Global asset pricing method considering cross-market overflow effect and heterogeneity adaptation

Abstract

The invention provides a global asset pricing method considering a cross-market overflow effect and heterogeneity adaptation, and the method comprises the steps: constructing a three-layer heterogeneous graph covering global macroscopic nodes, regional market nodes and individual share asset nodes, and achieving the multi-level message passing through a heterogeneous graph neural network; end-to-end modeling of nonlinear overflow effects among global markets, among large-class assets and among individual stocks is realized for the first time; by designing a feature embedding layer, an interaction adaptation layer and a normalization layer exclusive to the market, adaptive adaptation is carried out for system features, data distribution and pricing logic of different markets, and stable and accurate pricing of mature markets and emerging markets is realized; according to the method, global systematic risk information and regional specificity alpha information are effectively separated and deeply fused through a double-attention aggregation mechanism of a global attention branch and a local attention branch, so that the income prediction precision is improved, and the systematic risk exposure degree and a regional alpha score can be directly output.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a global asset pricing method that takes into account cross-market spillover effects and heterogeneity adaptation. Background Technology

[0002] Asset pricing is a core issue in the fields of financial investment and risk management. Its purpose is to accurately estimate the expected returns of assets, providing a basis for investment decisions and risk hedging. With the acceleration of global economic integration and the continuous expansion of cross-border investment, institutional investors such as sovereign wealth funds, insurance asset management companies, and mutual funds are increasingly demanding global asset allocation. Against this backdrop, how to achieve accurate pricing of assets in multiple global markets, capture the risk transmission and return spillover effects between different markets, and effectively separate global systemic risk from regionally specific alpha information has become a hot topic of common concern in academia and industry. In recent years, with the development of deep learning technology, asset pricing models based on graph neural networks, attention mechanisms, and deep interactive learning have gradually emerged, providing a new technical path for capturing the nonlinear interactions between high-dimensional company characteristics. For example, Chinese invention patent application number 202510134947X discloses an asset pricing method based on deep interactive learning. This method, through embedding learning, high-order interactions of graph neural networks, and attention aggregation, achieves accurate prediction of the excess returns of individual stocks in the Chinese A-share market, significantly outperforming traditional linear models and simple machine learning models in out-of-sample prediction capabilities.

[0003] However, existing technologies still face significant technical bottlenecks in global asset pricing scenarios. First, they generally fail to consider cross-market spillover effects. Current solutions only perform Granger causality modeling at the index level of two markets, failing to construct multi-level heterogeneous graphs encompassing "global macroeconomics - regional markets - individual assets," thus struggling to capture non-linear risk transmission and return spillovers between markets and asset classes. Second, existing technologies severely lack adaptability to the heterogeneity of different markets. Stock markets in different countries or regions exhibit significant differences in trading systems, investor structures, liquidity levels, market maturity, and regulatory rules. Existing technologies all employ a uniform embedding and interactive modeling approach, resulting in a significant decrease in pricing accuracy for global multi-factor models in emerging markets, failing to achieve stable pricing across the entire global market. Third, existing technologies cannot separate global systemic information from regionally specific information. Both gradient boosting tree models and heterogeneous graph risk transmission analysis methods focus only on single return predictions or risk path identification, failing to effectively separate global systemic risk factors from regionally specific alpha factors, thus failing to meet the core investment needs of "systemic risk hedging + regional alpha mining" in global asset allocation. In addition, existing technologies are insufficient in covering core variables of cross-border pricing. Most solutions do not fully incorporate core variables of cross-border transmission, such as exchange rates, cross-border capital flows, and global macroeconomic indicators, resulting in a significant decrease in pricing accuracy under cross-border shock scenarios such as Fed rate hikes and large exchange rate fluctuations.

[0004] Therefore, there is an urgent need in this field for a global asset pricing method that can comprehensively consider cross-market spillover effects, adapt to the heterogeneous characteristics of different markets, effectively separate global systemic information from regional specific information, and cover core variables of cross-border transmission, in order to solve the technical problems of limited application of existing technologies in global asset allocation scenarios, insufficient pricing accuracy, and lack of strategy empowerment. Summary of the Invention

[0005] The purpose of this invention is to provide a global asset pricing method that takes into account cross-market spillover effects and heterogeneity adaptation, so as to solve the problems existing in the prior art.

[0006] To achieve the above objectives, the present invention provides the following solution: This invention provides a global asset pricing method that considers cross-market spillover effects and heterogeneity adaptation, comprising the following steps: S1. Construct a global multi-market dataset, which includes individual stock samples from multiple global markets. Each sample contains company characteristics, market macroeconomic characteristics, global macroeconomic variables, exchange rates, and cross-border capital flow data. S2. Construct a global three-layer heterogeneous graph, which includes three types of nodes: global macro nodes, regional market nodes, and individual stock asset nodes. Construct edges between global macro nodes and regional market nodes, between regional market nodes and individual stock asset nodes, between regional market nodes and regional market nodes, and between individual stock asset nodes. Calculate edge weights through an attention mechanism. S3. Perform feature embedding for market heterogeneity adaptation. Set up market-specific feature embedding layers for different markets, map the company characteristics and macro characteristics of different markets into embedding vectors, and perform feature processing through market-specific interaction adaptation layers and normalization layers. S4. Based on the heterogeneous graph, multi-level message passing is performed through a heterogeneous graph neural network to update the representations of global macro nodes, regional market nodes and individual stock asset nodes, thereby realizing end-to-end modeling of cross-market spillover effects. S5. Perform dual attention aggregation through global attention branch and local attention branch. The global attention branch aggregates the stock representations of all markets to extract global systemic risk information, and the local attention branch aggregates the stock representations within each market to extract regional specific pricing information. Then, the aggregated global information and local information are fused with the stock node representation. S6. Construct a multi-task joint loss function, which includes excess return prediction loss, global systemic risk constraint term and market heterogeneity adaptation regularization term. The model is trained end-to-end by minimizing the multi-task joint loss function. S7 outputs individual stock excess return prediction results, global systemic risk exposure, regional alpha score, and a matrix of inter-market spillover effect strength.

[0007] Preferably, in step S2, the formula for calculating edge weights using the attention mechanism is: ; in, and They are nodes and nodes Embedded vector, For splicing operations, For a learnable parameter matrix, For nodes The set of neighboring nodes, This is the activation function.

[0008] Preferably, in step S3, the formula for the market-specific feature embedding layer is: ; in, For the market individual stocks The The first of the class features One original feature value, For the market The Middle Learnable embedding matrix of class features For bias terms, This is the corresponding embedding vector.

[0009] Preferably, in step S3, the formula for the market-specific normalization layer is: ; in, For the input feature vector, and Markets The mean and standard deviation of the features, It is a constant. and For the market Learnable scaling and offset parameters.

[0010] Preferably, in step S4, the message passing process of the heterogeneous graph neural network includes: For nodes The Layer representation The formula for aggregating neighbor information is: ; in, For edge weights, Indicates the node type. This is a learnable transformation matrix between node type pairs. For neighboring nodes The Layer representation; The formula for state update is: ; in, For gated loop unit, For nodes The initial embedding representation.

[0011] Preferably, in step S5, the aggregation formula for the global attention branch is: ; in, For market aggregation, For the market The collection of individual stocks in the middle, For individual stock nodes The representation after layer message passing, These are the global attention weights, calculated from the global query vector. The aggregation formula for the local attention branches is: ; in, For the market The local attention weights are calculated from the market-specific query vectors; The fusion formula is as follows: ; in, It is a multilayer perceptron. This is for splicing operations.

[0012] Preferably, in step S6, the formula for the multi-task joint loss function is: ; in, To predict losses from excess returns, mean squared error is used; As a global systemic risk constraint, the distribution of global attention weights is constrained by KL divergence. To adapt the regularization term to market heterogeneity, the maximum mean difference constrains the distribution differences of individual stock representations across different markets; and To balance the hyperparameters.

[0013] Preferably, in step S1, the company characteristics include transaction friction characteristics, momentum characteristics, value characteristics, growth characteristics, profitability characteristics, and financial liquidity characteristics; the market macroeconomic characteristics include market indices and risk-free interest rates; and the global macroeconomic variables include global economic growth expectations, global liquidity indices, and global risk aversion indices.

[0014] Preferably, the method further includes: in step S2, the regional market nodes in the global three-layer heterogeneous map cover mature markets and emerging markets, and the mature markets and emerging markets are heterogeneously adapted through the market-specific feature embedding layer and normalization layer in step S3.

[0015] This invention also provides a global asset pricing system that considers cross-market spillover effects and heterogeneity adaptation, for implementing the above method, comprising: The dataset building module is used to build global multi-market datasets; The heterogeneous graph construction module is used to construct a global three-layer heterogeneous graph and calculate edge weights; The heterogeneity adaptation module is used to embed market-specific features, adapt interactions, and normalize data for different markets. The message passing module is used for multi-level message passing through a heterogeneous graph neural network; The dual-attention aggregation module is used to perform dual-attention aggregation and feature fusion through global attention branches and local attention branches; The multi-task training module is used to construct a multi-task joint loss function and perform end-to-end training. The output module is used to output the predicted excess returns of individual stocks, global systemic risk exposure, regional alpha scores, and the matrix of inter-market spillover effects.

[0016] The present invention achieves the following beneficial technical effects compared to the prior art: This invention provides a global asset pricing method that considers cross-market spillover effects and heterogeneity adaptation, possessing significant technological advancements and industrial application value. Building upon the single-market deep interactive learning of the original patent, this invention constructs a three-layer heterogeneous graph covering global macroeconomic nodes, regional market nodes, and individual stock asset nodes. Combined with a heterogeneous graph neural network, it achieves multi-level message passing, realizing for the first time end-to-end modeling of nonlinear spillover effects between global markets, asset classes, and individual stocks, overcoming the limitations of fragmented and linear modeling in existing technologies. By designing market-specific feature embedding layers, interactive adaptation layers, and normalization layers, it adaptively adapts to the institutional characteristics, data distribution, and pricing logic of different markets, effectively solving the problem of a sharp drop in pricing accuracy in emerging markets caused by uniform modeling in existing technologies. This achieves stable and accurate pricing in both mature and emerging markets. The invention employs a dual-attention aggregation mechanism combining global and local attention branches to effectively separate and deeply integrate global systemic risk information with regionally specific alpha information. This not only improves the accuracy of return prediction but also directly outputs systemic risk exposure and regional alpha scores, providing direct technical support for risk hedging and alpha mining in cross-border investment. By incorporating core variables such as exchange rates, cross-border capital flows, and global macroeconomic indicators, and combining a multi-task joint loss function to jointly optimize excess return fitting, systemic risk constraints, and market heterogeneity adaptation, the invention significantly enhances the model's generalization ability and robustness across various global markets and cross-border shock scenarios. Experimental results show that the average out-of-sample prediction accuracy in global markets is improved by more than 25% compared to existing technologies, pricing accuracy in emerging markets is improved by more than 30%, and pricing accuracy in cross-border shock scenarios is improved by more than 35%. This fills the application gap of existing technologies in global asset allocation scenarios and possesses outstanding substantive features and significant technological advancements. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 The flowchart of the global asset pricing method that takes into account cross-market spillover effects and heterogeneity adaptation provided by the present invention is shown. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] The purpose of this invention is to provide a global asset pricing method that takes into account cross-market spillover effects and heterogeneity adaptation, in order to solve the problems existing in the prior art.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Example 1:

[0022] like Figure 1 As shown, the method of the present invention includes the following steps.

[0023] First, step S1 is executed to construct a global multi-market dataset. Specifically, this invention constructs a dataset covering multiple major global stock markets, with each market containing several stock samples. For stock i in each market m, its feature vector is collected at time t. This feature vector contains four types of information: first, company characteristics, including transaction friction features, momentum features, value features, growth features, profitability features, and financial liquidity features, which follow the six predictive factors based on financial theory in the original patent; second, market macroeconomic characteristics, including market index returns and risk-free interest rates; third, global macroeconomic variables, including global economic growth expectations, global liquidity index, and global risk aversion index, used to characterize the global systemic economic and financial environment; and fourth, core variables of cross-border transmission, including exchange rates and cross-border capital flows, used to capture the impact of cross-border capital flows and currency fluctuations on asset prices. All data are cross-sectionally standardized at a monthly frequency to ensure the comparability of different features in terms of dimensions.

[0024] Next, step S2 is executed to construct a global three-layer heterogeneous graph. This invention constructs a heterogeneous graph G = (V, E), where the node set V contains three types of nodes: global macro nodes, representing global systemic risk factors; regional market nodes, one node per market, representing the overall pricing environment of that market; and individual stock nodes, one node per stock within each market, representing stock-level characteristics. The edge set E contains four types of edges: edges between global macro nodes and regional market nodes, depicting the transmission of global risk factors to various markets; edges between regional market nodes and individual stock nodes, depicting the impact of market factors on individual stock returns; edges between regional market nodes, depicting the risk spillover and return transmission effects between different markets; and edges between individual stock nodes, depicting the correlation between stocks within the same market, such as industry or style correlations. For each edge, this invention dynamically calculates its weight using an attention mechanism. Specifically, for each node... To the node The weight of an edge is calculated using the following formula: ; in, and They are nodes and nodes Embedded vector, For splicing operations, For a learnable parameter matrix, For nodes The set of neighboring nodes, The activation function is used to introduce non-linearity; the denominator is a normalization term to ensure that the sum of the weights of all neighboring nodes is 1. Through this attention mechanism, the weight of each edge in the heterogeneous graph can adaptively reflect the strength of the interaction relationship between nodes, providing a foundation for subsequent message passing.

[0025] Then, step S3 is executed to perform feature embedding for market heterogeneity adaptation. Considering the significant differences in trading systems, investor structures, liquidity levels, market maturity, and regulatory rules among stock markets in different countries or regions, this invention designs market-specific embedding and normalization layers for different markets. First, for the j-th original feature value in the f-th type of feature of stock i in market m... It maps the feature vectors to embedding vectors through a market-specific feature embedding layer. The calculation formula is as follows: ; in, For the market individual stocks The The first of the class features One original feature value, For the market The Middle Learnable embedding matrix of class features For bias terms, Let T represent the matrix transpose, and T be the corresponding embedding vector. This market-specific embedding layer enables features with the same meaning in different markets to learn different embedding representations based on the data distribution of that market, thus adapting to market heterogeneity. After obtaining the embedding vectors of various features, drawing on the macro-micro interaction method based on the Hadamard product in the original patent (202510134947X), this invention interacts the embedding vectors of macro-market features with the embedding vectors of feature categories of each company to form preliminary interactive features. Furthermore, to adapt to the differences in data distribution across different markets, this invention introduces a market-specific normalization layer to adaptively normalize the feature vectors. For the input feature vector h, the normalized vector... Calculated by the following formula: ; in, For the input feature vector, and Markets The mean and standard deviation of the features, It is a constant. and For the market The learnable scaling and offset parameters are adaptively adjusted during training. This normalization layer enables the model to effectively cope with differences in data distribution across different markets, significantly improving the model's pricing accuracy in emerging markets.

[0026] Next, step S4 is executed, where multi-level message passing is performed based on the heterogeneous graph using a heterogeneous graph neural network to achieve end-to-end modeling of cross-market spillover effects. In this invention, a heterogeneous graph neural network is used for K-layer message passing on the heterogeneous graph G constructed in step S2. For nodes... The Layer representation The formula for aggregating neighbor information is: ; in, For edge weights, Indicates the node type. This is a learnable transformation matrix between node type pairs. For neighboring nodes The Layer representation. After information aggregation is completed, the nodes... The state is updated via a gated recurrent unit (GRU) combined with residual connections: ; in, For gated loop unit, For nodes The initial embedding representation is a randomly initialized vector for global macro nodes, an embedding vector of market macro features for regional market nodes, and a feature vector after embedding and normalization in step S3 for individual stock nodes. The residual connection is used to fuse the state of the node from the previous layer with the neighbor information aggregated in the current layer. It directly superimposes the initial representation onto the updated representation, which helps to alleviate the gradient vanishing problem in deep networks and preserves the original information of the node. After K layers of message passing, each individual stock node obtains a final representation that integrates global macroeconomic information, regional market information, cross-market spillover information, and its own characteristics.

[0027] Then, step S5 is executed, where dual attention aggregation is performed through a global attention branch and a local attention branch to achieve effective separation and deep fusion of global systemic information and regional specific information. This invention designs two parallel attention branches. The global attention branch is used to extract global systemic risk information, and its aggregation formula is: ; in, For market aggregation, For the market The collection of individual stocks in the middle, For individual stock nodes The representation after layer message passing, The global attention weights are calculated from the global query vector and implemented through an additive attention mechanism, giving higher weights to stocks that contribute more to global systemic risk. The output of the global attention branch. It is a vector that encodes overall information about global systemic risk. The local attention branch is used to extract region-specific pricing information within each market, and its aggregation formula is: ; in, For the market The local attention weights, calculated from the market-specific query vector, reflect the importance of a stock's specific pricing information within its respective market. For each market m, the local attention branch outputs a vector. This encodes the region-specific alpha information of the market. After obtaining global information and local information of each market, this invention deeply integrates the final representation of individual stock nodes with the global information and the local information of the market to obtain the final individual stock pricing features: ; in, It is a multilayer perceptron containing two fully connected layers, each followed by a ReLU activation function. This is used to perform nonlinear transformation and dimensionality reduction on the concatenated high-dimensional features, generating the final pricing feature vector. This is for splicing operations.

[0028] Finally, step S6 is executed to construct a multi-task joint loss function for end-to-end training of the model. This invention designs a multi-task joint loss function containing three sub-losses, its overall form being: ; in, To predict losses from excess returns, mean squared error is used; As a global systemic risk constraint, the distribution of global attention weights is constrained by KL divergence. To adapt the regularization term to market heterogeneity, the maximum mean difference constrains the distribution differences of individual stock representations across different markets; and To balance the hyperparameters. The first term... To predict loss from excess returns, mean squared error (MSE) is used to measure the difference between the model's predictions and the actual values; the second term The global systemic risk constraint term uses KL divergence to constrain the distribution of global attention weights, preventing the model from over-relying on a few individual stocks to represent global systemic risk; the third term... To adapt the regularization term to market heterogeneity, the maximum mean difference (MMD) constraint is used to constrain the distribution differences of individual stock representations across different markets, prompting the model to learn common features across markets. This constraint forces the distributions of individual stock representations in different markets to be as similar as possible, thereby improving the model's generalization ability in out-of-sample markets such as emerging markets. By minimizing the aforementioned multi-task joint loss function, the model simultaneously optimizes return prediction accuracy, the uniformity of global risk representation, and the consistency of cross-market representation distribution during training.

[0029] After model training is complete, step S7 is executed, outputting various pricing and risk information with practical application value. Specifically, for each individual stock, the model outputs its excess return prediction value, which can be directly used for investment decisions; it outputs its global attention weight, which reflects the stock's exposure to global systemic risk and can be used for systemic risk hedging; it outputs its local attention weight, which reflects the stock's alpha contribution within the regional market and can be used for regional alpha mining; and it outputs the inter-market spillover effect strength matrix, where the elements reflect the risk transmission strength from market m' to market m, which can be used for cross-border risk management and asset allocation.

[0030] In one specific embodiment, the present invention selected monthly data from 2000 to 2025 for 30 major global stock markets (including 15 developed markets and 15 emerging markets), constructed a model according to the steps described above, and trained it. Experimental results show that the average out-of-sample prediction accuracy (R_OOS^2) of the present invention in the global market is improved by more than 25% compared with the original patent solution, the pricing accuracy in emerging markets is improved by more than 30%, and the pricing accuracy under cross-border shock scenarios such as Fed rate hikes and large exchange rate fluctuations is improved by more than 35%, verifying the significant technical effect of the present invention.

[0031] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0032] It should be noted that the components mentioned in the above embodiments are all general standard parts or components known to those skilled in the art. Their structures and principles can be learned by those skilled in the art through technical manuals or conventional experimental methods.

[0033] This invention has illustrated its principles and implementation methods using specific examples. The descriptions of these embodiments are merely illustrative of the method and its core ideas; furthermore, those skilled in the art will recognize that modifications may be made to the specific implementation methods and application scope based on the principles of this invention. Therefore, the content of this specification should not be construed as limiting the invention.

Claims

1. A global asset pricing method that considers cross-market spillover effects and heterogeneity adaptation, characterized in that, Includes the following steps: S1. Construct a global multi-market dataset, which includes individual stock samples from multiple global markets. Each sample contains company characteristics, market macroeconomic characteristics, global macroeconomic variables, exchange rates, and cross-border capital flow data. S2. Construct a global three-layer heterogeneous graph, which includes three types of nodes: global macro nodes, regional market nodes, and individual stock asset nodes. Construct edges between global macro nodes and regional market nodes, between regional market nodes and individual stock asset nodes, between regional market nodes and regional market nodes, and between individual stock asset nodes. Calculate edge weights through an attention mechanism. S3. Perform feature embedding for market heterogeneity adaptation. Set up market-specific feature embedding layers for different markets, map the company characteristics and macro characteristics of different markets into embedding vectors, and perform feature processing through market-specific interaction adaptation layers and normalization layers. S4. Based on the heterogeneous graph, multi-level message passing is performed through a heterogeneous graph neural network to update the representations of global macro nodes, regional market nodes and individual stock asset nodes, thereby realizing end-to-end modeling of cross-market spillover effects. S5. Perform dual attention aggregation through global attention branch and local attention branch. The global attention branch aggregates the stock representations of all markets to extract global systemic risk information, and the local attention branch aggregates the stock representations within each market to extract regional specific pricing information. Then, the aggregated global information and local information are fused with the stock node representation. S6. Construct a multi-task joint loss function, which includes excess return prediction loss, global systemic risk constraint term and market heterogeneity adaptation regularization term. The model is trained end-to-end by minimizing the multi-task joint loss function. S7 outputs individual stock excess return prediction results, global systemic risk exposure, regional alpha score, and a matrix of inter-market spillover effect strength.

2. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S2, the formula for calculating edge weights using the attention mechanism is: ； in, and They are nodes and nodes Embedded vector, For splicing operations, For a learnable parameter matrix, For nodes The set of neighboring nodes, This is the activation function.

3. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S3, the formula for the market-specific feature embedding layer is: ； in, For the market individual stocks The The first of the class features One original feature value, For the market The Middle Learnable embedding matrix of class features For bias terms, This is the corresponding embedding vector.

4. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S3, the formula for the market-specific normalization layer is: ； in, For the input feature vector, and Markets The mean and standard deviation of the features, It is a constant. and For the market Learnable scaling and offset parameters.

5. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S4, the message passing process of the heterogeneous graph neural network includes: For nodes The Layer representation The formula for aggregating neighbor information is: ； in, For edge weights, Indicates the node type. This is a learnable transformation matrix between node type pairs. For neighboring nodes The Layer representation; The formula for state update is: ； in, For gated loop unit, For nodes The initial embedding representation.

6. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S5, the aggregation formula for the global attention branch is: ； in, For market aggregation, For the market The collection of individual stocks in the middle, For individual stock nodes The representation after layer message passing, These are the global attention weights, calculated from the global query vector. The aggregation formula for the local attention branches is: ； in, For the market The local attention weights are calculated from the market-specific query vectors; The fusion formula is as follows: ； in, It is a multilayer perceptron. This is for splicing operations.

7. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S6, the formula for the multi-task joint loss function is: ； in, To predict losses from excess returns, mean squared error is used; As a global systemic risk constraint, the distribution of global attention weights is constrained by KL divergence. To adapt the regularization term to market heterogeneity, the maximum mean difference constrains the distribution differences of individual stock representations across different markets; and To balance the hyperparameters.

8. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, In step S1, the company characteristics include transaction friction characteristics, momentum characteristics, value characteristics, growth characteristics, profitability characteristics, and financial liquidity characteristics; the market macro characteristics include market indices and risk-free interest rates; and the global macro variables include global economic growth expectations, global liquidity indices, and global risk aversion indices.

9. The global asset pricing method considering cross-market spillover effects and heterogeneity adaptation as described in claim 1, characterized in that, The method further includes: in step S2, the regional market nodes in the global three-layer heterogeneous map cover mature markets and emerging markets, and the mature markets and emerging markets are heterogeneously adapted through the market-specific feature embedding layer and normalization layer in step S3.

10. A global asset pricing system that considers cross-market spillover effects and heterogeneity adaptation, characterized in that, For performing the method according to any one of claims 1 to 9, comprising: The dataset building module is used to build global multi-market datasets; The heterogeneous graph construction module is used to construct a global three-layer heterogeneous graph and calculate edge weights; The heterogeneity adaptation module is used to embed market-specific features, adapt interactions, and normalize data for different markets. The message passing module is used for multi-level message passing through a heterogeneous graph neural network; The dual-attention aggregation module is used to perform dual-attention aggregation and feature fusion through global attention branches and local attention branches; The multi-task training module is used to construct a multi-task joint loss function and perform end-to-end training. The output module is used to output the predicted excess returns of individual stocks, global systemic risk exposure, regional alpha scores, and the matrix of inter-market spillover effects.

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