Yes, Libor Models can capture Interest Rate Derivatives Skew : A Simple Modelling Approach
AbstractWe introduce a simple extension of a shifted geometric Brownian motion for modelling forward LIBOR rates under their canonical measures. The extension is based on a parameter uncertainty modelled through a random variable whose value is drawn at an inÂ¯nitesimal time after zero. The shift in the proposed model captures the skew commonly seen in the cap market, whereas the uncertain volatility component allows us to obtain more symmetric implied volatility structures. We show how this model can be calibrated to cap prices. We also propose an analytical approximated formula to price swaptions from the cap calibrated model. Finally, we build the bridge between caps and swaptions market by calibrating the correlation structure to swaption prices, and analysing some implications of the calibrated model parameters
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 192.
Date of creation: 11 Nov 2005
Date of revision:
Libor Models; Volatility Skew; Interest Rate Derivatives;
Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-11-19 (All new papers)
- NEP-ETS-2005-11-19 (Econometric Time Series)
- NEP-FIN-2005-11-19 (Finance)
- NEP-FMK-2005-11-19 (Financial Markets)
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.:
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994.
"Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Discussion Paper Serie B
308, University of Bonn, Germany.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
- Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society.
- Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-84.
- Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-85.
- Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Marc Henrard, 2005. "Libor Market Model and Gaussian HJM explicit approaches to option on composition," Finance 0511016, EconWPA, revised 07 Dec 2005.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If references are entirely missing, you can add them using this form.