臺灣博碩士論文加值系統

傳統的選擇權定價模型當選擇權在價內(in-the-money)及價外(out-the-
money)時會有錯 價的情況，尤其當價內或是價外的程度很大時，錯價的
情況會更加的明顯， 這種情況我們一般稱為volatility smile。本篇論
文延伸Barone-Adesi and Whaley (1987) 美式選擇權的模型，加入了非
常態的skewness和kurtosis調整項，解決因為假設標的物報酬為常態分配
的誤差。所使用的方法是採用Gram-Charlier 展開式，將原本Barone-
Adesi and Whaley's (1987) 模型中的常態分配項加入skewness和
kurtosis的調整項。吾人採用 1997年2月和8月的歷史資料，將本模型和
傳統的美式選擇權模型如Barone-Adesi andWhaley (1987) 以及二元樹模
型做實證比較，結果發現本調整skewness和kurtosis過的模型，無論是在
價內(in-the-money)或是價外(out-the-money)甚或是價平(at-the-
money)的情況，定價均比傳統的模型來的精確。此結果和Corrado and Su
(1996) 調整後Black-Scholes歐式選擇權模型所得到的結果相同。

The traditional American pricing model frequently misprices
deep-in-the-money and deep-out-of-the-money options.
Practitioners popularly refer to these strike price biase as
volatility smiles. In this paper we exam in a methodto extend
the Barone-Adesi and Whaley (1987) American option pricing
modelto account for biases induced by nonnormal skewness and
kurtosis in stockreturn distributions. The method adapts a Gram-
Charlier series expansion ofthe normal density function to
provide skewness and kurtosis adjustment termsfor the Barone-
Adesi and Whaley's(1987) formula. Using this method, we
estimateoption implied coefficients of skewness and kurtosis in
S&P 500 index futuresreturns. We find significant nonnormal
skewness and kurtosis implied by option price.