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TU Dresden » Faculty of Mechanical Science and Engineering » Institute for Materials Science » Chair of Materials Science and Nanotechnology

» presentations   » 1999.07

Learning short-options valuation in presence of rare events

 M. Raberto , E. Scalas, F. Mainardi, G. Servizi, G. Cuniberti, and M. Riani

Applications of Physics in Financial Analysis

1999.07; Trinity College Dublin, Ireland

In this paper, 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. In order to generate a suitable learning set for a neural network, we use the method of Gorenflo et al. [2] based on fractional calculus. The input parameters of the network are: the simulated price of the underlying asset, its volatility and kurtosis, the interest rate, the option time to maturity, and the strike price. The learning-set option price is computed by means of a formula given by Bouchaud and Potters [3]. Option prices obtained by means of the learning scheme are compared with LIFFE option prices on Treasury bond futures.

[1] J. A. Hutchinson, A. Lo and T. Poggio, A nonparametric approach to the pricing and hedging of derivative securities via learning networks, Journal of Finance 49 (1994) 851-889.
[2] R. Gorenflo, G. De Fabritiis, and F. Mainardi, Discrete random walk models for symmetric Lévy-Feller diffusion processes, To be Published in Physica A (1999); cond-mat/990364.
[3] J. P. Bouchaud and M. Potters Théorie des Risques Financiers, Aléa Saclay (1997).

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