An inverse finance problem for estimation of the volatility

Authors:
A. Neisy;K. Salmani
Affiliations:
Department of Mathematics, Computer and Statistics, Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran;Department of Mathematics, Computer and Statistics, Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran
Venue:
Computational Mathematics and Mathematical Physics
Year:
2013

Citing 5
Cited 0

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Abstract

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.