Deep learning of the Heston model

Specialeforsvar ved Jie Lie og Emil Bille Tølbøll

Titel: Deep learning of the Heston model - Neural Network Representations of a Stochastic Volatility Model

 

Abstract: In this thesis we construct neural network (NN) representations of the a implied volatility function based on the Heston model. We derive the Breeden and Litzenberger formula that states the implied volatility function can be used to derive the risk-neutral density of an asset independently of the underlying model. We derive an analytic solution of European call option prices within the Heston model and use it to generate large samples of training data from which neural networks can learn. We investigate the performance of various learning techniques and hyper-parameter settings and apply them for the training of high-dimensional NN models. The complexity of the NN in terms of width and depth is experimentally analyzed. We find that NN representations can learn the structure of the analytic pricing formula and compute prices with an impressive speed. On top of being fast the NN are also accurate - the price computed yields a mean squared error of 4.39 · 10−8. 

 

Vejleder: Rolf Poulsen
Censor:   Cathrine Jessen, ATP