Libor Market Model and Gaussian HJM explicit approaches to option on composition
AbstractThe 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.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0511016.
Length: 11 pages
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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explicit formula; Libor market model; HJM model; shifted log-normal model; normal model; existence; option on composition;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-09 (All new papers)
- NEP-FIN-2005-12-09 (Finance)
- NEP-MAC-2005-12-09 (Macroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, EconWPA, revised 14 Aug 2004.
- 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.
- Henrard, Marc, 2007. "Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options," MPRA Paper 1534, University Library of Munich, Germany.
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