Pricing Risky Securities in Hidden Markov-Modulated Poisson Processes

10.6293/AQAFA.2009.07.05

Yu-Chuan Huang；Shih-Kuei Lin；Chin-Wen Wu

Markov-modulated poisson processes ； Credit risk ； Credit derivatives

Advances in Quantitative Analysis of Finance and Accounting

7期（2009 / 06 / 01）

95 - 119

英文

This paper makes two contributions to the literature. The first contribution is to investigate how to incorporate Markov-modulated Poisson processes with the reduced-form model to price risky securities. For its application, from the investor's point of view, since they do not have complete information about the operating condition of the reference entities, this pricing approach allows credit risk modeling when there is dependence between the default characteristics of reference entities and the unobservable status of operating condition. The higher transition rate from a good operating condition with lower default intensity to a bad one with higher default intensity is associated with higher default probability, and vice versa. Using the arbitrage-free valuation techniques, the second contribution of this article is to provide the closed-form pricing formulas for a variety of risky securities such as corporate debts, credit default swaps, credit linked notes, options on risky debts, risky convertible bonds, and the products with default correlations.

1. Abate, J.,Whitt, W.(1992).Numerical inversion of probability generating functions.Operations Research Letters,12,245-251.
2. Anderson, L.,Sidenius, J.(2004).Extensions to the gaussian copula: Random recovery and random factor loadings.Journal of Credit Risk,1(1),29-70.
3. Artzner, P.,Delbaen, F.(1995).Default risk insurance and incomplete markets.Mathematical Finance,5(3),187-195.
4. Black, F.,Cox, J. C.(1976).Valuing corporate securities: Some effects of bond indenture provision.The Journal of Finance,31(2),351-367.
5. Chance, D. M.(1990).Default risk and the duration of zero-coupon bonds.The Journal of Finance,45(1),265-274.
6. Duffie, D.,Singleton, K. J.(1999).Modeling term structures of defaultable bonds.The Review of Financial Studies,12(4),687-720.
7. Harrison, J. M.,Pliska, S. R.(1981).Martingales and stochastic integrals in the theory of continuous trading.Stochastic Processes and Their Applications,11(3),215-260.
8. Heath, D.,Jarrow, R.,Morton, A.(1992).Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation.Econometrica,60(1),77-105.
9. Ho, T. S. Y.,Singer, R. F.(1982).Bond indenture provisions and the risk of corporate debt.Journal of Financial Economics,10(4),375-406.
10. Hui, C. H.,Lo, C. F.,Lee, H. C.(2003).Pricing vulnerable black-scholes options with dynamic default barriers.Journal of Derivatives,10(4),62-69.
11. Hull, J. C.(2000).Options, futures, and other derivatives.Englewood Liffs:Prentice Hall.
12. Hull, J. C.,White, A.(1995).The impact of default risk on the prices of options and other derivative securities.Journal of Banking and Finance,19(2),299-322.
13. Hull, J. C.,White, A.(2004).Valuation of a CDO and an N-th to default CDS without monte carlo simulation.Journal of Derivatives,12(2),8-23.
14. Jarrow, R. A.,Lando, D.,Turnbull, S. M.(1997).A markov model for the term structure of credit risk spreads.The Review of Financial Studies,10(2),481-523.
15. Jarrow, R. A.,Madan, D. B.(1995).Option pricing using the term structure of interest rates to hedge systematic discontinuities in asset returns.Mathematical Finance,5(4),311-336.
16. Jarrow, R. A.,Turnbull, S. M.(1997).Pricing derivatives on financial securities subject to credit risk.The Journal of Finance,50(1),53-85.
17. Jarrow, R. A.,Turnbull, S. M.(2000).The intersection of market and credit risk.Journal of Banking and Finance,24(1, 2),271-299.
18. Jarrow, R. A.,Yu, F.(2001).Counterparty risk and the pricing of defaultable securities.The Journal of Finance,56(5),1765-1799.
19. Johnson, H.,Stulz, R.(1987).The pricing of options with default risk.The Journal of Finance,42(2),267-280.
20. Kim, I. J.,Ramaswamy, K.,Sundaresan, S.(1993).Does default risk in coupons affect the valuation of corporate bonds?.Financial Management,22(3),117-131.
21. Klein, P.(1996).Pricing black-scholes options with correlated credit risk.Journal of Banking and Finance,20(7),1211-1229.
22. Klein, P.,Inglis, M.(1999).Valuation of European options subject to financial distress and interest rate risk.Journal of Derivatives,6(3),44-56.
23. Klein, P.,Inglis, M.(2001).Pricing vulnerable European options when the option's payoff can increase the risk of financial distress.Journal of Banking and Finance,25(5),993-1012.
24. Lando, D.(1998).On cox processes and credit risky securities.Review of Derivatives Research,2(2-3),99-120.
25. Lando, D.(1994).Cornell University.
26. Last, G.,Brandt, A.(1995).Marked point processes on the real line: The dynamic approach.New York:Springer-Verlag.
27. Laurent, J. P.,Gregory, J.(2005).Basket default swaps, CDOs and factor copula.The Journal of Risk,7(4),1-21.
28. Li, D. X.(2000).On default correlation: A copula approach.The Journal of Fixed Income,9(4),43-54.
29. Merton, R. C.(1976).Option pricing when underlying stock returns are discontinuous.Journal of Financial Economics,3(1-2),125-144.
30. Merton, R. C.(1974).On the pricing of corporate debt: The risk structure of interest rates.The Journal of Finance,29(2),449-470.
31. Nelsen, R. B.(1998).An introduction to copulas.New York:Springer.
32. Samuelson, P. A.(1973).Mathematics of speculative price.SIAM Review,15(1),1-42.