Abstract
We extend the neural-network approach for the valution of financial derivatives developed by Hutchinson et al. [1] to the case of fat-tailed distributions of the underlying asset returns. We use a two-layer perceptron with three inputs, four hidden neurons, and one output. The input parameters of the network are: the simulated price of the underlying asset F divided by the strike price E, the time-to-maturity T, and the ratio |F-E|/T. The latter takes into account the volatility smile, whereas the price F is generated by the method of Gorenflo et al. [2] based on fractional calculus. The output parameter is the call price C over E. The learning-set option price C is computed by means of a formula given by Bouchaud and Potters [3, 4]. Option prices obtained by means of this learning scheme are compared with LIFFE option prices on German treasury bond (BUND) futures.
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