Frontiers of Mathematics in China >
A contagion model with Markov regime-switching intensities
Received date: 19 Dec 2012
Accepted date: 08 May 2013
Published date: 01 Feb 2014
Copyright
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.
Yinghui DONG , Guojing WANG . A contagion model with Markov regime-switching intensities[J]. Frontiers of Mathematics in China, 2014 , 9(1) : 45 -62 . DOI: 10.1007/s11464-013-0311-0
| 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
|
/
| 〈 |
|
〉 |