An Analytic Valuation Method for Multivariate Contingent Claims with Regime-Switching Volatilities

In this paper, we provide an analytic valuation method for European-type contingent claims written on multiple assets in a stochastic market environment. We employ a two-state Markov regime-switching volatility in order to reflect the stochastically-changing market condition. The method is developed by exploiting the probability density of the occupation time for which the underlying asset processes are in a certain regime during a time period. In order to show its usefulness, we derive closed-form valuation formulas for quanto options and exchange options with two underlying assets, as examples. In addition, we develop an approximation formula for valuing a wide range of financial contingent claims written on more than two underlying assets