All Title Author
Keywords Abstract

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

DOI: 10.4236/me.2015.66067, PP. 707-716

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

Full-Text   Cite this paper   Add to My Lib


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.


[1]  Chen, A. and Sandmann, K. (2009) In Arrear Term Structure Products: No Arbitrage Pricing Bounds and the Convexity Adjustments.
[2]  Mallier, R. and Alobaidi, G. (2004) Interest Rate Swaps under CIR. Journal of Computational and Applied Mathematics, 164-165, 543-554.
[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.
[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.
[6]  Goard, J. (2000) New Solutions to the Bond-Pricing Equation via Lie’s Classical Method. Mathematical and Computer Modelling, 32, 299-313.
[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.
[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.
[10]  Goard, J.M. (2003) Noninvariant Boundary Conditions. Applicable Analysis, 82, 473-481.
[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.
[14]  Howison, S. (2005) Matched Asymptotic Expansions in Financial Engineering. Journal of Engineering Mathematics, 53, 385-406.
[15]  Maplesoft (2008) Maple 12 Users Manual. Maplesoft, Waterloo.


comments powered by Disqus

Contact Us


微信:OALib Journal