Credible Delta-Gamma-Normal Value-at-Risk for European Call Option Risk Valuation

This paper formulates a new risk measure called as credible delta-gamma-normal Value-at-Risk (CredDGN). CredDGN is a generalization of credible Value-at-Risk (CredVaR), which determines risk by combining CredVaR with deltagamma-normal VaR. This novel method is proposed as an appropriate tool for measuring European call option portfolio risk because it considers the nonlinear dependence of the market risk factors that determine a European call option value based on the Black-Scholes Formula. We apply this method to evaluate simulated financial data representing the profit/loss of several assets over ten investment periods. The new method is also utilized to analyze the risk of a portfolio composed of the active stocks which trade the options. Based on Kupiec's backtesting results, the performance of CredDGN effectively measures the risk of an option portfolio at 80%, 90%, and 95% confidence levels even when the profit/loss (P/L) is nonnormally distributed.