market and crdit risk
The intersection of market and credit risk*1
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Robert A. Jarrow1, , a and Stuart M. Turnbull, , b
a Johnston Graduate School of Management, Cornell University, Ithaca, New York, USA
b Canadian Imperial Banck of Commerce, Global Analytics, Market Risk Management Division, BCE Place, Level 11, 161 Bay Street, Toronto, Ont., Canada M5J 2S8
Available online 15 December 1999.
Abstract
Economic theory tells us that market and credit risks are intrinsically related to each other and not separable. We describe the two main approaches to pricing credit risky instruments: the structural approach and the reduced form approach. It is argued that the standard approaches to credit risk management – CreditMetrics, CreditRisk+ and KMV – are of limited value when applied to portfolios of interest rate sensitive instruments and in measuring market and credit risk.
Empirically returns on high yield bonds have a higher correlation with equity index returns and a lower correlation with Treasury bond index returns than do low yield bonds. Also, macro economic variables appear to influence the aggregate rate of business failures. The CreditMetrics, CreditRisk+ and KMV methodologies cannot reproduce these empirical observations given their constant interest rate assumption. However, we can incorporate these empirical observations into the reduced form of Jarrow and Turnbull (1995b). Drawing the analogy. Risk 5, 63–70 model. Here default probabilities are correlated due to their dependence on common economic factors. Default risk and recovery rate uncertainty may not be the sole determinants of the credit spread. We show how to incorporate a convenience yield as one of the determinants of the credit spread.
For credit risk management, the time horizon is typically one year or longer. This has two important implications, since the standard approximations do not apply over a one year horizon. First, we must use pricing models for risk management. Some practitioners have taken a different approach than academics in the pricing of credit risky bonds. In the event of default, a bond holder is legally entitled to accrued interest plus principal. We discuss the implications of this fact for pricing. Second, it is necessary to keep track of two probability measures: the martingale probability for pricing and the natural probability for value-at-risk. We discuss the benefits of keeping track of these two measures.
Author Keywords: Credit risk modeling; Pricing; Default probabilities
JEL classification codes: G28; G33; G2
Article Outline
1. Introduction
2. Pricing credit risky instruments
2.1. Structural approach
2.2. Reduced form approach
3. Empirical evidence
4. The reduced form model of Jarrow and Turnbull
4.1. Two factor model
4.2. Correlation
4.3. Claims of bond holders
4.3.1. Risky zero-coupon bonds
4.3.2. Credit risky coupon bonds
4.4. Convenience yields on treasury securities
4.5. Change of probability measure
5. Summary
6. For further reading
Acknowledgements
Appendix A. Two factor model
References
Corresponding author. Tel.: +1-416-956-6973; fax: +1-416-594-8528
*1 The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Canadian Imperial Bank of Commerce.
1 Tel.: +1-607-255-4729.
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