GARCH 選擇權訂價模型在台灣市場的實證表現

Abstract

資產的對數報酬服從常態分布以及波動率為一常數是 Black-Scholes 選擇權估價模型的重要假設。然而，資產報酬有著較常態分布大的尾端機率及波動率叢聚現象。這些現象被解讀為財務資產的波動隨機結構，而這也成為財務工程的重要議題。 我們介紹由段錦泉教授在1995年所提出的 GARCH 選擇權訂價模型。在局部風險中立測度下以蒙地卡羅模擬法計算台灣加權股價指數選擇權價格。我們會呈現數個不同的評價準則以比較原始的、修正的 Black-Scholes 模型，與隨時間更新、不隨時間更新的 GARCH 選擇權模型評價表現。

A central hypothesis of the Black-Scholes model is that the return on the underlying asset distributed log-normally with constant volatility. However, it has been widely recognized that financial asset return processes possess heavy-tailed marginal distributions and volatility clustering. These features are interpreted as the evidence of the stochastic volatility of financial assets, and estimating the term structure of volatility has become an important issue in finance engineering. We introduced the GARCH option pricing model of Duan (1995), using the LRNVR change measure to price options by Monte Carlo simulation runs and evaluate the empirical performance of different option pricing models on Taiwan Stock Exchange Capitalization Weighted Stock Index Options. We considered the improved and constant volatility (non-update) Black-Scholes models, and the update and non-update GARCH option pricing models. We then compare their pricing performance according to several criteria.