隨機波動和跳躍對選擇權定價與避險之影響：以台灣和美國市場為例

Abstract

這篇文章致力於研究在台指選擇權和美國個股選擇權市場中加入隨機波動或跳躍能否改善選擇權定價及避險表現。我們首先分析加入隨機波動和跳躍的選擇權定價模型的性質以及比較它們數值積分和傅利葉轉換法的效率性與正確性。之後我們選用CBOE交易最熱絡的二十家短期個股選擇權以及短期台指選擇權，用三種衡量標準︰樣本內定價績效，樣本外定價績效，以及delta，gamma和vega中立避險績效來做實証分析。我們的實証結果顯示在兩個市場中加入隨機跳躍對選擇權定價是有助益的。另一方面，我們發現在兩個市場中加入隨機波動和跳躍對選擇權避險都是有助益的。在二十家短期個股選擇權中加入隨機波動的避險改善幅度比加入隨機跳躍大，然而在短期台指選擇權中，避險順序剛好相反。

This study aims to investigate whether incorporating stochastic volatility or random jumps is beneficial for short-term option pricing and hedging in Taiwan index and U.S. equity option markets. We first analyze the properties of the option pricing models that incorporate stochastic volatility and random jumps and compare the efficiency and accuracy of numerical integral and Fourier transform computational approaches of these models. We use 20 most actively traded short-term individual equity options listed on CBOE and short-term Taiwan Stock Exchange Capitalization Weighted Stock Index Options (TXO) to implement our empirical tests with three criterions: in-sample pricing performance, out-of-sample pricing performance, and delta-, gamma-, and vega-neutral hedging performance. The empirical results reveal that incorporating random jumps is beneficial for option pricing in both markets. On the other hand, we find that incorporating both random jumps and stochastic volatility are beneficial for option hedging in both markets. The hedging improvement of incorporating stochastic volatility is larger than that of incorporating random jumps in 20 short-term individual equity options. However, the hedging order in short-term TXO is opposite.