遠期生效選擇權之評價 —以歐元和日元為例—

Pricing Forward Start Option — Cases of Euro and Japanese Yen

張麗卿(Li-Ching Chang)

指導教授 ： 胡為善

中原大學/商學院/企業管理研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300498

摘要

摘要

本研究主要探討藉由二項式模型與三項式模型之數值方法，對遠期生效選擇權做評價，以比較二者差異，並藉由調整參數之數值，探討參數變動對遠期生效選擇權的影響。所採用的標的資產為歐元及日元，根據本研究實證結果得到如下的結論：

1. 無論使用二項式或三項式評價模型對歐式遠期生效選擇權作實證研究，當其 的次數逐漸增加時，此二種模型評價所得之值皆呈現穩定且收斂，表示採此二種方式評價歐式遠期生效選擇權是適宜的。

2. 雖然在使用三項式評價模型時，計算過程相當耗時，但由本研究實證結果發現其 的次數不需很大即能收斂，而二項式評價模型卻需要較大的次數才能收斂，表示無論在穩定性或效率方面，三項式優於二項式評價模型，因此在評價歐式遠期生效選擇權買權方面，三項式是較佳的評價模型。

3. 根據本研究之敏感度分析研究結果，無論使用二項式或三項式評價模型分析，參數的變動對買權價值有顯著的影響。無論歐元或日元，歐式遠期生效選擇權之買權與(1)即期匯率；(2) 契約期間長短 ；(3) 國內無風險利率；(4) 匯率波動性呈正相關趨勢。歐式遠期生效選擇權之買權卻與生效期間長短及國外無風險利率呈負相關趨勢。

展望未來，金融市場進入微利時代，匯率及利率逐漸透明化，遠期生效選擇權的金融商品會在國內不斷地推陳出新，以滿足客戶所需，因此本研究的分析結果，將為理論和實務界提供參考依據。

關鍵字

二項式評價模型 ； 三項式評價模型 ； 遠期生效選擇權

並列摘要

Abstract

The purpose of this study is to pricing forward start option by using binomial and trinomial model as well as to compare these two models. Furthermore, this work explores the change of parameters on value of start option by adjusting the value of parameters. The targets of this investigation were Euro and Japanese Yen. The conclusions are summarized as follows:

1. Under both binomial and trinomial models, this study indicated that as N value increased, the value of these two models were stable and converge. It showed that both models are appropriate for pricing European-style forward start option.
2. Although trinomial model consumes a lot of time, yet the results demonstrated that it may converge even it did not have a large N value. However, the binomial model converges as N value increased. These results implied that or the trinomial model is better than the binomial model for pricing European-style forward start option in stability and efficiency.
3. According to the empirical results of sensitivity analysis, this work found that the change of parameters has significant influence on call option value for pricing European-style forward start option in both binomial and trinomial models. Additionally, the European-type forward start call option price had a positive correlation with spot exchange rate, the time to maturity, the domestic risk-free rate and volatility for both Euro and Japanese Yen. It indicates that as the parameters’ values increases, the forward start call option value will increase. The results also demonstrated that the European-type forward start call option price had negative correlation with (1) the length of the effective period; and (2) the international risk free rate.

Looking into the future, we will face against a tiny-profit financial market, the exchange rate and interest rate will be more flexible than before. Various derivative products of forward start option will be introduced into Taiwan’s financial markets, in order to meet the needs of customers. Finally, this work provides the suggestions and recommendations to investors and organizations.

並列關鍵字

binomial pricig model ； trinomial pricing option ； forward start option

參考文獻

6.邱育寬 後定選擇權之評價與模擬分析，中原大學企業管理研究所未出版碩士論文，民國

19.謝承熹 隨機利率下歐式遠期生效選擇權之評價與避險， 財務金融學刊， 民國91年4月，

1.Biger, Nahum and John Hull, 1983 , “The Valuation of Currency Options“,

Financial Management, pp.24-28.

2.Cox, J.C., S.A. Ross and M. Rubinstein, 1979, “Option Pricing: A Simplified