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研究生：	鄭閔中 CHENG, MIN-CHUNG
論文名稱：	間斷性雙重障礙外匯選擇權之評價 The Valuation of Discrete Double Barrier Foreign Currency Option
指導教授：	王明隆 Wang, Min Long
學位類別：	碩士 Master
系所名稱：	管理學院 - 財務金融研究所 Graduate Institute of Finance
論文出版年：	2006
畢業學年度：	94
語文別：	英文
論文頁數：	50
中文關鍵詞：	外匯選擇權、雙重障礙選擇權、定積分法、起始值
外文關鍵詞：	initial value, integral method, double-barrier option, Foreign currency option
相關次數：	點閱：212 下載：0
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　　從1973年布列敦森林協定崩解之後，為了規避外匯風險，外匯衍生性商品被廣泛的運用。外匯選擇權在交易市場上越來越盛行，尤其是櫃臺買賣市場。在1990代中期，新奇選擇權交易量的成長率也逐漸增加，而障礙選擇權則是成長率最高的。在此篇論文中，我們利用定積分法來評價間斷時間的外匯雙重障礙選擇權。這個方法是將Garmen and Kohlhagen (1983) 所推導出來的PDE轉換成熱傳導方程式，並根據起始值的條件由後向前求解PDE。間斷時間的外匯雙重障礙選擇權評價可以被視為求解一系列的起始值問題。藉由將起始值以及格林函數作積分，我們可以很輕易的求解熱傳導方程式，選擇權的價格也就可以很輕易的求出。定積分法可以被應用在評價更複雜的選擇權，例如波動度以及償金會改變。這是個對於處理障礙選擇權既有效率而且有用的方法。

　　Foreign currency derivatives are widely used in order to hedge the exchange risk since the collapse of Bretton Wood agreement in 1973. Foreign currency options are more and more popular in the trading market especially in OTC market. In the mid 1990s, the growth rate of trading exotic currency options increased, and barrier options became the highest. In this paper, we price discrete time double barrier foreign currency option by using integral method. This method transfer PDE of Garmen and Kohlhagen (1983) into the Heat equation and solve PDE with initial conditions. Pricing discrete double barrier foreign currency option can be regarded as solving a sequence of the initial values. By integrating the initial values and the Green’s function we can solve Heat equation easily then the value of option can be obtained. The integral method can be applied to price an option with complex features such as changing volatility and changing rebates. It is an efficient and useful method to deal with pricing barrier options.

Ⅰ. Introduction................................................................1
Ⅱ. Literature Review...........................................................6
1. Valuation of currency options................................................6
2. Valuation of currency options under stochastic interest rates................6
3. Valuation of currency options under stochastic volatility....................7
4. Barrier options..............................................................8
A. Closed-form solution.........................................................8
B. Lattice Method...............................................................8
C. Adaptive mesh model.........................................................10
D. Correction Method...........................................................11
E. Finite difference Method....................................................12
F. Monte Carlo Method..........................................................12
G. Quadrature Method...........................................................13
H. Other Methods...............................................................13
5. Double Barrier Options......................................................14
Ⅲ.Methodology.................................................................16
1. Model’s assumption.........................................................16
2. Transform the PDE of Currency option into Heat equation.....................18
3. Initial value problems......................................................20
4. Valuation of a double barrier knock-out call option.........................22
Ⅳ. Numerical Results..........................................................30
1. The convergence in different integral partitions............................32
2. The difference between two continuous valuations with the partition number 50	
   ............................................................................33
3. The impact of checking frequencies on call value with rebate................34
4. The impact of checking frequencies on call value with rebate................35
5. The double barrier knock-out call value for different exchange prices with 
   rebate......................................................................36
6. The double barrier knock-out call value for different strike prices with 
   rebate......................................................................37
7. The double barrier knock-out call value for different volatilities with rebate  
   ............................................................................38
8. The double barrier knock-out call value for different rD-rF with rebate.....39
9. The double barrier knock-out call value for different barrier levels with 
   rebate......................................................................40
10. The double barrier knock-out call value for different rebates..............41
11. The double barrier knock-out call value for a different length of time with 
    rebate.....................................................................42
12. The double barrier knock-out call value for different length of time with 
    rebate.....................................................................43
Ⅴ. Conclusions and further research...........................................44
1. Conclusions.................................................................44
2. Further researches..........................................................45
Reference......................................................................46
                                    

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