An inverse finance problem for estimation of the volatility

Article

DOI: 10.1134/S0965542513010090

Cite this article as:
Neisy, A. & Salmani, K. Comput. Math. and Math. Phys. (2013) 53: 63. doi:10.1134/S0965542513010090
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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.

Keywords

calibration jump-diffusion model inverse problem numerical methods boundary value problem Tikhonov regularization θ method 

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Computer and Statistics, Faculty of EconomicsAllameh Tabataba’i UniversityTehranIran

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