CONTINUOUS-TIME GARCH (COGARCH) MODELING OF TURKISH INTEREST RATES

We proposed a continuous time GARCH known as COGARCH(p,q) model for modeling the volatility of Turkish interest rates. COGARCH (p,q) models have been statistically proven successful in capturing the heavy-tail behaviour of the interest rates . We demonstrate the capabilities of COGARCH(p,q) model by using Turkish short rate. The Turkish Republic Central Bank’s benchmark bond prices are used to calculate the short-term interest rates between the period of 15.07.2006 and 15.07.2008. COGARCH(1,1) model is chosen as best candidate model in modeling the Turkish short rate for the sample period

Keywords:

interest rate models, continuous-time models, stochastic volatility, Lévy process GARCH , COGARCH,

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Ait-Sahalia, Yacine (1996), “Testing Continuous Time Models of the Spot
Interest Rates”, Review of Financial Studies, Vol. 9, pp.385-426. Ait-Sahalia, Yacine (1999), “Transition Densities for Interest Rate and Other
Nonlinear Diffusions”, Journal of Finance, Vol. 54, pp.1361-1395.
Barndorff-Nielsen, Ole E., Neil Shephard (2001), “Modelling by Lévy Processes for Financial Economics”, (in: Ole Barndorff-Nielsen, T. Mikosch, S. Resnicky- Eds, Lévy Processes: Theory and Application), Birkhauser:Boston, pp.283-318.
Barndorff-Nielsen, Ole E., Neil Shepherd (2001), “Non-Gaussian Ornstein
Uhlenbeck Based Models and some of their Use in Financial Economics (with discussions)”, Journal of Royal Statistics Society Series B, Vol. 63, pp.167-241
Brockwell, Peter, Erdenebaatar Chadraa and Alexander Lindner (2006),
“Continuous-time GARCH Processes”, The Annals of Applied Probability, Vol. , No. 2, pp.790-826
Chan, K.C., Andrew G. Karolyi, Francis A. Longstaff, Anthony B. Sanders (1992), “An Empirical Comparison of Alternative Models of the Short-Term
Interest Rate”, Journal of Finance, Vol. 47, pp.1209-1227.
Chapman, David, Neil Pearson (2000), ” Is the Short Rate Drift Actually
Nonlinear?”, Journal of Finance, Vol. 55, pp. 355-388. Gray, Stephen F. (1996), “Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process”, Journal of Financial Economics”, Vol. 42, p. 27
Hong, Yongmiao, Hai Li, F. Zhao (2004), “Out of Sample Performance of
Discrete-Time Spot Interest Rate Models”, Journal of Business and Economic Statistics, Vol. 22, pp.457-474. Klüppelberg, Claudia, Alexander Lindner and Ross Maller (2004), “A Continuous
Time GARCH Process Driven by a Lévy Process:Stationary and Second Order Behaviour”, Journal of Applied Probability, Vol. 41, pp.601-622
Klüppelberg, Claudia, Alexander Lindner and Ross Maller (2006), “Continuous
Time Volatility Modelling: COGARCH versus Ornstein-Uhlenbeck Models”, (in: Yuri Kabanov, Robert Lipster and Jordan Stoyanov-Eds, From Stochastic Calculus to Mathematical Finance,), Springer:Berlin, pp. 393-419 Nelson, Daniel B. (1990),
Approximations”, Journal of Econometrics, Vol. 45, pp.7-38
“ARCH Models as Diffusion Pritsker, Matt (1998), “Nonparametric Density Estimation and Tests of
Continuous Time Interest Rate Models”, Review of Financial Studies, Vol. 11, pp.449-487. Stanton, Richard (1997), “A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk”, Journal of Finance, Vol. 52, pp.1973