This paper develops a lattice method for option evaluation in the presence of regime shifts in the correlation structure of assets, aiming at investigating whether the option prices reflect such shifts. We try to investigate whether option prices reflect switches in the correlation between the underlying asset of an option and risk-free rates.We develop and test two models.In the first model we allow all the parameters to follow a regime-switching process while in the second model, in order to isolate the regime-switching correlation effect on the option prices, we allow only the correlation to follow a regime-switching process. We use pentanomial lattices to represent the evolution of the regime-switching underlying assets. This is then applied in our empirical analysis, which focuses on crude oil. We use grid- and patternsearch based techniques to fit our models. Our findings suggest that prices of market traded options reflect the regime-switches and that a model which considers these switches produces significantly more accurate results than a single-regime model. We demonstrate that there is an asymmetry between parameter values obtained from historical data (backward looking) and those that are implied by traded options (for- ward looking) by employing the Kim filter to estimate our model.

中文翻译：

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具有制度转换资产相关结构的期权评估的格方法

本文研究了一种在资产相关结构存在制度转移的情况下进行期权评估的格方法，旨在研究期权价格是否反映了这种转移。我们尝试研究期权价格是否反映了期权基础资产与无风险利率之间的相关性变化。我们开发并测试了两个模型。在第一个模型中，我们允许所有参数遵循以下规则进行制度转换过程：在第二种模型中，为了隔离政权转换相关性对期权价格的影响，我们只允许相关性遵循政权转换过程。我们使用五项式格来表示政权转换基础资产的演变。然后将其应用到我们的经验分析中，重点是原油。我们使用基于网格和模式搜索的技术来拟合我们的模型。我们的发现表明，市场交易期权的价格反映了制度转换，并且考虑到这些转换的模型所产生的结果比单制度模型要准确得多。通过使用Kim滤波器估计模型，我们证明了从历史数据获得的参数值（向后看）与交易期权所隐含的参数值（向前看）之间存在不对称性。