NGARCH組合型權證定價模型的評價與避險績效

Abstract

當個別標的股票報酬彼此間相關且服從nonlinear GARCH (NGARCH)過程下，本文推導出NGARCH組合型權證定價模型，並比較其與Chen-Cheng (2000)組合型權證定價模型（簡稱為CC組合型權證定價模型）、Black-Scholes (1973)選擇權定價模型（簡稱為BS選擇權定價模型）的定價能力與與避險績效。本文利用1997/9/4至2002/7/1在臺灣證券交易所上市且期滿的9支普通型組合型權證為研究對象，發現NGARCH組合型權證定價模型與CC組合型權證定價模型皆比BS選擇權定價模型的理論價格顯著接近於組合型權證實際交易價格，且NGARCH組合型權證定價模型的理論價格較CC組合型權證定價模型的理論價格接近於組合型權證實際交易價格，在不同價內程度(moneyness)也發現同樣的結果。此外，NGARCH組合型權證定價模型在動態避險績效的表現，無論在平均絕對誤差或絕對誤差避險優異天數也優於其他組合型權證定價模型，此或許可歸因於NGARCH組合型權證定價模型不僅能同時捕捉組合型權證波動性與標的股票個股報酬的相關性，也能捕捉其與標的股票個股波動性路徑的相依性。

This paper develops a NGARCH basket options pricing model, which the return of components underlying stocks of basket options follows a nonlinear GARCH (NGARCH) process and correlates each other. The pricing ability and hedging performance of the NGARCH basket options pricing model are compared with Chen-Cheng (2000) basket options pricing model (CC basket options pricing model) and Black-Scholes (1973) options pricing model (BS options pricing model). Nine basket options listed and expired from 1997/9/24 to 2002/7/1 on TSE were discussed. The theoretical prices of both the NGARCH basket options pricing model and the CC basket options pricing model more approximate the actual trading price than the BS options pricing model, and the theoretical price of the NGARCH basket options pricing model approximates the actual trading price than the CC basket options pricing model. Additionally, the NGARCH basket options pricing model dominates the other model at different moneyness. Based on self-financing, the NGARCH basket options pricing model dominates the other model on dynamic hedging performances. This may be attributed to that the NGARCH basket options pricing model either simultaneously captures the correlations between the volatility of the basket option price and the constituent underlying stock returns or captures the dependence of path in volatilities of the constituent underlying spot price.