Libor Market Model and Gaussian HJM explicit approaches to option on composition
The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation are very good, with an error well below the uncertainty due to the simulation. The appendices proves the existence of the (modified) normal and shifted log-normal LLM used in the pricing. The link of the latter with the Ho and Lee continuous time model is described.
|Date of creation:||29 Nov 2005|
|Date of revision:||07 Dec 2005|
|Note:||Type of Document - pdf; pages: 11. Draft version, comments welcome|
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- Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, EconWPA, revised 14 Aug 2004.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Eymen Errais & Fabio Mercurio, 2005. "Yes, Libor Models can capture Interest Rate Derivatives Skew : A Simple Modelling Approach," Computing in Economics and Finance 2005 192, Society for Computational Economics.
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