Abstract
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
References
- 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
Abstract
References
- 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
Details
| Other ID | JA98HC29FA |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | June 1, 2011 |
| Published in Issue | Year 2011 Volume: 3 Issue: 1 |