Conditional VaR of Taiwan Index Option:Application of Merton-Jump-Copula Model

[[abstract]]Black and Scholes 在1973年發表選擇權評價模型後，因選擇權評價模型的假設不符實際市場狀況，且在市場的無風險利率變動和波動性變化或預期報酬呈現厚尾分佈下，造成修正選擇權評價模型隨之蘊育而生；在考慮報酬分配具厚尾分佈，因此Black-Scholes-Merton在1974年發表跳躍過程的選擇權評價模型，故本文再加入一因子高斯關聯結構而導出Merton跳躍關聯結構模型。 本文利用風險值(VaR)與條件風險值(CVaR)分析台灣金融保險類股價指數選擇權與電子類發行量加權股價指數選擇權的損失分配，本文的實證結果指出2010年平均條件風險值金融股價指數選擇權為237 6，而電子股價指數為88 59，此外因金融指數選擇權波動性大於電子指數選擇權，所以金融股價指數條件風險值大於電子股價指數條件風險值。[[abstract]]Black and Scholes presented their option pricing model in 1973 the assumptions of option pricing model may not fit to the real environments when investors face an environment with stochastic interest rate stochastic volatility and fat-tail return distribution modified Black and Scholes model is proposed by researches Considering the fat-tail phenomenon of return distribution Black-Scholes-Merton (1974) derived a option pricing formula with jump process However when the diffusion process yields a property of one-factor Copula structure our Merton-Jump-Copula model is advised Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) is used in this paper to analysis the loss distribution of Taiwan Stock Exchange Finance Sector Index options and Electronic Sector Index options Our empirical result shows that the average CVaR for Finance-Index-Options and Electronic-Index-Options are 237 6 and 88 59 respectively Moreover the CVaR of Finance Sector Index options are higher than Electronic Sector Index options since Finance-Index-Options are more volatile than Electronic-Index-Option