A Lattice Method for Option Evaluation with Regime-Switching Asset Correlation Structure

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. Specifically we try to investigate whether option prices reflect switches in the correlation between the underlying asset of an option and the risk-free bond returns. 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. In order to implement these models 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 pattern-search 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 better and more accurate results than a single-regime model