In-Arrears Interest Rate Derivatives under the 3/2 Model

Joanna Goard

doi:10.4236/me.2015.66067

Home > Journals > Business & Economics > ME

Modern Economy > Vol.6 No.6, June 2015

In-Arrears Interest Rate Derivatives under the 3/2 Model ()

Joanna Goard

School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia.

DOI: 10.4236/me.2015.66067 PDF HTML XML 3,088 Downloads 3,690 Views

Abstract

Lie symmetry methods are used to find a closed form solution for in-arrears swaps under the 3/2 model

. As well, approximate solutions are found for short-tenor in-arrears caplets and floorlets under the same interest rate model. Comparisons are made of the approximate option values with those obtained with a computationally-intensive numerical scheme. The approximate pricing is found to be substantially fast and easy to implement, while the relative errors with respect to the “true” prices are very small.

Keywords

In-Arrears Swaps, Interest Rate Options, 3/2 Model

Share and Cite:

Goard, J. (2015) In-Arrears Interest Rate Derivatives under the 3/2 Model. Modern Economy, 6, 707-716. doi: 10.4236/me.2015.66067.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Chen, A. and Sandmann, K. (2009) In Arrear Term Structure Products: No Arbitrage Pricing Bounds and the Convexity Adjustments. http://www.finance.uni-bonn.de/pdf-datei/download-datei-11
[2]	Mallier, R. and Alobaidi, G. (2004) Interest Rate Swaps under CIR. Journal of Computational and Applied Mathematics, 164-165, 543-554. http://dx.doi.org/10.1016/S0377-0427(03)00490-4
[3]	Chan, K., Karolyi, A., Longstaff, F. and Sanders, A. (1992) Empirical Comparison of Alternate Models of the Short-Term Interest Rate. Journal of Finance, 47, 1209-1227. http://dx.doi.org/10.1111/j.1540-6261.1992.tb04011.x
[4]	Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1996) The Econometrics of Financial Markets. Princeton University Press, Princeton.
[5]	Ahn, D. and Gao, B. (1999) A Parametric Nonlinear Model of Term Structure Dynamics. Review of Financial Studies, 12, 721-762. http://dx.doi.org/10.1093/rfs/12.4.721
[6]	Goard, J. (2000) New Solutions to the Bond-Pricing Equation via Lie’s Classical Method. Mathematical and Computer Modelling, 32, 299-313. http://dx.doi.org/10.1016/S0895-7177(00)00136-9
[7]	Goard, J.M. and Hansen, N. (2004) Comparison of the Performance of a Time-Dependent Short-Interest Rate Model with Time-Dependent Models. Applied Mathematical Finance, 11, 147-164. http://dx.doi.org/10.1080/13504860410001686034
[8]	Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions. Dover Publications, New York.
[9]	Bluman, G.W. and Kumei, S. (1989) Symmetries and Differential Equations. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4757-4307-4
[10]	Goard, J.M. (2003) Noninvariant Boundary Conditions. Applicable Analysis, 82, 473-481. http://dx.doi.org/10.1080/0003681031000109639
[11]	Wilmott, P. (1997) Derivatives: The Theory and Practice of Financial Engineering. John Wiley and Sons, New York.
[12]	Sherring, J. (1993) DIMSYM Users Manual. La Trobe University, Melbourne.
[13]	Black, F. (1976) The Pricing of Commodity Contracts. Journal of Financial Economics, 3, 167-179. http://dx.doi.org/10.1016/0304-405X(76)90024-6
[14]	Howison, S. (2005) Matched Asymptotic Expansions in Financial Engineering. Journal of Engineering Mathematics, 53, 385-406. http://dx.doi.org/10.1007/s10665-005-7716-z
[15]	Maplesoft (2008) Maple 12 Users Manual. Maplesoft, Waterloo.