In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

在这项研究中，我们考虑了马尔可夫制度切换 GARCH-jump (RS-GARCH-jump) 模型下的期权定价。更具体地说，我们推导了风险中性动态，并提出了一种格算法来为该框架中的欧式和美式期权定价。我们还在我们的 RS-GARCH-jump 设置中使用基础时间序列的历史数据提供了一种参数估计方法。为了衡量所提出算法的定价性能，我们研究了基于树的结果与真实期权价值的收敛性，并表明该算法表现出良好的收敛性。通过比较RS-GARCH-jump模型与制度切换GARCH（RS-GARCH）模型、GARCH-jump模型、GARCH模型、Black-Scholes（BS）模型和制度切换（RS）模型的定价结果，我们表明，适应跳跃效应和制度转换会显着改变期权价格。实证结果还表明，RS-GARCH-jump 模型在解释期权价格方面表现良好，并证实了允许跳跃分量和状态转换的重要性。