
Learning shortoptions 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 fattailed
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
learningset 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)
851889. [2] R. Gorenflo, G. De Fabritiis, and F.
Mainardi, Discrete random walk models for symmetric
LévyFeller diffusion processes, To be Published in
Physica A (1999); condmat/990364. [3] J.
P. Bouchaud and M. Potters Théorie des Risques
Financiers, Aléa Saclay (1997).



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