Credible delta gamma (Theta) normal value at risk for assessing European call option risk

Abstract

The current research introduces a novel risk metric called credible delta-gamma (theta)-normal Value-at-Risk (CredDGTN VaR) for the purpose of the option risk assessment. CredDGTN VaR represents an extension of the credible Value-at-Risk (CredVaR) framework, whereby risk assessment is conducted through the integration of CredVaR with delta-gamma(theta)-normal VaR. The present study introduces a novel approach that is deemed suitable for evaluating the risk of a portfolio of European call options. The proposed method takes into account the nonlinear interdependence of the market risk factors determining the value of a European call option, according to the Formula of Black-Scholes. The present methodology is employed to assess simulated financial data that portrays the return of multiple assets throughout ten investment periods. The novel approach is additionally employed to assess the level of risk associated with a portfolio comprised of actively traded stock options. According to Kupiec’s backtesting, CredDGTN’s efficacy in gauging the risk of an option portfolio is noteworthy, as it accurately measures the risk at 80%, 90%, and 95% confidence levels, even in cases where the profit/loss (P/L) exhibits non-normal distribution. Furthermore, the performance of CredDGTN VaR empirically outperforms credible delta-normal VaR (CredDN VaR) and credible delta-gamma-normal VaR (CredDGN VaR) in similar cases. Moreover, CredDN VaR, CredDGN VaR, and CredDGTN VaR will provide equal VaR when delta and gamma are zero.