Correlation Risk and the Term Structure of Interest Rates

We study the implications of a term structure model that grants a new element of flexibility in the joint modeling of market prices of risk and conditional second moments of risk factors. Different than more traditional models, this approach allows for stochastic correlation among the priced risk factors, for a market price of risk that can be negative in some states of the world (Duffee, 2002), and for a simple equilibrium interpretation. The empirical analysis documents the importance of modeling explicitly the stochastic factor correlation: We find that even a very parsimonious specification provides a consistent explanation of a set of empirical regularities such as (i) the predictability of excess bond returns, (ii) the persistence of conditional volatilities and correlations of yields, (iii) the hump in the term structure of forward rate volatilities and implied volatilities of caps. Moreover, the model can also successfully accommodate more complex features of the bond market such as the Cochrane-Piazzesi (2005) returnforecasting factor, or the unspanned dynamics of interest rate derivatives. JEL classification: D51, E43, G13, G12

[1]  Patrick Cheridito,et al.  A NOTE ON THE DAI–SINGLETON CANONICAL REPRESENTATION OF AFFINE TERM STRUCTURE MODELS * , 2010 .

[2]  Peter Feldhütter.  Can Affine Models Match the Moments in Bond Yields? , 2008 .

[3]  Andrea Buraschi,et al.  Habit Formation and Macroeconomic Models of the Term Structure of Interest Rates , 2007 .

[4]  O. Scaillet,et al.  LINEAR‐QUADRATIC JUMP‐DIFFUSION MODELING , 2007 .

[5]  P. Gagliardini,et al.  Ambiguity Aversion and the Term Structure of Interest Rates , 2007 .

[6]  Luca Benzoni,et al.  Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models , 2007 .

[7]  Challenges in macro-finance modeling, December 2007 , 2007 .

[8]  Yacine Aït-Sahalia,et al.  Saddlepoint Approximations for Continuous-Time Markov Processes ∗ , 2006 .

[9]  Claudio Tebaldi,et al.  Option pricing when correlations are stochastic: an analytical framework , 2006 .

[10]  C. Gourieroux,et al.  Continuous Time Wishart Process for Stochastic Risk , 2006 .

[11]  Christophe Pérignon,et al.  Sources of time variation in the covariance matrix of interest rates , 2006 .

[12]  Glenn D. Rudebusch,et al.  The Bond Yield 'Conundrum' from a Macro-Finance Perspective , 2006 .

[13]  K. Singleton.  Empirical Dynamic Asset Pricing: Model Specification and Econometric Assessment , 2006 .

[14]  Haitao Li,et al.  Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives , 2006 .

[15]  S. Dreyfus,et al.  Lifetime Portfolio Selection under Uncertainty: the Continuous-time Case , 2006 .

[16]  J. Casassus,et al.  Unspanned stochastic volatility and fixed income derivatives pricing , 2005 .

[17]  Bing Han.  Stochastic Volatilities and Correlations of Bond Yields , 2005 .

[18]  M. Yor,et al.  Some Properties of the Wishart Processes and a Matrix Extension of the Hartman-Watson Laws † , 2004 .

[19]  S. B. Thompson.  Identifying Term Structure Volatility from the Libor-Swap Curve , 2004 .

[20]  Robert L. Kimmel.  Modeling the term structure of interest rates: A new approach , 2004 .

[21]  Jefferson Duarte,et al.  Evaluating an Alternative Risk Preference in Affine Term Structure Models , 2004 .

[22]  Patrick Cheridito,et al.  Market price of risk speci-fications for a ne models: theory and evidence , 2004 .

[23]  K. Singleton,et al.  Predictability of Bond Risk Premia and Affine Term Structure Models , 2004 .

[24]  C. S. Jones.  Nonlinear Mean Reversion in the Short-Term Interest Rate , 2003 .

[25]  P. Klaassen,et al.  The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions , 2002, Journal of Financial and Quantitative Analysis.

[26]  Qiang Dai.  Term Structure Dynamics in a Model with Stochastic Internal Habit , 2003 .

[27]  K. Singleton,et al.  PRICING COUPON‐BOND OPTIONS AND SWAPTIONS IN AFFINE TERM STRUCTURE MODELS , 2002 .

[28]  Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rate Derivatives , 2002 .

[29]  D. Duffie,et al.  Affine Processes and Application in Finance , 2002 .

[30]  K. Singleton,et al.  Term Structure Dynamics in Theory and Reality , 2002 .

[31]  H. D. Witte,et al.  Empirical Analysis of the Yield Curve: The Information in the Data Viewed through the Window of Cox, Ingersoll, and Ross , 2002 .

[32]  M. Musiela,et al.  Martingale Methods in Financial Modelling , 2002 .

[33]  Sanjiv Ranjan Das,et al.  Pricing Interest Rate Derivatives: A General Approach , 2002 .

[34]  Joost Driessen,et al.  On the Information in the Interest Rate Term Structure and Option Prices , 2002 .

[35]  D. Bolder,et al.  Affine Term-Structure Models: Theory and Implementation , 2001 .

[36]  R. Goldstein,et al.  Stochastic Correlation and the Relative Pricing of Caps and Swaptions in a Generalized-Affine Framework , 2001 .

[37]  Liuren Wu,et al.  Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates? , 2001 .

[38]  Hao Zhou,et al.  Term Structure of Interest Rates with Regime Shifts , 2001 .

[39]  D. Brigo,et al.  Interest Rate Models , 2001 .

[40]  G. Duffee.  Term premia and interest rate forecasts in affine models , 2000 .

[41]  R. Engle.  Dynamic Conditional Correlation : A Simple Class of Multivariate GARCH Models , 2000 .

[42]  Eduardo S. Schwartz,et al.  The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence , 2000 .

[43]  Robert F. Dittmar,et al.  Quadratic Term Structure Models: Theory and Evidence , 2000 .

[44]  Andrew Ang,et al.  A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables , 2003 .

[45]  D. Duffie,et al.  An Econometric Model of the Term Structure of Interest-Rate Swap Yields , 1997 .

[46]  Ton Vorst,et al.  Pricing American interest rate claims with humped volatility models , 1997 .

[47]  K. Singleton,et al.  Specification Analysis of Affine Term Structure Models , 1997 .

[48]  Timothy G. Conley,et al.  Short-term interest rates as subordinated diffusions , 1997 .

[49]  D. Duffie,et al.  A YIELD-FACTOR MODEL OF INTEREST RATES , 1996 .

[50]  Yacine Ait-Sahalia.  Testing Continuous-Time Models of the Spot Interest Rate , 1995 .

[51]  John Y. Campbell,et al.  Some Lessons from the Yield Curve , 1995 .

[52]  A. Morton,et al.  Implied volatility functions in arbitrage-free term structure models , 1994 .

[53]  Michael R. Gibbons,et al.  A Test of the Cox, Ingersoll, and Ross Model of the Term Structure , 1993 .

[54]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[55]  Eduardo S. Schwartz,et al.  Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model , 1992 .

[56]  Robert B. Litterman,et al.  Common Factors Affecting Bond Returns , 1991 .

[57]  E. Fama,et al.  The Information in Long-Maturity Forward Rates , 1987 .

[58]  Stephen J. Brown,et al.  The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates , 1986 .

[59]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[60]  E. Fama,et al.  The information in the term structure , 1984 .

[61]  J. Magnus,et al.  The Commutation Matrix: Some Properties and Applications , 1979 .

[62]  Charles Loan.  A generalized horner algorithm for computing integrals involving the matrix exponential , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[63]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[64]  F. Black.  The pricing of commodity contracts , 1976 .

[65]  K. Mårtensson,et al.  On the matrix riccati equation , 1971, Inf. Sci..

[66]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .