在雙指數跳躍擴散過程下動態保本型商品之評價分析

Pricing Dynamic Guaranteed Funds under a Double Exponential Jump Diffusion Model

本文在假設標的基金嫁得服從雙重指標跳躍擴散的過程下，來擴展過去文獻對於動態保本型基金之評價分析。首先，本文推導出動態保本型基金價格拉普拉斯轉換之封閉解，並進一步應用Gaver-Stehfest演算法進行拉普拉斯逆轉換，以求得動態保本型基金的價格。從文章中之數值結果，我們發現本文所提出之評價方法相較於蒙地卡羅模擬法更具有效率性但卻不失準確性。另一方面，本文亦研究在考慮價格跳躍的情況下，動態保本型基金之價格改變行為，和連續型動態保本基金價格與間斷型動態保本基金價格之差異分析。最後，本文亦提供動態保本型基金價格與相關模型參數之敏感性分析。

This paper complements the extant literature to evaluate the prices of dynamic guar-anteed funds when the price of underlying naked fund follows a double exponential jump-diffusion process. We first derive the closed-form solution for the Laplace transform of dynamic guaranteed fund price, and then apply the efficient Gaver-Stehfest algorithm to Laplace inversion to obtain the prices of dynamic guaranteed funds. Based on the numerical pricing results, we find that the proposed pricing method is much more efficient than the Monte Carlo simulation approach although it loses a sufficiently small accuracy. On the other hand, we also provide an investigation on the behavior of prices of dynamic guaranteed funds when jump is taken into consideration. In addition, the sensitivity analyses of the prices of dynamic guaranteed funds with respect to jump-related parameters and the relative errors between the prices of continuous-monitored and discretely-monitored dynamic guaranteed fund are given in this paper as well.