Geodesic
An inverse finance problem for estimation of the volatility
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1

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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. 
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     author = {A. Neisy and K. Salmani},
     title = {An inverse finance problem for estimation of the volatility},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a6/}
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A. Neisy; K. Salmani. An inverse finance problem for estimation of the volatility. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a6/