Evaluation the effect of stochastic fluctuations on operational risk of hedging European options: Application of Markov Switching and Black Scholes Standard

Operational risk is not general definition and it has a unique definition for each company, which depends on the industry and the market of the company. The purpose of this research is to evaluate the effect of stochastic fluctuations on operational risk hedging European options on the S & P500 index. So this research will compare the operational risk level in the Markov Switching and Black Scholes models using the Var. The implicit volatility values for the three confidence levels of 90, 95 and 99% for different values of call options K, different maturity T, and different interest rate r were calculated for both models using S & P500 index call options information. The results of this study showed that due to higher gamma and random variation of operational risk, the coverage of transaction options in the Markov Switching Model compared to the Black Scholes Standard model was higher by using the criterion of value-at-risk op Var's coverage is at 90, 95, and 99 levels. The results show that OP VaR is inversely proportional to  ,    It also reduced doubling of the OP Variant's maturity over the agreed price. Finally, the results show that the interest rate has an asymmetric effect on OP VaR. As is clear from the figure, for K <S, the OP VaR has been lowered by rising interest rates, and for K> S interest rates have reduced OP VaR .