NN-OPT: Neural Network for Option Pricing Using Multinomial Tree

Abstract

AbstractWe provide a framework for learning to price complex options by learning risk-neutral measures (Martingale measures). In a simple geometric Brownian motion model, the price volatility, fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of allowable risk-neutral measures. We then propose a framework for learning the appropriate risk-neural measure. In particular, we provide an efficient algorithm for backpropagating gradients through multinomial pricing trees. Since the risk-neutral measure prices all options simultaneously, we can use all the option contracts on a particular stock for learning. We demonstrate the performance of these models on historical data. Finally, we illustrate the power of such a framework by developing a real time trading system based upon these pricing methods.KeywordsOption PriceTrading CostMartingale MeasureForward PropagationTerm Interest RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.