Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
The equivalent martingale measure: an introduction to pricing using expectations
IEEE Transactions on Neural Networks
Learning to trade via direct reinforcement
IEEE Transactions on Neural Networks
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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 riskneutral 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.