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.
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
![\"\"](\"Edit_42466f32-4d7e-4a57-ae1f-687244b56cb8.bmp\")
