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 Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 1, Page 73 (Mi zvmmf9795)

An inverse finance problem for estimation of the volatility

A. Neisy, K. Salmani

Department of Mathematics, Computer and Statistics, Faculty of Economics, Allameh Tabataba'i University, Iran

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.

Key words: calibration, jump-diffusion model, inverse problem, numerical methods, boundary value problem, Tikhonov regularization, $\theta$ method.

DOI: https://doi.org/10.7868/S0044466913010109

Full text: PDF file (96 kB)

English version:
Computational Mathematics and Mathematical Physics, 2013, 53:1, 63–77

Bibliographic databases:

UDC: 519.627.2
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Citation: A. Neisy, K. Salmani, “An inverse finance problem for estimation of the volatility”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013), 73; Comput. Math. Math. Phys., 53:1 (2013), 63–77

Citation in format AMSBIB
\Bibitem{NeiSal13} \by A.~Neisy, K.~Salmani \paper An inverse finance problem for estimation of the volatility \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2013 \vol 53 \issue 1 \pages 73 \mathnet{http://mi.mathnet.ru/zvmmf9795} \crossref{https://doi.org/10.7868/S0044466913010109} \zmath{https://zbmath.org/?q=an:06183604} \elib{https://elibrary.ru/item.asp?id=18446740} \transl \jour Comput. Math. Math. Phys. \yr 2013 \vol 53 \issue 1 \pages 63--77 \crossref{https://doi.org/10.1134/S0965542513010090} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314309400006} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84893009400} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Xu Z., Jia X., “The Calibration of Volatility For Option Pricing Models With Jump Diffusion Processes”, Appl. Anal., 98:4 (2019), 810–827
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