A contagion model with Markov regime-switching intensities

Abstract

We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ‘change of measure’ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps (CDSs) on two underlyings.

Keywords

Credit default swap (CDS) / contagion model / regime-switching / change of measure

References

[1] Ang A, Bekaert G. Regime switches in interest rates. J Bus Econ Stat, 2002, 20: 163-182

[2] Ang A, Bekaert G. Short rate nonlinearities and regime switches. J Econ Dyn Control, 2002, 26: 1243-1274

[3] Bao Q F, Chen S, Li S D. Unilateral CVA for CDS in contagion model: with Volatilities and correlation of spread and interest. Econ Model, 2012, 29: 471-477

[4] Buffington J, Elliott R J. American options with regime switching. Int J Theor Appl Financ, 2002, 5: 497-514

[5] Collin-Dufresne P, Goldstein R, Hugonnier J. A general formula for valuing defaultable securities. Econometrica, 2004, 72: 1377-1407

[6] Elliott R J. New finite dimensional filters and smoothers for noisily observed Markov chains. IEEE Trans Inf Theory, 1993, 39: 265-271

[7] Elliott R J, Aggoun L, Moore J B. Hidden Markov Models: Estimation and Control. Berlin-Heidelberg-New York: Springer-Verlag, 1994

[8] Elliott R J, Leunglung C, Siu T K. Option pricing and Esscher transform under regime switching. Ann Financ, 2005, 1: 423-432

[9] Giesecke K, Longstaff F A, Schaefer S, Strebulaev I. Corporate bond default risk: A 150-year perspective. J Financ Econ, 2011, 102: 233-250

[10] Guo X. Information and option pricings. Quant Financ, 2001, 1: 38-44

[11] Hackbarth D, Miao J J, Morellec E. Capital structure, credit risk, and macroeconomic conditions. J Financ Econ, 2006, 82: 519-550

[12] Hardy M R. A regime-switching model of long-term stock returns. N Am Actuar J, 2001, 5: 41-53

[13] Hardy M R, Freeland R K, Till M C. Validation of long-term equity return models for equity-linked guarantees. N Am Actuar J, 2006, 10: 28-47

[14] Jarrow R, Yu F. Counterparty risk and the pricing of defaultable securities. J Finan, 2001, 56: 1765-1799

[15] Kusuoka S. A remark on default risk models. Adv Math Econom, 1999, 1: 69-82

[16] Leung S Y, Kwok Y K. Credit default swap valuation with counterparty risk. Kyoto Econ Rev, 2005, 74: 25-45

[17] Ma J, Yun Y Y. Correlated intensity, counter party risks, and dependent mortalities. Insur Math Econ, 2010, 47: 337-351

[18] Naik V. Option valuation and hedging strategies with jumps in the volatility of asset returns. J Finan, 1993, 48: 1969-1984

[19] Shaked M, Shanthikumar J G. The multivariate hazard construction. Stoch Proc Appl, 1987, 24: 241-258

[20] Siu T K. Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows. Appl Math Comput, 2010, 216: 3184-3190

[21] Siu T K, Erlwein C, Mamon R S. The pricing of credit default swaps under a Markovmodulated Merton’s structural model. N Am Actuar J, 2008, 12: 19-46

[22] Yu F. Correlated defaults in intensity-based models. Math Financ, 2007, 17: 155-173

[23] Zhou C S. The term structure of credit spreads with jump risk. J Bank Finan, 2001, 25: 2015-2040

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg