Implied Bond and Derivative Prices Based on Non-Linear Stochastic Interest Rate Models


In this paper we expand the Box Method of Sorwar et al. (2007) to value both default free bonds and interest rate contingent claims based on one factor non-linear interest rate models. Further we propose a one-factor non-linear interest rate model that incorporates features suggested by recent research. An example shows the extended Box Method works well in practice.

Share and Cite:

Sorwar, G. and Mozumder, S. (2010) Implied Bond and Derivative Prices Based on Non-Linear Stochastic Interest Rate Models. Applied Mathematics, 1, 37-43. doi: 10.4236/am.2010.11006.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] K. C. Chan, G. A. Karolyi, F. A. Longstaff and A. B. Sanders, “An Empirical Comparison of Alternative Mod-els of the Short-Term Interest Rate,” Journal of Finance, Vol. 47, No. 3, 1992, pp. 1209-1227.
[2] J. C. Cox and S. A. Ross, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, Vol. 7, No. 3, 1979, pp. 229-264..
[3] G. Barone-Adesi, E. Dinenis and G. Sorwar, “A Note on the Convergence of Binomial Approximations for Interest Rate Models,” Journal of Financial Engineering, Vol. 6, No. 1, 1997, pp. 71-78.
[4] Y. Ait-Sahalia and Y. Testing “Continuous-Time Models of the Spot Interest Rate,” Review of Financial Studies, Vol. 9, No. 2, 1996, pp. 385-426.
[5] T. G. Conley, L. P. Hansen, E. G. J. Luttmer and J. A. Scheinkman, “Short-Term Interest Rates as Subordinated Diffusions,” Review of Financial Studies, Vol. 10, No. 3, 1997, pp. 525-577.
[6] O. A. Vasicek, “An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, Vol. 5, No. 2, 1977, pp. 177-188.
[7] 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. 385-407.
[8] S. J. Brown, P. H. Dybvig, “The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates,” Journal of Finance, Vol. 41, No. 3, 1986, pp. 617-630.
[9] M. R. Gibbons and K. Ramaswamy, “A Test of the Cox, Ingersoll, and Ross Model of the Term Structure,” Review of Financial Studies, Vol. 6, No. 3, 1993, pp. 619-658.
[10] G. Courtadon, “The Pricing of Options on Default-Free Bonds,” Journal of Financial and Quantitative Analysis, Vol. 17, No. 1, 1982, pp. 75-100.
[11] A. Settari and K. Aziz, “Use of Irregular grid in Reservoir Simulation,” Society of Petroleum Engineering Journal, Vol. 12, No. 2, 1972, pp. 103-114.
[12] G. Sorwar and G. Barone-Adesi, W. Allegretto, “Valua-tion of Derivatives Based on Single-Factor Interest Rate Models,” Global Finance Journal, Vol. 18, No. 2, 2007, pp. 251-269.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.