easily observable by gradually generating deep company features. Summary of the invention

[0005] The purpose of the present invention is to provide an asset pricing method based on deep interactive learning (FCDIN) to solve the problems mentioned in the background technology.

[0006] To achieve the above object, the present invention provides an asset pricing method based on deep interactive learning, comprising the following steps: S1. Based on deep learning methods, we build an asset pricing model that takes different types of company characteristics as input and the corresponding stock excess return prediction value as output; S2. Obtain the company characteristics of the stock and input them into the model, and use the embedding learning technology to perform representation learning on the company characteristics that affect the returns through the model; S3. Through the model, a graph neural network is used to perform high-order interactions on the deep features learned from the company feature representation; S4. Through the model, the attention mechanism is used to aggregate multi-order deep company features and the multi-layer perceptron is used to obtain the final asset pricing result.

[0007] Preferably, step S2 comprises: S21. Extract different depth company features and macroeconomic depth features from the original input data based on embedding learning technology: Assumptions represents a set of macroeconomic variables and six categories of firm characteristics, where Represent the characteristics of macroeconomic variables, transaction frictions, momentum, value, growth, profitability and financial flows respectively; for a given stock sample , expressed as: (1) For any given categorical predictor , expressed as: (2) in represents the number of firm characteristics in each category; In FCDIN, each feature is converted into a real-valued vector through embedding learning technology. The process is expressed as: (3) in, is a learnable parameter vector belonging to the set of real numbers Elements in is the bias term; The quantity that represents the characteristics of a given category of companies; Represents the dimension of the embedding vector; for a category , the embedding technique converts the original company features into an embedding matrix, expressed as: (4) Among them, es represents the size of the embedding (that is, the dimension of the embedding vector); and is the bias term; represents the number of firm characteristics in each category; S22. For different types of predictors, an attention mechanism is designed to aggregate the embedding matrix into a composite deep company feature. For the same type of company features, the attention representation formula is as follows: (5) in, represents the embedding vector; represents the attention weight; attention weight The calculation formula is as follows: (6) in is the attention value; Represents the attention value of the jth feature; in FCDIN, it is calculated using the additive attention mechanism : (7) in ∈ and is a learnable matrix; is the query vector; is the activation function; is the bias term; Denotes the concatenation operator, the deep macroeconomic characteristics and the six deep firm characteristics can be expressed as ; In FCDIN, taking the interaction effect between deep macroeconomic characteristics and deep transaction friction characteristics as an example, it can be expressed as: (8) in represents the Hadamard product; the interactions between deep firm characteristics and deep macroeconomic characteristics of the remaining five categories are ; The obtained embedding matrix is: (9).

[0008] Preferably, S3 includes: Based on the deep feature high-order interaction network of graph neural network GNN, each node corresponds to a type of company feature. The importance of the interaction relationship is represented by the weight of the edge. The high-order interaction between two deep company features can be converted into modeling node interaction on the graph structure. The interaction process is as follows: S31. Initialization, assuming that the interaction relationship is a graph , where each node Corresponding to a class of company features, different company features can interact through edges; since there may be hidden relationships between each pair of company features, G is a fully connected graph. GNN can model the interaction between any two categories of company features. In the initial state of graph G, each node is associated with a hidden state vector , which is a vector representation of firm characteristics through embedding techniques. For example, for the transaction friction factor, ). Similarly, the initial state set of all nodes is expressed as: (10) S32, the core idea of ​​interaction between different company characteristics is to aggregate pricing information from neighbors in the kth interaction. For a given node , the aggregated information is the sum of the transition state information of its neighbors: (11) in, Representation and Node Neighboring nodes State information after the k-1th interaction; Adjacent, all included ; is the conversion function; is the adjacency matrix containing edge weights. It is a slave node arrive The weight value reflects the importance of the interaction between them.

[0009] (12) In order to describe the strength of the interaction and reflect the differences between the six company feature categories, the weight of the edge is calculated through the attention mechanism, which is formulated as follows: (13) in is the initial vector representation obtained through embedding technology; represents the initial vector of node j; is a learnable matrix; represents the concatenation operator; LeakyRelu(x) is the activation function.

[0010] In formula (11), All interactions are shared, which limits the flexibility of the model. To enhance the ability to capture nonlinear representations between pricing factors, a learnable output matrix is ​​used for each node. and a learnable input matrix Afterwards, the conversion function is defined as: (14) According to formula (14), when the node Slave Node When aggregating neighbor pricing information, nodes The information will be passed Convert and pass the node The input matrix Considering the above situation, formula (11) can be rewritten as: (15) S33, update the state of the interaction representation, when the node Aggregate pricing information from other categories of firm characteristics, that is, when a round of interaction is completed, the node Its vector representation will be updated.

[0011] The interaction representation is updated through the gated recurrent unit GRU and residual connection. The update process can be written as: (16) After the kth interaction, the set of high-order representations of company features can be expressed as: (17).

[0012] Preferably, step S4 comprises: The attention mechanism is used to aggregate multi-order deep company features and a multi-layer perceptron is used to obtain the final asset pricing result. The set of multi-order deep company features is expressed as: (18) in is a set of deep firm features represented by embeddings; It is a collection of deep firm characteristics interacting with deep macroeconomic characteristics; It is a set of deep company characteristics after high-level interactions.

[0013] The attention mechanism is used to aggregate multi-level deep company features. The aggregation result can be expressed as: (19) in It is a vector representation Representing a collection size; is the importance weight value, which is calculated as follows: (20) in is the attention value and is calculated as follows: (twenty one) in and is a learnable matrix; q is the query vector; tanh(x) is the activation function; is the bias term; Represents the concatenation operator.

[0014] Preferably, a multi-layer perceptron MLP is used to obtain the final asset pricing result: (twenty two) Where L is the number of layers in the MLP; , They are The learnable matrices, bias terms, and vector representations in the layer; the final output is expressed as: (twenty three) in and are the learnable matrix and bias term in the output layer, respectively.

[0015] Therefore, the present invention adopts the above-mentioned asset pricing method based on deep interactive learning, which has the following beneficial effects: (1) FCDIN generates multiple deep features represented by vectors based on representation learning, which enhances the ability to capture potential pricing information and is more flexible; (2) FCDIN uses graph neural networks (GNN) to adaptively simulate the interaction effects between company characteristics, which not only mines more possible interaction information but also avoids the redundancy caused by traditional manual construction of interaction terms. (3) FCDIN not only effectively reduces high dimensionality, but also improves the ability to adapt to the complex capital market environment; (4) Unlike the interactions of simple machine learning methods, FCDIN mitigates the risk of failure of traditional pricing factors in more efficient markets through deeper interactions.

[0016] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the overall structure of FCDIN according to an embodiment of the present invention; Figure 3 Schematic diagram of the factor interaction process based on GNN according to an embodiment of the present invention; Figure 4 A schematic diagram of attention scores of deep features of a company according to an embodiment of the present invention; Figure 5 It is a schematic diagram of the regression coefficient of the deep-level company feature importance score over time according to an embodiment of the present invention; Figure 6 A schematic diagram of visualizing the importance of different interaction relationships through attention scores according to an embodiment of the present invention; Figure 7 A schematic diagram of the importance of macroeconomic variables according to an embodiment of the present invention; Figure 8 A schematic diagram of the importance of each macroeconomic variable of the FCDIN model in an embodiment of the present invention; Fig. 9 A schematic diagram of the importance of company characteristics according to an embodiment of the present invention; Fig.10 This is a schematic diagram of the characteristics of the top 20 companies ranked by variable importance according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] See also Figure 1 , an asset pricing method based on deep interactive learning, comprising the following steps: S1. Based on deep learning methods, an asset pricing model is constructed with different types of company characteristics as input and corresponding stock excess return prediction values ​​as output; Figure 2 .

[0020] S2. Obtain the company characteristics of the stock and input them into the asset pricing model. Use the embedding learning technology through the asset pricing model to learn the company characteristics that affect the returns. Different types of deep company characteristics include: Deep company features extracted from raw input data based on embedding learning techniques and attention mechanisms, as well as deep company features that integrate different deep company features with macroeconomic deep features based on the interaction of Hadamard products.

[0021] S21. Extract different depth company features and macroeconomic depth features from the original input data based on embedding learning technology: Assumptions represents a set of macroeconomic variables and six categories of firm characteristics, where Represent the characteristics of macroeconomic variables, transaction frictions, momentum, value, growth, profitability and financial flows respectively; for a given stock sample , expressed as: (1) For any given categorical predictor , expressed as: (2) in represents the number of firm characteristics in each category; In FCDIN, each feature is converted into a real-valued vector through embedding learning technology. The process is expressed as: (3) in, is a learnable parameter vector belonging to the set of real numbers Elements in is the bias term; The quantity that represents the characteristics of a given category of companies; Represents the dimension of the embedding vector; for a category , the embedding technique converts the original company features into an embedding matrix, expressed as: (4) where es represents the size of the embedding (i.e., the dimension of the embedding vector), and is the bias term; represents the number of firm characteristics in each category; S22. For different types of predictors, an attention mechanism is designed to aggregate the embedding matrix into a composite deep company feature. The core idea of ​​the attention mechanism is to adaptively evaluate the importance of deep company features and merge these features into a single representation. For the same type of company features, the formula for attention representation is as follows: (5) in, represents the embedding vector; represents the attention weight; attention weight The calculation formula is as follows: (6) in is the attention value; Represents the attention value of the jth feature; in FCDIN, it is calculated using the additive attention mechanism : (7) in ∈ and is a learnable matrix; is the query vector; is the activation function; is the bias term; Denotes the concatenation operator, the deep macroeconomic characteristics and the six deep firm characteristics can be expressed as ; In FCDIN, taking the interaction effect between deep macroeconomic characteristics and deep transaction friction characteristics as an example, it can be expressed as: (8) in represents the Hadamard product; the interactions between deep firm characteristics and deep macroeconomic characteristics of the remaining five categories are ; The obtained embedding matrix is: (9).

[0022] S3. Through the asset pricing model, a graph neural network is used to perform high-order interactions on the deep features learned from the company’s feature representation.

[0023] Based on the deep feature high-order interaction network of graph neural network GNN, each node corresponds to a type of company feature. The importance of the interaction relationship is represented by the weight of the edge. The high-order interaction between two deep company features can be converted into modeling node interaction on the graph structure. The interaction process is as follows: S31. Initialization, assuming that the interaction relationship is a graph , where each node Corresponding to a class of company features, different company features can interact through edges; since there may be hidden relationships between each pair of company features, G is a fully connected graph. It can also be observed that GNN is able to model the interaction between any two categories of company features. In the initial state of graph G, each node is associated with a hidden state vector , which is a vector representation of firm characteristics through embedding techniques. For example, for the transaction friction factor, . Similarly, the initial state set of all nodes is expressed as: (10) S32, interact, such as Figure 3 , the core idea of ​​the interaction between different firm characteristics is to aggregate pricing information from neighbors in the kth interaction. For a given node , the aggregated information is the sum of the transition state information of its neighbors: (11) in, Representation and Node Neighboring nodes State information after the k-1th interaction; Adjacent, all included in N; is the conversion function; is the adjacency matrix containing edge weights. It is a slave node arrive The weight value reflects the importance of the interaction between them.

[0024] (12) In order to describe the strength of the interaction and reflect the differences between the six company feature categories, the weight of the edge is calculated through the attention mechanism, which is formulated as follows: (13) in is the initial vector representation obtained through embedding technology; represents the initial vector of node j; is a learnable matrix; represents the concatenation operator; LeakyRelu(x) is the activation function.

[0025] In formula (11), All interactions are shared, which limits the flexibility of the model. To enhance the ability to capture nonlinear representations between pricing factors, a learnable output matrix is ​​used for each node. and a learnable input matrix Afterwards, the conversion function is defined as: (14) According to formula (14), when the node Slave Node When aggregating neighbor pricing information, nodes The information will be passed Convert and pass the node The input matrix Considering the above situation, formula (11) can be rewritten as: (15) S33, update the state of the interaction representation, when the node Aggregate pricing information from other categories of firm characteristics, that is, when a round of interaction is completed, the node Its vector representation will be updated.

[0026] The interaction representation is updated through the gated recurrent unit GRU and residual connection. The update process can be written as: (16) After the kth interaction, the set of high-order representations of company features can be expressed as: (17).

[0027] S4. Through the asset pricing model, the attention mechanism is used to aggregate multi-order deep company features and the multi-layer perceptron is used to obtain the final asset pricing result.

[0028] The set of multi-level deep firm features can be expressed as: (18) in is a set of deep firm features represented by embeddings; It is a collection of deep firm characteristics interacting with deep macroeconomic characteristics; It is a set of deep company characteristics after high-level interactions.

[0029] The attention mechanism is used to aggregate multi-level deep company features. The aggregation result can be expressed as: (19) in It is a vector representation Representing a collection size; is the importance weight value, which is calculated as follows: (20) in is the attention value and is calculated as follows: (twenty one) in and is a learnable matrix; q is the query vector; tanh(x) is the activation function; is the bias term; Represents the concatenation operator.

[0030] Use multi-layer perceptron MLP to obtain the final asset pricing results: (twenty two) in is the number of layers in the MLP; , and They are The learnable matrices, bias terms, and vector representations in the layer; the final output is expressed as: (twenty three) in and are the learnable matrix and bias term in the output layer, respectively.

[0031] Validation and analysis: Out-of-sample forecasts using unmeaned To evaluate the predictive performance of individual stock excess return forecasts. For a given model, this measure is defined as: (twenty four) in and They are Actual and predicted stock returns for the next month. The range is , the higher the value, the better the pricing ability of the model.

[0032] Validation and analysis: A sliding window is used to split the training data and the test data. In this study, the sliding window size is set to five. Specifically, five years of data are used to train the model and adjust the parameters, and then the next year is used for out-of-sample evaluation. Before training the deep learning model, The monthly cross-sectional data for each variable are standardized, where Represent the mean and standard deviation of the original data, respectively. In addition, a grid search is used to determine the optimal parameters.

[0033] Out-of-sample forecasting To explore the prediction performance of the model of this embodiment and discuss the predictability of different subsamples. 18 commonly used models are compared, including ordinary least squares regression (OLS), ridge regression (Ridge), lasso regression (LASSO), elastic network (Elastic), gradient boosted regression tree (GBRT), lightweight gradient boosting machine (LGBM), neural network architectures with one to three hidden layers (NN1, NN2, NN3), ensemble artificial neural network (ENANN), gated recurrent unit (GRU), three generative adversarial networks (GAN1, GAN2, WGAN), and four FCDIN models with one to four interactions (FCDIN_1, FCDIN_2, FCDIN_3, FCDIN_4). The results are summarized in Table 1.

[0034] As shown in Table 1, first, when all companies are included, OLS (0.2996), Ridge (0.1999), Lasso (0.0144) and Elastic (0.0104) are obtained. is a negative value, indicating poor prediction ability. Secondly, the tree-based models (GBRT and LGBM), four neural network models (NN1, NN2, NN3, EN_ANN) and GRU model improve All seven models achieve positive , where GBRT and GRU perform better.

[0035] Table 1 Comparison of different methods Performance Comparison ;

[0036] We attribute these results to the ability of machine learning models to capture complex interactions between pricing factors. Third, the three GAN models perform better, especially GAN2 and WGAN, which They reached 0.0556 and 0.0502 respectively. These results show that GAN has better adaptability in dynamic markets compared with linear and simple machine learning models.

[0037] It is worth noting that the FCDIN model proposed in this example performs better than the other models. The FCDIN_3 model achieved the best performance with an out-of-sample It is 0.0733.

[0038] This improvement demonstrates the superiority of the FCDIN method in further capturing the complex interaction effects between predictors. In addition, the Diebold and Mariano (DM) test was used to further evaluate the differences in pricing power between different models. Compared with other machine learning or deep learning models, the advantages of the four FCDIN models are significant.

[0039] Importance of deep features: Deep company features jointly determine the performance of pricing. This example will discuss which deep company features contribute most to the output in FCDIN_3, based on the attention score. Table 2 summarizes the types of deep features generated, whether they interact with macroeconomic features, and whether they contain high-order interactions. Figure 4 Visualizes the attention scores of deep firm features calculated by averaging all cross sections. The transaction friction features after high-order interactions obtain the highest attention scores. In contrast, the financial flow features without any interaction operations have relatively low attention scores.

[0040] Table 2 Summary of Deep-Level Company Characteristics ;

[0041] In addition, the deep company features generated from the interaction between the original input data and the deep macroeconomic features can improve the attention score, which means that the macroeconomic variables provide more pricing information. More importantly, the attention score of the base-level company features increases significantly after high-order interaction operations, indicating that high-order interactions have excellent ability in capturing market dynamics that are ignored by traditional machine learning methods.

[0042] Additional regression analysis was conducted to determine whether the importance of different deep-level firm characteristics changes over time or remains stable. The regression model can be expressed as: (25) in is the attention score of the i-th deep company feature in the t-th sliding window; is the regression coefficient, indicating the degree of change in the deep company characteristic attention score over time.

[0043] As Figure 5 As shown in Figure 2, the importance of different types of deep firm characteristics changes significantly over time. Specifically, the regression coefficients of deep firm characteristics, including transaction friction_higher order, value_higher order, value, value_macroeconomics, growth_macroeconomics, profitability_macroeconomics, momentum_higher order, momentum_macroeconomics, financial flow_macroeconomics, growth_higher order, and financial flow_higher order, are all positive, which means that the importance of these deep firm characteristics gradually increases over time. More importantly, most of these deep firm characteristics are constructed through macroeconomic variable interactions and high-order interactions. However, the regression coefficients of deep firm characteristics, including transaction friction_macroeconomics, growth, profitability_higher order, momentum, financial flow, transaction friction, and profitability, are all negative, which means that the importance of these deep firm characteristics gradually decreases over time. Except for profitability_higher order, the rest of the deep firm characteristics are generated by the original input firm characteristics without further interaction process. Figure 5 It is also confirmed that the interactions with the macroeconomic variables module and the higher-order interaction module can capture more unobserved pricing information.

[0044] In fact, stock returns can be regarded as the result of nonlinear interactions between many influencing factors. FCDIN emphasizes quantifying the contribution of different interaction effects to pricing performance from a macro perspective. With the help of the attention mechanism used in interaction modeling in FCDIN, the interaction relationship that actually dominates stock returns in the Chinese A-share market can be quantitatively analyzed. Figure 6 The attention scores of various interaction relations calculated by formula (13) are reported.

[0045] is a collection of six feature categories, among which They represent transaction friction, momentum, value, growth, profitability, and financial flow respectively. Figure 6 middle, Representation characteristics and It can be observed that the interaction effect between value and profitability features obtains a higher attention score. This example supplements the conclusion from a data-driven perspective and gives new insights that the joint nonlinear effect between value and profitability features may require more attention. In contrast, the interaction effects between growth and profitability, growth and financial flow, profitability and financial flow, momentum and financial flow are weaker.

[0046] This embodiment speculates that the reason for this phenomenon may be related to the attention of investors. First, profitability is one of the important indicators for investors to measure the investment value of an enterprise. In the process of investment decision-making, investors will refer to the profitability of the enterprise to predict future returns. If a company has strong profitability, investors will believe that it has great growth potential, which in turn increases the demand for the company's stock, thereby driving the increase in the company's value. Secondly, the relationship between profitability and value reflects the competitiveness of the enterprise. When a company achieves high profitability in full competition, it proves that it has a certain position and advantage in the market. Investors tend to invest their hopes and funds in highly competitive companies, which also increases the intrinsic value of the company.

[0047] As a robustness check, we set the edge weights between two specific category features to zero when constructing the high-order interaction network mentioned above, retrain the model, estimate the out-of-sample prediction performance, and calculate In Table 3, when the interaction between value and profitability is removed, the four FCDIN They decreased by 24.70%, 52.83%, 26.68% and 25.35% respectively, which had the greatest impact on pricing performance.

[0048] Table 3 Performance of FCDIN after removing interactions ;

[0049] This example investigates the importance of ten macroeconomic variables to the FCDIN model. For a particular model, calculate the probability that all values ​​of a given predictor are set to zero in each training sample. , and average them into a single importance metric for each predictor. Figure 7 The importance of macroeconomic variables is reported. The columns correspond to the individual models, and the color gradient within each column represents the variables from the most influential (dark blue) to the least influential (white). In addition, Figure 8 A detailed ranking of the importance of macroeconomic variables for each FCDIN model is reported.

[0050] like Figure 7 and Figure 8As shown, most models provide insights that the RMB exchange rate (RE), economic climate index (ECI), consumer confidence index (CCI) and inflation rate (INF) are more important than monthly trading volume (MTR), stock variance (SVAR) and gross domestic product (GDP) in predicting the monthly returns of the Chinese stock market. It can be seen that the stock returns of the Chinese stock market are affected by internal factors (such as CCI, ECI, INF, etc.) and external factors (such as RE, etc.). Specifically, among the internal factors, CCI is a key indicator reflecting investor sentiment, while ECI reflects the current economic operation from multiple aspects such as industrial production, employment, investment, consumption, foreign trade, national taxation, corporate profits and household income. Among the external factors, RE is crucial to the stability and healthy development of the national financial system, and has an important impact on international capital flows, investment structure and even the real estate market. The market environment and international situation of RE are becoming more and more complex and more volatile, and have a greater impact on domestic asset prices.

[0051] This example investigates the importance of 96 company characteristics to the FCDIN model. The importance estimation method is consistent with the above method. Fig. 9 The overall importance ranking of all company characteristics for each model is shown. In addition, Fig.10 The importance of firm characteristics is reported for the top 20 most influential variables in each model.

[0052] from Fig. 9 and Fig.10 In the study, it was found that the four FCDIN models reached a consensus that characteristics such as 6-month momentum change (momchg), Beta squared (betasq), return volatility (retvol) and Beta are the most important for the Chinese A-share market. In addition, short-term reversals (lagretn), RMB trading volume (vold), dividend-to-price ratio (dp) and sales-to-price ratio (sp), as well as 6-month momentum (mom6) also play an important role. However, from Fig. 9 It can be seen that the importance of features such as inventory change (invchg), capital expenditures and inventory (invest), quick ratio (qr), idiosyncratic skewness (idskewness), sales to receivables ratio (salerec), and change in the number of analysts (chnanalyst) is not very obvious.

[0053] In addition, 96 company characteristics are classified into six categories, including transaction friction, momentum, value, growth, profitability, and financial flow. Specifically, the company characteristics belonging to a specific category are set to zero, the model is retrained, the out-of-sample prediction performance is estimated, and the As shown in Table 4, when removing the features related to transaction friction, the results are most affected. They decreased by 44.93%, 28.36%, 22.28% and 18.86% respectively. In contrast, the characteristics related to financial flows have less impact. The trading friction characteristics measure the liquidity of stocks and the degree of trading activities, which is more important for emerging markets.

[0054] Table 4 Performance of FCDIN after removing characteristics of different categories of companies ;

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. An asset pricing method based on deep interactive learning, characterized by: S1. Based on deep learning methods, we build an asset pricing model that takes different types of company characteristics as input and the corresponding stock excess return prediction value as output; S2. Obtain the company characteristics of the stock and input them into the asset pricing model. Use the embedding learning technology through the asset pricing model to learn the company characteristics that affect the returns. S3. Through the asset pricing model, a graph neural network is used to perform high-order interactions on the deep features learned from the company's feature representation. Based on the deep feature high-order interaction network of graph neural network GNN, each node corresponds to a type of company feature. The importance of the interaction relationship is represented by the weight of the edge. The high-order interaction between two deep company features is converted to modeling the node interaction on the graph structure. The interaction process is as follows: S31. Initialization, assuming that the interaction relationship is a graph , where each node Corresponding to a class of company characteristics, different company characteristics interact through edges; in the initial state of graph G, each node is associated with a hidden state vector Related, for the transaction friction factor, ; The initial state set of all nodes is expressed as: （10）； S32, the core idea of ​​interaction between different company characteristics is to aggregate pricing information from neighbors in the kth interaction; for a given node , the aggregated information is the sum of the transition state information of its neighbors: （11） in, Representation and Node Neighboring nodes State information after the k-1th interaction; Adjacent, all included in N; W is the transfer function; A is the adjacency matrix containing edge weights; It is a slave node arrive The weight value of: （12） The weight of the edge is calculated through the attention mechanism. The formula is as follows: （13） in is the initial vector representation obtained through embedding technology; Representation Node The initial vector of is a learnable matrix; represents the connection operator; LeakyRelu(x) is the activation function; In formula (11), All interactions are shared, using a learnable output matrix for each node and a learnable input matrix Afterwards, the conversion function is defined as: （14） According to formula (14), when the node Slave Node When aggregating neighbor pricing information, nodes The information will be passed Convert and pass the node The input matrix Transformation; Formula (11) is rewritten as: （15）； S33, update the state of the interaction representation, when the node Aggregating pricing information from other categories of company characteristics, when a round of interaction is completed, the node Its vector representation will be updated; The interaction representation is updated through the gated recurrent unit GRU and residual connection. The update process is written as: （16） After the kth interaction, the set of high-order representations of company features is expressed as: （17）； S4. Through the asset pricing model, the attention mechanism is used to aggregate multi-order deep company features and the multi-layer perceptron is used to obtain the final asset pricing result.

2. The asset pricing method based on deep interactive learning according to claim 1, characterized in that: Step S2 includes: S21. Extract different depth company features and macroeconomic depth features from the original input data based on embedding learning technology: Assumptions represents a set of macroeconomic variables and six categories of firm characteristics, where Represent the characteristics of macroeconomic variables, transaction frictions, momentum, value, growth, profitability and financial flows respectively; for a given stock sample , expressed as: （1） For any given categorical predictor , expressed as: （2） in represents the number of firm characteristics in each category; In FCDIN, each feature is converted into a real-valued vector through embedding learning technology. The process is expressed as: （3） in, is a learnable parameter vector belonging to the set of real numbers Elements in is the bias term; The quantity that represents the characteristics of a given category of companies; Represents the dimension of the embedding vector; for a category , the embedding technique converts the original company features into an embedding matrix, expressed as: （4） Where es represents the embedding size; represents the number of firm characteristics in each category; S22. For different types of predictors, an attention mechanism is designed to aggregate the embedding matrix into a composite deep company feature. For the same type of company features, the attention representation formula is as follows: （5） in, represents the embedding vector; represents the attention weight; attention weight The calculation formula is as follows: （6） in is the attention value; Indicates The attention value of each feature; in FCDIN, the additive attention mechanism is used to calculate : （7） in ∈ and is a learnable matrix; is the query vector; is the activation function; is the bias term; represents the connection operator, the deep macroeconomic characteristics and the six deep firm characteristics are expressed as ; In FCDIN, the interaction effect between deep macroeconomic characteristics and deep transaction friction characteristics is expressed as: （8） in represents the Hadamard product; the interactions between the deep firm characteristics and the deep macroeconomic characteristics of the remaining five categories are ; The obtained embedding matrix is: （9）。 3. The asset pricing method based on deep interactive learning according to claim 2, characterized in that: Step S4 includes: The attention mechanism is used to aggregate multi-order deep company features and a multi-layer perceptron is used to obtain the final asset pricing result. The set of multi-order deep company features is expressed as: （18） in is a set of deep firm features represented by embeddings; It is a collection of deep firm characteristics interacting with deep macroeconomic characteristics; It is a set of deep company characteristics after high-level interactions; The attention mechanism is used to aggregate multi-level deep company features, and the aggregation result is expressed as: （19） in It is a vector representation Representing a collection size; is the importance weight value, which is calculated as follows: （20） in is the attention value, which is calculated as follows: （21） in and is a learnable matrix; is the query vector; is the activation function; is the bias term; Represents the concatenation operator.

4. The asset pricing method based on deep interactive learning according to claim 3 is characterized by: Use multi-layer perceptron MLP to obtain the final asset pricing results: （22） Where L is the number of layers in the MLP; , and They are The learnable matrices, bias terms, and vector representations in the layer; the final output is expressed as: （23） in and are the learnable matrix and bias term in the output layer, respectively.

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