Market Risks Estimation in Option Strategies

This paper concerns about relevance of Value-at-Risk measure for option’s portfolio market risks, since recently introduced Expected Shortfall is proved to be more advantageous measure. Different options’ strategies are considered, and skewness of the payoff distributions based on Historical Simulation is obtained. There are considered two option portfolio strategies with highly negative and positive skewness given a measure by full valuation Edgeworth approximation option pricing. Short call and long combo strategies are taken in order to compare Value-at-Risk and Expected Shortfall risk metrics for different distributions’ left tails. Historical Simulation, simulation-based delta and gamma approximations, full valuation using Black-Scholes model and Edgeworth approximation pricing are used in order to test optimality of Value-at-Risk forecasts. The models are taken in an order from less sensitive to more complex capturing distributional fit. This paper tests each of them for both 1-day and 10-day time horizon as it is proposed by Basel III. The back-tests, specifically, unconditional Kupiec, Conditional Christoffersen and Engle and Manganelli are conducted. Empirical performance of these tests is analyzed. The results show an evidence of Value-at-Risk optimality for a strategy with positively skewed distribution. There appears no evidence of 10-day VaR optimality, however, full valuation using Edgeworth approximation pricing is nevertheless considered to be the most accurate. The difference of moments between Value-at-Risk and Expected Shortfall losses is calculated and the result obtained shows that metrics are very close when distribution is positively skewed.