Risk Assessment on Option Portfolio: Cross-Period Analysis of Value at Risk and Expected Tail Loss

• Main Authors: Guo, Yau-Rung, 郭曜榮
• Other Authors: Lee, Tai-Ming
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/87142502816379076596

碩士 === 輔仁大學 === 金融研究所 === 97 === This research is based on measuring risk on Option Portfolio. Estimate Value at Risk and Expected Tail Loss as the Risk Measuring. To differ other literatures in the past that only estimating the risk at specific time point, our research use Cross-Period analysis to estimate VaR and ETL, and discuss this Risk Measuring changing on the different holding period. At the same time, compare and discuss different Risk Measuring estimated method. To make it more clearly, our research to use actual market data estimate the Risk Measuring on cross-period. First, price option value using Black-Scholes(1973), Delta-Gamma Approximation, and Delta-Gamma-Theta Approximation. To proceed, we use simulated underlying assets price paths substitution to option valuing formula, to obtain the option gains and losses distribution. And observe the option gains and losses distribution statistical characteristic on the different holding period. Then use Direct Sum Average method, Monte Carlo Integration method, and Importance Sampling method to estimate the ETL. Finally, we use Cross-Period analysis to discuss the estimated results of Risk Measuring. The results demonstrate that following the holding period increase, the Delta-Gamma Monte Carlo Simulation method underestimate the VaR, and Delta-Gamma-Theta Monte Carlo Simulation method overestimate the VaR. In another word, the Delta-Gamma and Delta-Gamma-Theta Monte Carlo Simulation method in increasing holding period are not applicable. Estimate ETL in Cross-Period analysis, Direct Sum Average method is the simplest, but the results to be short of accurate and underestimate the risk easily in the less sample data. Monte Carlo Integration method has more accurate and consistent results that need more computer sampling times. And the estimated results variation degree is larger. The Importance Sampling method has better estimated results than Monte Carlo Integration method, and not easier to underestimate the risk than Direct Sum Average method.