Pricing Foreign-Currency Options: A Comparison of the Modified Black-Scholes Model and a Modified Merton Model

論外匯選擇權之訂價：Black-Scholes修正模型與Merton修正模型之比較分析

劉德明(Der-Ming Lieu)

《中國財務學刊》 2卷1期 (1994/07) Pp. 75-104

https://doi.org/10.6545/JoFS.1994.2(1).5

摘要

本文擴充Merton（1976）之股票選擇權訂價模型，假設外匯價格比率變動遵循混合常態與普松分配，導出跳躍式的外匯選擇權定價模式，並就1983至1985之PHLX外匯選擇權資料做實證研究，結果顯示Merton修正模型可以彌補Black-Scholes修正模型之部分偏差，其解釋能力之相對高低顯然和榜的外匯價格之實際變化有關，外匯價格變化若越背離對數常態分配，則修正的Merton模型之解釋能力就越好。

並列摘要

This paper presents a pricing model for foreign-currency option s with a mixed-jump process. The new option-pricing model incorporates Merton (1976)'s techniques and is empirically tested against the modified Black-Scholes model in the foreign-currency options markets using the transact ion data from the Philadelphia Stock Exchange. Preliminary evidence suggests that the modified Merton's model can eliminate some of the bias that the modified Black-Scholes model exhibits. The relatively better performance from the modified Merton model appears to relate to the underlying destribution for foreign-currency price changes. The more seriously the underlying currency price changes depart from a lognormal process, the better the modified Merton model performs.