Calculating the Greeks for option contracts on regime-switching instruments

Abstract

We study regime-switching models for stocks and interest rates. We define these models modifications of the classical models created by Black & Scholes and Vasicek for stocks and interest rates, respectively. The problem is to calculate the Greeks for option contracts with the underlying instrument modled by a regime-switching model. We investigate a new method for calculating the Greeks based on Mallivian calculus and create a new algorithm for computing the delta for various standard option contracts. We compare the new method with existing methods for classical models. Then we present delta calculations for option contracts on underlying instruments modeled by regime-switching models using the new algorithm.