Deep Learning Algorithms For Multi-asset Option Pricing Under SLV Models

In this thesis,we solve the multi-dimension partial differential equations(PDEs)for option pricing under SLV models,using deep learning algorithms.We propose two deep learning algorithms to solve the partial differential equations.The first algorithm is physics-informed neural networks,which is a combination of data-driven and physical model-driven algorithm.It is not only necessary to make the error of the network model trained by the algorithm on the sample data as small as possible,but also to make its residual error on the partial differential equation as small as possible.In order to accelerate the convergence speed of the loss function in the training of the network model,an adaptive activation function is introduced.The second deep learning algorithm is based on the multidimensional Feynman-Kac theorem.A large number of sample data required for the algorithm network model is generated from the stochastic diffusion equations that the underlying asset obeys,and then the appropriate network structure is built to obtain the network model that can solve the multi-asset option pricing.Furthermore,the studies are extended to that the maturity time,risk-free interest rate,exercise price,and various parameters in the stochastic process of the underlying assets are set as the input variables of the training data.Finally,the two algorithms and their extensions are used to approximate the initial price of the European best call option and the worst call option of multi-asset.Numerical results confirm the effectiveness of the algorithms.