有跳躍的GARCH模型

Abstract

在這一篇文章裡，我們主要是用一個含有跳躍項的GARCH模型來描述匯率市場的行為，並且比較有跳躍項及沒有跳躍項兩者之間的差異。此外，我們還利用平賭理論以及效用最佳化的論點來推導出在風險中立下所對應的隨機過程並且進而利用蒙地卡羅模擬來計算在我們模型之下的選擇權價格。

In this paper, we mainly use the GARCH model with Jumps to describe the exchange rates market and compare the performance of models with jumps and without jumps. In addition, we will use the martingale theory and the argument of the utility maximization to derive the risk-neutral process and use the Monte Carlo simulation to find the option price.