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A Markov Model for the Term Structure of Credit Risk Spreads
 Review of Financial Studies
, 1997
"... This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data ..."
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Cited by 237 (12 self)
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This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data. This model is useful for pricing and hedging corporate debt with imbedded options, for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging (foreign) government bonds subject to default risk (e.g., municipal bonds), for pricing and hedging credit derivatives, and for risk management. This article presents a simple model for valuing risky debt that explicitly incorporates a firm's credit rating as an indicator of the likelihood of default. As such, this article presents an arbitragefree model for the term structure of credit risk spreads and their evolution through time. This model will prove useful for the pricing and hedging of corporate debt with We would like to thank John Tierney of Lehman Brothers for providing the bond index price data, and Tal Schwartz for computational assistance. We would also like to acknowledge helpful comments received from an anonymous referee. Send all correspondence to Robert A. Jarrow, Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853. The Review of Financial Studies Summer 1997 Vol. 10, No. 2, pp. 481523 1997 The Review of Financial Studies 08939454/97/$1.50 imbedded options, for the pricing and hedging of OTC derivatives with counterparty risk, for the pricing and hedging of (foreign) government bonds subject to default risk (e.g., municipal bonds), and for the pricing and hedging of credit derivatives (e.g. credit sensitive notes and spread adjusted notes). This model can also...
The Surprise Element: Jumps in Interest Rates
 Journal of Econometrics
, 2002
"... Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short ra ..."
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Cited by 61 (2 self)
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Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Estimators are used based on analytical derivations of the characteristic functions and moments of jumpdiffusion stochastic processes for a range of jump distributions, and are extended to discretetime models. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing models would be wellenhanced by jump and ARCHtype processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the nonlinearity of interest rate drifts, so prevalent in purediffusion models. Dayofweek effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.
00 The Importance of ForwardRate Volatility Structures in Pricing Interest RateSensitive
"... Studies of the sensitivity of the prices of interest rate claims to alternative specifications of the volatility of spot and forward interest rates have drawn different conclusions. One possible explanation for this is that it is difficult to adjust the volatility structure without disturbing the in ..."
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Studies of the sensitivity of the prices of interest rate claims to alternative specifications of the volatility of spot and forward interest rates have drawn different conclusions. One possible explanation for this is that it is difficult to adjust the volatility structure without disturbing the initial set of bond prices. In this chapter we use a term structureconstrained model that lets us change the volatility structure for spot and forward rates without altering either their initial values or the set of initial bond prices. Consequently, any differences in prices of interest ratesensitive claims can be attributed solely to alternative assumptions on the structure of spot and forwardrate volatilities rather than to variations in the initial conditions. We show that even when the initial conditions are common, option prices on interest rates and on bonds are sensitive to the specification of the volatility structure of spot rates. Further, we find that using a simple generalised Vasicek model to price claims can lead to significant mispricings if interest rate volatilities do indeed depend on their levels. In the last decade, overthecounter trading in interest rate derivatives has expanded dramatically to a multitrillion dollar market of notional principal. The majority of claims in this market are now quoted and priced relative to an existing term structure. As a result, recent research has attempted to represent the comovements of all bond prices so that information from the existing term structure is more fully reflected in model values. A key ingredient of all models of the term structure is the choice of a volatility structure for spot and forward interest rates. Our goal is to investigate the importance of *This paper was first published in the Journal of Derivatives, Fall (1995), pp. 25–41, and is reprinted with the permission of Institutional Investor Journals. The authors thank the participants of the seminar series
PaperChrisandLes 2Pricing Interest Rate Exotics in MultiFactor Gaussian Interest Rate Models
, 1998
"... For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or curvature of the yield curve and hence are mor ..."
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For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or curvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction of short rate trees becomes computationally intractable as we increase the number of factors and in particular as we move to nonMarkovian models. In this paper we describe a general framework for pricing a wide range of interest rate exotic options under a very general family of multifactor Gaussian interest rate models. Our framework is based on a computationally efficient implementation of Monte Carlo integration utilising analytical approximations as control variates. These techniques extend the analysis of Clewlow, Pang, and Strickland [1997] for pricing interest rate caps and swaptions.