Financial network construction of a set of coupled stochastics differential equations using generative adversarial network

Abstract

Prices and volumes of financial instruments are often represented as stochastic processes. Inter-relatedness of different financial instrument, i.e. financial networks, are often of strong interest, especially in market analysis. Currently, the financial networks are mainly constructed using the minimum spanning tree method or the maximally filtered graph method. Here we study a set of general coupled stochastic differential equations with correlation coefficients ρij. The thresholded values of ρij can be written as the entries in the adjacent matrix that represents the edges of a financial network. We use a simple generative adversarial network (GAN) method to recover the correlation coefficients. The discriminator of the GAN consists of a single layer artificial neural network. The dropout rate of the discriminator is set to 0.5 and using the sigmoid activation function. The generator of the GAN consists of two layers that have a fully connected perceptrons. The output layer uses an exponential linear unit activation function and the GAN encoder is a two-layer perceptron with ReLU activation function. The loss function used is the cross-entropy loss. The method is able to recover the given hand-crafted networks correctly. We also demonstrated the use of the GAN method to build a correlation network between currencies. The networks built are able to show progressive changes in the relationship between currencies over the years.Prices and volumes of financial instruments are often represented as stochastic processes. Inter-relatedness of different financial instrument, i.e. financial networks, are often of strong interest, especially in market analysis. Currently, the financial networks are mainly constructed using the minimum spanning tree method or the maximally filtered graph method. Here we study a set of general coupled stochastic differential equations with correlation coefficients ρij. The thresholded values of ρij can be written as the entries in the adjacent matrix that represents the edges of a financial network. We use a simple generative adversarial network (GAN) method to recover the correlation coefficients. The discriminator of the GAN consists of a single layer artificial neural network. The dropout rate of the discriminator is set to 0.5 and using the sigmoid activation function. The generator of the GAN consists of two layers that have a fully connected perceptrons. The output layer uses an exponential linear u...