An online estimation scheme for a Hull–White model with HMM-driven parameters

This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial dataset of 30-day Canadian Treasury bill yields. We also provide standard errors for the model parameter estimates. Our analysis shows that within the dataset and period studied, a model with two regimes is sufficient to describe the interest rate dynamics on the basis of very small prediction errors and the Akaike information criterion.

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

[2]  D. Brigo,et al.  Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit , 2001 .

[3]  E. Otranto,et al.  A NONPARAMETRIC BAYESIAN APPROACH TO DETECT THE NUMBER OF REGIMES IN MARKOV SWITCHING MODELS , 2002 .

[4]  S. Chib,et al.  Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts , 1993 .

[5]  Robert J. Elliott,et al.  Financial Signal Processing: A Self Calibrating Model , 2000 .

[6]  Martin D. D. Evans.  Real Risk, Inflation Risk, and the Term Structure , 2002 .

[7]  Bruce E. Hansen,et al.  Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP , 1996 .

[8]  Mary R. Hardy,et al.  A Regime-Switching Model of Long-Term Stock Returns , 2001 .

[9]  Alan G. White,et al.  Pricing Interest-Rate-Derivative Securities , 1990 .

[10]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[11]  René Garcia,et al.  Série Scientifique Scientific Series an Analysis of the Real Interest Rate under Regime Shifts , 2022 .

[12]  Robert J. Elliott,et al.  New finite-dimensional filters for parameter estimation of discrete-time linear Gaussian models , 1999, IEEE Trans. Autom. Control..

[13]  James D. Hamilton.  Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates , 1988 .

[14]  Martin Sola,et al.  On Model Selection and Markov Switching: An Empirical Examination of Term Structure Models with Regime Shifts , 2003 .

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

[16]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[17]  Paul H. Garthwaite,et al.  Statistical Inference , 2002 .

[18]  Fred L. Collopy,et al.  Error Measures for Generalizing About Forecasting Methods: Empirical Comparisons , 1992 .

[19]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[20]  E. Nicolato,et al.  Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type , 2003 .

[21]  Zacharias Psaradakis,et al.  ON THE DETERMINATION OF THE NUMBER OF REGIMES IN MARKOV‐SWITCHING AUTOREGRESSIVE MODELS , 2002 .

[22]  Stephen Gray.  Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process , 1996 .

[23]  Robert J. Elliott,et al.  Exact adaptive filters for Markov chains observed in Gaussian noise , 1994, Autom..

[24]  Robert J. Elliott,et al.  An interest rate model with a Markovian mean reverting level , 2002 .

[25]  Robert J. Elliott,et al.  Filtering and Parameter Estimation for a Mean Reverting Interest Rate Model , 1999 .

[26]  Michael R. Gibbons,et al.  A comparison of inflation forecasts , 1984 .

[27]  Orestes Soldatos.  Modelling electricity price risk for the valuation of power contingent claims : the case of Nord Pool , 2007 .

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

[29]  Yihong Xia,et al.  Dynamic Asset Allocation Under Inflation , 2000 .

[30]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

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

[32]  F. Black,et al.  Bond and Option Pricing when Short Rates are Lognormal , 1991 .

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

[34]  Antoon Pelsser.  Efficient Methods for Valuing Interest Rate Derivatives , 2010 .

[35]  Eduardo S. Schwartz,et al.  Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange , 2000 .

[36]  Daniel R. Smith.  Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates , 2002 .

[37]  Camilla Landén,et al.  Bond pricing in a hidden Markov model of the short rate , 2000, Finance Stochastics.

[38]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[39]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[40]  Chang‐Jin Kim,et al.  Dynamic linear models with Markov-switching , 1994 .

[41]  Mário A. T. Figueiredo,et al.  A sequential pruning strategy for the selection of the number of states in hidden Markov models , 2003, Pattern Recognit. Lett..

[42]  James D. Hamilton.  Analysis of time series subject to changes in regime , 1990 .