摘要
本文主要在討論基金價格的利率風險以及跳躍風險，文章中假設標的基金價格服從雙重指數跳躍擴散過程，另外假設利率過程服從Vasicek model。文章中推導出動態保本型基金的價格公式，並利用Laplace轉換求出價格封閉解，最後利用Gaver-Stehfest演算法進行拉普拉斯逆轉換，有效求出動態保本型基金價格。
最後文章中給出了敏感性分析，分析了在不同參數之下利率以及跳躍過程對基金價格的影響。而我們發現無論是利率風險或是跳躍性擴散風險均會對基金價格造成相當程度的影響。

In this thesis we discuss how the interest rate risk and jump diffusion risk effect the value of dynamic guaranteed fund. We assume the dynamic underlying of the guaranteed fund follows a double exponential jump process and stochastic interest rate process follows Vasicek model. We then derive the dynamic guaranteed fund’s pricing formula, and use Laplace transform to obtain closed-form solution. Finally, in order to calculate more efficiently, we apply Gaver-Stehfest algorithm to Laplace inverse to obtain dynamic guaranteed fund values. We also provide numerical results. We analyze the different results with different jump-related parameters and interest rate-related parameters. We find that both of the interest rate risk and jump risk can significantly affect the value of dynamic guaranteed funds.
Key Words: Dynamic Guaranteed Fund, Vasicek Model, Double Exponential Jump, Laplace Transform, Gaver-Stehfest Algorithm

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