Talk - Option Pricing by Neural Stochastic Differential Equations: A Simulation Optimization Approach

Abstract

The classical option pricing models rely on prior assumptions on the dynamics of the underlying assets. Though empirical evidence shows that these models may partially explain the option prices, their performance may be poor when the actual situations deviate from the assumptions. Neural network models are capable of learning the underlying relationship through the data. However, they require massive amount of data to avoid over-fitting, which is typically not available for option pricing problems. Thus, we propose a new model by integrating neural networks to a classical stochastic differential equation pricing model to balance the model flexibility and the data requirement. Besides, some more specific models are also constructed by using neural network as a model calibration method of the classical models. Furthermore, we show that the training of the model can be formulated into a simulation optimization problem and can be solved in a way that is compatible to the training of neural networks as well. Preliminary numerical results show that our approach appears to work better compared with some existing models. This is a joint work with Shoudao Wang and Nifei Lin.