Utility indifference valuation of corporate bond with rating migration risk

Abstract

A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a multi-rating bond and obtain closed formulae in a three-rating case. Based on the pricing formulae, the impacts of the parameters on the indifference price are analyzed and some reasonable financial explanations are provided as well.

Keywords

Utility indifference price / credit rating migration / HJB equation / Markov-modulated

References

[1] Bäuerle N, Rieder U. Portfolio optimization with Markov-modulated stock prices and interest rates. Automatic Control, 2004, 49(3): 442−447

[2] Bronson R. Matrix Methods: An Introduction. New York: Academic Press, 1991

[3] Davis M H A, Panas V, Zarphopoulou T. European option pricing with transaction costs. Control Optim, 1993, 31: 470−493

[4] Duffe D, Singleton K J. Modeling term structures of defaultable bonds. Rev Financial Stud, 1999, 12: 687−720

[5] Elliott R J, Siu T K. On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. Ann Oper Res, 2010, 176(1): 271−291

[6] Henderson V, Hobson D. Utility Indifference Pricing: An Overview Indifference Pricing. Princeton: Princeton University Press, 2004

[7] Hodges S D, Neuberger A. Optimal replication of contingent claims under transaction costs. Rev Futures Markets, 1989, 8: 222−239

[8] Jarrow R, Turnbull S. Pricing derivatives on financial securities subject to credit risk. J Finance, 1995, 50: 53−86

[9] Lando D. On Cox processes and credit-risky securities. Rev Derivatives Res, 1998, 2: 99−120

[10] Rieder U, Bäuerle N. Portfolio optimization with unobservable Markov-modulated drift process. J Appl Probab, 2005, 42(2): 362−378

[11] Sircar R, Zariphopoulou T. Utility valuation of credit derivatives: single and two-name cases. Adv Math Finance, 2007: 279−301

[12] Sircar R, Zariphopoulou T. Utility valuation of multi-name credit derivatives and application to CDOs. Quant Finance, 2010, 10(2): 195−208

[13] Sotomayor L R, Cadenillas A. Explicit solutions of consumption-investment problems in financial markets with regime switching. Math Finance, 2009, 19(2): 251−279

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Higher Education Press and Springer-Verlag Berlin Heidelberg