Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Pricing and hedging contingent claims with regime switching risk

Pages: 477 – 498

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n2.a6

Authors

Robert J. Elliott (School of Mathematical Sciences, University of Adelaide, Australia)

Tak Kuen Siu (Department of Actuarial Studies, Macquarie University, Sydney, Australia)

Abstract

We study the pricing and hedging of contingent claims in a Markov regime-switching market with a money market account, a zero-coupon bond, and an ordinary share. General contingent claims with payoffs depending on both the share price and the state of a Markov chain describing regime switching are considered. A general pricing kernel defined by the product of two density processes is used to explicitly take into account regime switching risk. Under some differentiability and boundedness conditions, a martingale representation result is established and the integrands in the representation are explicitly identified with respect to the general pricing kernel. We then determine a pricing kernel and a hedging strategy by minimizing the residual risk due to incomplete hedging. Our analysis is also extended to Asian-style and American-style general contingent claims.

Keywords

contingent claims, regime switching risk, valuation, hedging, product density processes, martingale representation, stochastic flows, zero-coupon bonds, residual risk, Asian options, American options

2010 Mathematics Subject Classification

60H30

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