Pricing Callable Bonds Based on Monte Carlo Simulation Techniques
Affiliation(s)
aculty of Science and Technology, University of Macau, Macao, China. Faculty of Business Administration, University of Macau, Macao, China.
aculty of Science and Technology, University of Macau, Macao, China. Faculty of Business Administration, University of Macau, Macao, China.
ABSTRACT
In this paper, a Monte Carlo method, which is based on some new simulation techniques proposed recently, is presented to numerically price the callable bond with several call dates and notice under the Cox-Ingersoll-Ross (CIR) interest rate model. The corresponding algorithms are also presented to practical callable bond pricing. The numerical experiments show that this method works very well for callable bond under the CIR interest rate model.
In this paper, a Monte Carlo method, which is based on some new simulation techniques proposed recently, is presented to numerically price the callable bond with several call dates and notice under the Cox-Ingersoll-Ross (CIR) interest rate model. The corresponding algorithms are also presented to practical callable bond pricing. The numerical experiments show that this method works very well for callable bond under the CIR interest rate model.
Cite this paper
D. Ding, Q. Fu and J. So, "Pricing Callable Bonds Based on Monte Carlo Simulation Techniques," Technology and Investment, Vol. 3 No. 2, 2012, pp. 121-125. doi: 10.4236/ti.2012.32015.
D. Ding, Q. Fu and J. So, "Pricing Callable Bonds Based on Monte Carlo Simulation Techniques," Technology and Investment, Vol. 3 No. 2, 2012, pp. 121-125. doi: 10.4236/ti.2012.32015.
References
[1] Z. L. Zheng and C. F. Kang, “Pricing and Hedging of Chinese Interest Rate Derivatives,” Peking University Press, Beijing, 2006. [2] H.-J. Buttler, “Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy,” The Economic Journal, Vol. 105, No. 429, 1995, pp. 374-384. doi:10.2307/2235497 [3] H.-J. Buttler and J. Waldvogel, “Pricing Callable Bonds by Means of Green’s Function,” Mathematical Finance, Vol. 6, No. 1, 1996, pp. 53-88. [4] Y. D’Halluin, P. A. Forsyth, K. R. Vetzal and G. Labahn, “A Numerical PDE Approach for Pricing Callable Bonds,” Applied Mathematical Finance, Vol. 8, No. 1, 2001, pp. 49-77. doi:10.1080/13504860110046885 [5] J. Farto and C. V’azquez, “Numerical Techniques for Pricing Callable Bonds with Notice,” Applied Mathematics and Computation, Vol. 161, No. 3, 2005, pp. 9891013. doi:10.1016/j.amc.2003.12.079 [6] H. Ben-Ameur, M. Breton, L. Karoui and P. L’Ecuyer, “A Dynamic Programming Approach for Pricing Options Embedded in Bonds,” Journal of Economic Dynamics and Control, Vol. 31, No. 7, 2007, pp. 2212-2233. doi:10.1016/j.jedc.2006.06.007 [7] G. N. Milstein, E. Platen and H. Schurz, “Balanced Implicit Methods for Stiff Stochastic Systems,” SIAM Journal on Numerical Analysis, Vol. 35, No. 3, 1998, pp. 1010-1019. doi:10.1137/S0036142994273525 [8] C. Kahl and H. Schurz, “Balanced Milstein Methods for Ordinary SDEs,” Monte Carlo Methods and Applications, Vol. 12, No. 2, 2006, pp. 143-170. doi:10.1515/156939606777488842 [9] P. Glasserman, “Monte Carlo Methods in Financial Engineering,” 2nd Edition, Springer, New York, 2004. [10] D. Ding and C. I. Chao, “An Efficient Numerical Scheme for Simulation of Mean-Reverting Square-Root Diffusions,” Journal of Numerical Mathematics and Stochastics, Vol. 1, No. 1, 2009, pp. 45-55. [11] O. Vasicek, “An Equilibrium Characteriaztion of the Term Structure,” Journal of Financial Economices, Vol. 5, No. 2, 1977, pp. 177-188. doi:10.1016/0304-405X(77)90016-2 [12] J. C. Cox, J. E. Ingersoll and S. A. Ross, “A Theory of the Term-Structure of Interest Rates,” Econometrica, Vol. 53, No. 2, 1985, pp. 385-408. doi:10.2307/1911242
[1] Z. L. Zheng and C. F. Kang, “Pricing and Hedging of Chinese Interest Rate Derivatives,” Peking University Press, Beijing, 2006. [2] H.-J. Buttler, “Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy,” The Economic Journal, Vol. 105, No. 429, 1995, pp. 374-384. doi:10.2307/2235497 [3] H.-J. Buttler and J. Waldvogel, “Pricing Callable Bonds by Means of Green’s Function,” Mathematical Finance, Vol. 6, No. 1, 1996, pp. 53-88. [4] Y. D’Halluin, P. A. Forsyth, K. R. Vetzal and G. Labahn, “A Numerical PDE Approach for Pricing Callable Bonds,” Applied Mathematical Finance, Vol. 8, No. 1, 2001, pp. 49-77. doi:10.1080/13504860110046885 [5] J. Farto and C. V’azquez, “Numerical Techniques for Pricing Callable Bonds with Notice,” Applied Mathematics and Computation, Vol. 161, No. 3, 2005, pp. 9891013. doi:10.1016/j.amc.2003.12.079 [6] H. Ben-Ameur, M. Breton, L. Karoui and P. L’Ecuyer, “A Dynamic Programming Approach for Pricing Options Embedded in Bonds,” Journal of Economic Dynamics and Control, Vol. 31, No. 7, 2007, pp. 2212-2233. doi:10.1016/j.jedc.2006.06.007 [7] G. N. Milstein, E. Platen and H. Schurz, “Balanced Implicit Methods for Stiff Stochastic Systems,” SIAM Journal on Numerical Analysis, Vol. 35, No. 3, 1998, pp. 1010-1019. doi:10.1137/S0036142994273525 [8] C. Kahl and H. Schurz, “Balanced Milstein Methods for Ordinary SDEs,” Monte Carlo Methods and Applications, Vol. 12, No. 2, 2006, pp. 143-170. doi:10.1515/156939606777488842 [9] P. Glasserman, “Monte Carlo Methods in Financial Engineering,” 2nd Edition, Springer, New York, 2004. [10] D. Ding and C. I. Chao, “An Efficient Numerical Scheme for Simulation of Mean-Reverting Square-Root Diffusions,” Journal of Numerical Mathematics and Stochastics, Vol. 1, No. 1, 2009, pp. 45-55. [11] O. Vasicek, “An Equilibrium Characteriaztion of the Term Structure,” Journal of Financial Economices, Vol. 5, No. 2, 1977, pp. 177-188. doi:10.1016/0304-405X(77)90016-2 [12] J. C. Cox, J. E. Ingersoll and S. A. Ross, “A Theory of the Term-Structure of Interest Rates,” Econometrica, Vol. 53, No. 2, 1985, pp. 385-408. doi:10.2307/1911242