NN-OPT: Neural Network for Option Pricing Using Multinomial Tree
We 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 Price Trading Cost Martingale Measure Forward Propagation Term Interest Rate
Unable to display preview. Download preview PDF.
- 3.Cox, J.C., Ross, S.A.: The valuation of options for alternative stochastic processes. Journal of Financial Economics, 145–166 (1976)Google Scholar
- 4.Harrison, J.M., Pliska, S.R.: A stochastic calculus model of continuous trading: Complete markets. Stochastic Processes and their Applications, 313–316 (1983)Google Scholar
- 5.Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modeling. Applications of Mathematics, 36. Springer, New York (1977)Google Scholar
- 7.Amari, S.I., Xu, L.C.L.: Option pricing with neural networks. Progress in Neural Information Processing 2, 760–765 (1996)Google Scholar
- 9.Cox, J.C., Ross, S.A., Rubinstein, M.: Option pricing: A simplified approach. Journal of Financial Economics, 229–263 (1979)Google Scholar
- 13.Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
- 14.Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice-Hall, Englewood Cliffs (1998)Google Scholar