A Closed-Form Solution for GARCH-Jump Option Pricing Models

Abstract

本論文考慮股價不連續情況下之選擇權定價。 Heston, Nandi (2000) 的 GARCH 選擇權定價模型 以及 Ahn (1992) 的系統性跳躍風險選擇權定價模型是本論文定價模型的特例。 Bates (1996) 的隨機波動度及跳躍選擇權定價模型會是本論文模型的一種極限模型。本論文亦導出本論文選擇權定價模型的封閉解。本論文的封閉解是文獻上第一個 GARCH-Jump 選擇權定價模型的封閉解。

This thesis considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns. Our model nests the GARCH option model of Heston and Nandi (2000) and the model of Ahn (1992), where the jump risk is priced. It contains Bates’s (1996) stochastic volatility and jump model as a continuous-time limit. We also provide a closed-form solution for our model. This is the first closed-form solution for GARCH-Jump models in the literature.