Nonlinear Feature Space Research Articles

Beyond Black–Scholes: A Neural Networks-Based Approach to Options Pricing

The paper presents two alternative schemes for pricing European and American call options, both based on artificial neural networks. The first method uses binomial trees linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the non-linear feature space. Neural networks are used to infer future volatility levels from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. In the second approach neural networks are trained with genetic algorithms in order to reverse-engineer the Black–Scholes formulae. The standard Black–Scholes model provides a starting point for an evolutionary training process, which yields improved options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black–Scholes model and the proposed options pricing schemes. The proposed models produce as good as and often better options prices than the conventional Black–Scholes formulae.

Stochastic volatility options pricing with wavelets and artificial neural networks

The paper describes an alternative options pricing method which uses a binomial tree linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the nonlinear feature space. Neural networks are used to infer future volatility from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black‐Scholes model and a new options pricing scheme. The proposed dynamic volatility model produces as good as and often better options prices than the conventional Black‐Scholes formulae.

Patterns and symbols treated in a three-layered associative memory network

This paper presents a new network for inference using patterns and symbols. Patterns are spatial distributions of feature vectors in nonlinear feature space made from original images. The new network is for acquiring concepts and inferring meanings of original images. Simulations using similar/different patterns are done to show the unique feature of the proposed network.