Summary
This paper considers the estimation in models of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we set up the stochastic dynamics for the discretely compounded market observed rates and propose a dynamic Bayesian estimation algorithm (i.e. a filtering algorithm) for a time-discretised version of the resulting interest rate dynamics. The filter solution is computed via a further spatial discretization (quantization) and the convergence of the latter to its continuous counterpart is discussed in detail. The method is applied to simulated data and is found to give a reasonable estimate of the conditional density function and to be not too demanding computationally.
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References
Andersen, T. and Lund, J. (1997): Estimating continuous-time stochastic volatility models of the short-term interest rate. Journal of Econometrics 77, 343–377.
Bali, T.G. (1999): An empirical comparison of continuous time models of the short-term interest rate. The Journal of Futures Markets 19, 777–797.
Bergstrom, A. (1990): Continuous time econometric modelling,Oxford University Press.
Bhar, R. and Chiarella, C. (1997): Transformation of Heath-Jarrow-Morton models to Markovian systems European Jounal of Finance 3, 1–26.
Brenner, R., Harjes, R. and Kroner, K. (1996): Another look at models of the short-term interest rate. Journal of Financial and Quantitative Analysis 31, 85–107.
Chan, K., Karolyi, A., Longstaff, F. and Sanders, A. (1992): An empirical comparison of alternative models of the short-term interest rate. Journal of Finance 47, 1209–1227.
Chapman, D., Long, J. and Pearson, N. (1999): Using proxies for the short rate: when are three months like an instant? Review of Financial Studies 12 (4), 763–806.
Chiarella, C., Pasquali, S. and Runggaldier, W.J. (2001): On Filtering in Markovian Term Structure Models (an approximation approach), University of Technology, Sydney, Quantitative Finance Research Group, Working paper 65.
Cheyette, 041992): Term structure dynamics and mortgage valuation. The Journal of Fixed Income pp. 28–41.
Cox, J., Ingersoll, J. and Ross, S. (1985): A theory of the term structure of interest rates. Econometrica 53, 385–407.
Episcopos A. (2000): Further evidence on alternative continuous time models of the short-term interest rate. Journal of International Financial Markets, Institutions e4 Money 10, 199–212.
Inui, K. and Kijima, M. (1997): A Markovian framework in multi-factor HeathJarrow-Morton models. Journal of Financial and Quantitative Analysis 33 (3), 423–440.
Koedijk, K., Nissen, F., Schotman, P. and Wolff, C. (1997): The dynamics of the short-term interest rate volatility reconsidered. European Finance Review 1, 105–130.
Longstaff, F. and Schwartz, E. (1992): Interest rate volatility and the term structure of interest rates. Journal of Finance 47, 1259–1282.
Nowman, K. (1997): Gaussian estimation of single-factor continuous time models of the term structure of interest rates. Journal of Finance 52, 1695–1706.
Nowman, K. (1998): Continuous-time short term interest rate models. Applied Financial Economics 8, 401–407.
Ritchken, P. and Sankarasubramanian, L. (1995): Volatility structures of forward rates and the dynamics of the term structure. Mathematical Finance 5 (1), 55–72.
Sandmann, K, and Sondermann, D. (1997): A note on the stability of lognormal interest rate models and the pricing of Eurodollar futures. Mathematical Finance 7 (2), 119–125.
Vasicek, O. (1997): An equilibrium characterization of the term structure. Journal of Financial Economics 5, 177–188.
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Bhar, R., Chiarella, C., Runggaldier, W.J. (2002). Estimation in Models of the Instantaneous Short Term Interest Rate by Use of a Dynamic Bayesian Algorithm. In: Sandmann, K., Schönbucher, P.J. (eds) Advances in Finance and Stochastics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04790-3_10
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DOI: https://doi.org/10.1007/978-3-662-04790-3_10
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