Closed‐form approximated pricing of multivariate derivatives under switching regime models

Markov switching regime models have played an increasingly important role in finance and economics, especially for business cycles and long swings in currencies. Regime-switching models provide a simple way to capture stochastic volatility and thus overcomes the drawback of the classical lognormality assumption characterized by constant volatility. This paper considers multivariate Black and Scholes type models with a Markov regime-switching mechanism. We show that the pricing of some multivariate derivatives under models where the Markov chain has two or three states, can be approximated accurately in closed-form, based on linear and quadratic Taylor polynomials. Closed form approximation methods are computationally advantageous as they perform in constant time, compared with alternative methods such as Monte-Carlo, where the accuracy of the estimation is directly linked to the number of executed simulations.