Analytical Valuation of Compound Options under Regime-Switching Dynamics

We propose an analytical formula for the evaluation of compound options when the underlying asset is described by a two-states Markov regime-switching log-normal model. This model has been shown to capture several empirical properties of market returns, and often performs better than more complex econometric models when predicting the behavior of stocks or indexes. Many traded financial products can be expressed or approximated as a combination of compound options and other simpler instruments. One specific application of interest is the pricing of principal protected notes with an early redemption feature. Our approach provides practitioners with a Black-Scholes-type formula under a realistic assumption about market prices behavior. We report on numerical experiments evaluating the sensitivity of principal protected callable notes to the model specification.