Kou 的跳躍擴散模型擴展：納入雙伽瑪分佈的跳躍幅度

Abstract

本論文主要在研究在將Kou 的雙指數跳躍擴展成雙伽瑪跳躍擴散模型。我們採用快速傅立葉轉換方法來獲取兩個模型的選擇權價格。通過將模型擴展為雙伽瑪分佈不僅能夠再現Kou 模型的結果，還能夠提供更大的靈活性來模擬市場，允許對模型進行微調。數值結果顯示雙伽瑪分佈變數如何影響分配的動差，從而導致選權權價值的變化。

This paper aims to extend Kou’s double exponential jump-diffusion model to the double gamma jump-diffusion model. We employ the Fast Fourier Transform method to obtain option prices for both models. By extending the model to the double gamma distribution not only reproduces the results of Kou’s model but also provides enhanced flexibility in simulating the market, allowing for fine-tuning of the model. The numerical results show how the double gamma distribution variables affect the moments leading to changes in the call value.