HEDGING STRATEGY WITH LANGEVIN EVOLUTION

S. Mariani, G. Rotundo () and B. Tirozzi ()
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S. Mariani: Department of Mathematics for Economics, Financial and Insurance Decisions, University of Rome "La Sapienza", Italy
G. Rotundo: Department of Mathematics for Economics, Financial and Insurance Decisions, University of Rome "La Sapienza", Italy
B. Tirozzi: Department of Physics, University of Rome "La Sapienza", Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2000, vol. 03, issue 03, 553-556

Abstract: In recent years there has been much attention paid to pricing and hedging models that are more general than the Black and Scholes' one, whose hypotheses often aren't satisfied by true market data. Sato and Takayasu proposed a market model that can produce price fluctuations with infinite variance from a deterministic behaviour of many market's dealers as it emerged from their simulations. We check the possibility to apply this model to an Italian stock, the "Assicurazioni Generali" and determine the density function of the multiplicative and additive noise appearing in the proposed Langevin equation.We find also the Lévy distribution for the changes. This distribution is consistent with the histograms and the Kernel estimates. These results are used for hedging following the approach of Sornette and Bouchaud.

Date: 2000
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DOI: 10.1142/S0219024900000553

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