Attainable contingent claims in a Markovian regime-switching market

Abstract

It is known that the market in a Markovian regime-switching model is, in general, incomplete, so not all contingent claims can be perfectly hedged. We show, in this paper, how certain contingent claims are attainable in the regime-switching market using a money market account, a share and a zero-coupon bond. General contingent claims with payoffs depending on both the share price and the state of the regime-switching process are considered. We apply a martingale representation result to show the attainability of a European-style contingent claim. We also extend our analysis to Asian-style and American-style contingent claims.