臺灣博碩士論文加值系統

本文在風險中立之架構下，假設利率與匯率波動均為隨機過程，利用Kunitomo & Kim（2001）之漸進展開法，建構了一「函數式」的歐式外匯選擇權封閉解。雖然該「函數式」之封閉解無法直接用於實證研究，然而在假定利率與匯率波動均符合CIR（Cox, Ingersoll, Ross, 1985）類型之隨機過程後，本文進一步將其封閉解化簡為可供模擬及實證之評價模式；同時，我們發現在不同的參數值假設條件下，許多過去文獻中的外匯選擇權評價模型均成為本模型之特例；另外，經過數值模擬分析結果顯示，本模型之評價績效顯著優於固定利率與固定匯率波動之B-S(Black-Scholes)模型。

In risk neutral principal, and under stochastic interest rates and volatility of the exchange rate, we have used the Kunitomo & Kim’s (2001) asymptotic expansion method to construct a functional closed-form solution for the European foreign currency options. Although the functional closed-form solution can’t be used to empirical study, but when CIR（Cox, Ingersoll, Ross, 1985）type stochastic interest rates and volatility incorporated, then it can be simplified to be a model for simulation and empirical study. Under different parameters setup, most existing currency option models are as special cases. Numerical examples show our model is more accurate to evaluate currency options than modified B-S(Black-Scholes) model.

目 錄
中文摘要…………………………………………………………i
英文摘要…………………………………………………………ii
誌謝………………………………………………………………………iii
目錄………………………………………………………………iv
表目錄……………………………………………………………v
圖目錄……………………………………………………………vi
第壹章、緒論……………………………………………………………1
第一節 研究背景與動機…………………………………………………………1
第二節 研究目的…………………………………………………………………2
第三節 研究架構…………………………………………………………………3
第貳章、理論基礎與文獻回顧…………………………………………6
第一節 選擇權之基本理論與文獻探討…………………………………………6
第二節 外匯選擇權理論與文獻探討…………………………………………9
第參章、隨機利率與隨機匯率波動之外匯選擇權評價模型…………24
第一節 漸進展開法之函數式封閉解……………………………………………24
第二節 納入CIR型態之利率及匯率波動隨機過程……………………………31
第肆章、數值模擬分析………………………………………………36
第一節 使用模型…………………………………………………………………36
第二節 數值及參數假設…………………………………………………………37
第三節 數值模擬結果分析………………………………………………………38
第伍章、結論與建議…………………………………………………40
第一節 結論…………………………………………………………………40
第二節 建議…………………………………………………………………41
參考文獻………………………………………………………………42
附錄一…………………………………………………………………44
附錄二…………………………………………………………………59
附錄三：蒙地卡羅模擬電腦程式………………………………………62

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