Value-at-Risk of Option under GARCH Model

• Main Authors: Hsueh-Chen Lee, 李雪真
• Other Authors: Yi-Ping Chang
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/56398909199872081414

碩士 === 東吳大學 === 商用數學系 === 91 === In 1973, Black and Scholes developed the famous Black-Scholes option pricing model to price the options related derivatives. The assumption of constant volatility in Black-Scholes model has been shown inconsistent with the market behavior in most empirical studies. In this paper, we release the constant volatility assumption by using the DGARCH pricing model developed by Duan (1995). In Dec. 24, 2001, Taiwan Futures Exchange issued its first stock option on the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the market volume has grown rapidly since then. Up to now, most of the Value-at-Risk estimation models have focus on the evaluations for linear securities like stock or foreign exchange exposures. The Study of VaR for non-linear claims like options is more complicate due to the non-linearity in value function. To estimate the VaR of daily call option, in this paper, we develop an option VaR estimation algorithm which can be accompanied with various pricing models. The purpose of this paper is to evaluate the option VaR estimation performances of various Black-Scholes and DGARCH pricing models for options traded in Taiwan. In general, our empirical findings indicate that DGARCH models (with or without variance reduction methods) perform better than the Black-Scholes models. Also, the option VaR estimations work more stable for calls with a longer time to maturity and for at or in the money calls.