A Hybrid Particle Swarm Optimization-Nelder- Mead Algorithm (PSO-NM) for Nelson-Siegel- Svensson Calibration
Today, insurers may use the yield curve as an indicator
evaluation of the profit or the performance of their portfolios;
therefore, they modeled it by one class of model that has the ability
to fit and forecast the future term structure of interest rates. This class
of model is the Nelson-Siegel-Svensson model. Unfortunately, many
authors have reported a lot of difficulties when they want to calibrate
the model because the optimization problem is not convex and has
multiple local optima. In this context, we implement a hybrid Particle
Swarm optimization and Nelder Mead algorithm in order to minimize
by least squares method, the difference between the zero-coupon
curve and the NSS curve.
[1] Bliss R. and Fama E. The Information in Long Maturity Forward Rates
American Economic Review,Vol. 77 , 680.692.1987.
[2] Bonnin F., Planchet F. and Juillard M Application of stochastic techniques
for the prospective analysis of the fiscal impact of interest rate
risk-Example on financial expenses of a complex bond debt French
Bulletin of Actuarial,vol. 11, no 21,2011.
[3] Diebold F.X. and LI C Forecasting the term structure of government bond
yields. Journal of Econometrics,vol. 130, no 2, 337.364,2006.
[4] Diebold F. X.and Rudebusch G. D.and Borag[caron]an Aruoba S The
macroeconomy and the yield curve: A dynamic latent factor approach.
Journal of Econometrics Vol.131,309-338, 2006.
[5] Gilli. M. and Grosse.S and Schumann. E. Calibrating the
Nelson-Siegel-Svensson Model. Computational Optimization Methods in
Statistics, Econometrics and Finance, 2010.
[6] Gimeno. R. and Nave, Juan Migue. Genetic Algorithm Estimation of
Interest Rate Term Structure.. Banco de Espana Research Paper No.
WP-0634,2010.
[7] Hautsch N. E and Ou Y. Analyzing interest rate risk: Stochastic volatility
in the term structure of government bond yields. Journal of Banking and
Finance Vol.36, 2988-3007,2012.
[8] Kao Y.T., E. Zahara, and I. W. Kao A hybridized approach to data
clustering. Expert Systems with Applications, vol. 34, no. 3, pp.
17541762, 2008.
[9] Kennedy, J. and Eberhart, R. Particle Swarm Optimization In Proceedings
of IEEE International Conference on Neural Network, volume IV, 1995.
[10] Koduru P., S. Das, S. M. Welch, J. L. Roe. Fuzzy Dominance
Based Multi-objective GA-Simplex Hybrid Algorithms Applied to Gene
Network Models Lecture Notes in Computer Science: Proceedings of the
Genetic and Evolutionary Computing Conference, Seattle, Washington,
(Eds. Kalyanmoy Deb et al.), Springer-Verlag, Vol 3102, pp. 356-367,
2004.
[11] Liu.A, and Yang M.T A New Hybrid Nelder-Mead Particle Swarm
Optimization for Coordination Optimization of Directional Overcurrent
Relays. Hindawi Publishing Corporation Mathematical Problems in
Engineering Volume 2012, Article ID 456047, 18 pages,2012.
[12] McCulloch J.H The Tax-Adjusted Yield Curve The Journal of Finance
Vol.30, 811-830,1975.
[13] Nelson C. and Siegel A. F Parsimonious Modeling of Yield Curves
Journal of Business, Vol. 60, 473.489,1987.
[14] Svensson L. E. O Estimating and Interpreting Forward Interest Rates:
Sweden 1992-1994 IMFWorking Paper , 1.49,1994.
[15] Vasicek O. A. and Fong H. G. Term Structure Modeling Using
Exponential Splines. Journal of Finance,Vol. 73,339.348,1982.
[1] Bliss R. and Fama E. The Information in Long Maturity Forward Rates
American Economic Review,Vol. 77 , 680.692.1987.
[2] Bonnin F., Planchet F. and Juillard M Application of stochastic techniques
for the prospective analysis of the fiscal impact of interest rate
risk-Example on financial expenses of a complex bond debt French
Bulletin of Actuarial,vol. 11, no 21,2011.
[3] Diebold F.X. and LI C Forecasting the term structure of government bond
yields. Journal of Econometrics,vol. 130, no 2, 337.364,2006.
[4] Diebold F. X.and Rudebusch G. D.and Borag[caron]an Aruoba S The
macroeconomy and the yield curve: A dynamic latent factor approach.
Journal of Econometrics Vol.131,309-338, 2006.
[5] Gilli. M. and Grosse.S and Schumann. E. Calibrating the
Nelson-Siegel-Svensson Model. Computational Optimization Methods in
Statistics, Econometrics and Finance, 2010.
[6] Gimeno. R. and Nave, Juan Migue. Genetic Algorithm Estimation of
Interest Rate Term Structure.. Banco de Espana Research Paper No.
WP-0634,2010.
[7] Hautsch N. E and Ou Y. Analyzing interest rate risk: Stochastic volatility
in the term structure of government bond yields. Journal of Banking and
Finance Vol.36, 2988-3007,2012.
[8] Kao Y.T., E. Zahara, and I. W. Kao A hybridized approach to data
clustering. Expert Systems with Applications, vol. 34, no. 3, pp.
17541762, 2008.
[9] Kennedy, J. and Eberhart, R. Particle Swarm Optimization In Proceedings
of IEEE International Conference on Neural Network, volume IV, 1995.
[10] Koduru P., S. Das, S. M. Welch, J. L. Roe. Fuzzy Dominance
Based Multi-objective GA-Simplex Hybrid Algorithms Applied to Gene
Network Models Lecture Notes in Computer Science: Proceedings of the
Genetic and Evolutionary Computing Conference, Seattle, Washington,
(Eds. Kalyanmoy Deb et al.), Springer-Verlag, Vol 3102, pp. 356-367,
2004.
[11] Liu.A, and Yang M.T A New Hybrid Nelder-Mead Particle Swarm
Optimization for Coordination Optimization of Directional Overcurrent
Relays. Hindawi Publishing Corporation Mathematical Problems in
Engineering Volume 2012, Article ID 456047, 18 pages,2012.
[12] McCulloch J.H The Tax-Adjusted Yield Curve The Journal of Finance
Vol.30, 811-830,1975.
[13] Nelson C. and Siegel A. F Parsimonious Modeling of Yield Curves
Journal of Business, Vol. 60, 473.489,1987.
[14] Svensson L. E. O Estimating and Interpreting Forward Interest Rates:
Sweden 1992-1994 IMFWorking Paper , 1.49,1994.
[15] Vasicek O. A. and Fong H. G. Term Structure Modeling Using
Exponential Splines. Journal of Finance,Vol. 73,339.348,1982.
@article{"International Journal of Business, Human and Social Sciences:73029", author = "Sofia Ayouche and Rachid Ellaia and Rajae Aboulaich", title = "A Hybrid Particle Swarm Optimization-Nelder- Mead Algorithm (PSO-NM) for Nelson-Siegel- Svensson Calibration", abstract = "Today, insurers may use the yield curve as an indicator
evaluation of the profit or the performance of their portfolios;
therefore, they modeled it by one class of model that has the ability
to fit and forecast the future term structure of interest rates. This class
of model is the Nelson-Siegel-Svensson model. Unfortunately, many
authors have reported a lot of difficulties when they want to calibrate
the model because the optimization problem is not convex and has
multiple local optima. In this context, we implement a hybrid Particle
Swarm optimization and Nelder Mead algorithm in order to minimize
by least squares method, the difference between the zero-coupon
curve and the NSS curve.", keywords = "Optimization, zero-coupon curve, Nelson-Siegel-
Svensson, Particle Swarm Optimization, Nelder-Mead Algorithm.", volume = "10", number = "4", pages = "1365-5", }
