Title: Jump OpVaR on option liquidity

Authors: Alireza Bahiraie; Mohammad Alipour

Addresses: Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Iran ' Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Iran

Abstract: The impact of operational risk on the option pricing through the extension of Mitra's model with Merton's jump diffusion model is assessed. A partial integral differential equation (PIDE) is derived and the impact of parameters of Merton's model on operational risk and option value by operational Value-at-Risk measure, which is derived by Mitra (2013), is studied. The option values in the presence of operational risk on S&P500 index are computed. The result shows that most operational risks occur around at-the-money options. The result shows that the parameters T, λ, μ and δ have the similar impact on OpVaR, i.e., the OpVaR decreases with increase in the parameters' values. However, the interest rate showed marginal effect, which decreases with an increase for K < S and OpVaR increases as r increases for K > S.

Keywords: option pricing; operational risk; option liquidity; operational value at risk; hedging.

DOI: 10.1504/IJCSM.2020.111119

International Journal of Computing Science and Mathematics, 2020 Vol.12 No.2, pp.147 - 156

Received: 13 Mar 2019
Accepted: 07 May 2019
Published online: 10 Nov 2020 *

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