Heuristic option pricing with neural networks and the neuro-computer synapse 3

Abstract

Today’s option and warrant pricing is based on models developed by Black, Scholes and Merton in 1973 and Cox, Ross and Rubinstein in 1979. The price movement of the underlying asset is modeled by continuous-time or discrete-time stochastic processes. Unfortunately these models are based on severely unrealistic assumptions. Permanently an unsatisfactory and quite artificial adaption to the true market conditions is necessary (future volatility of the underlying price). Here, an alternative heuristic approach with a highly accurate neural network approximation is presented. Market prices of options and warrants and the values of the influence variables form the usually very large output/ input data set. Thousands of multi-layer perceptrons with various topologies and with different weight initializations are trained with a fast sequential quadratic programming (SQP) method. The best networks are combined to an expert council network to synthesize market prices accurately. All options and warrants can be compared to single out overpriced and underpriced ones for each trading day. For each option and warrant overpriced and underpriced trading days can be used to ascertain a better buy and sell timing. Furthermore the neural model gains deep insight into the market price sen-sitivities (option Greeks), e.g., ▵, Г, Θ and Ω. As an illustrative example we inves-tigate BASF stock call warrants. Time series from the beginning of 1996 to mid 1997 of 74 BASF call warrant prices at the Frankfurter Wertpapierborse (Frankfurt Stock Exchange) form the data basis. Finally a possible speed up of the training with the neuro-computer SYNAPSE 3 is briefly discussed