Valuation of Convexity Related Interest Rate Derivatives
We investigate valuation of derivatives with payoff defined as a nonlinear though close to linear function of tradable underlying assets. Interest rate derivatives involving Libor or swap rates in arrears, i.e. rates paid at wrong time, are a typical example. It is generally tempting to replace the future unknown interest rates with the forward rates. We show rigorously that indeed this is not possible in the case of Libor or swap rates in arrears. We introduce formally the notion of linear plain vanilla derivatives as those that can be replicated by a finite set of elementary operations and show that derivatives involving the rates in arrears are not (linear) plain vanilla. We also study the issue of valuation of such derivatives. Beside the popular convexity adjustment formula, we develop an improved two or more variable adjustment formula applicable in particular on swap rates in arrears. Finally, we get a precise fully analytical formula based on the usual assumption of log-normality of the relevant tradable underlying assets applicable to a wide class of convexity related derivatives. We illustrate the techniques and different results on a case study of a real life controversial exotic swap.
Volume (Year): 2009 (2009)
Issue (Month): 4 ()
|Contact details of provider:|| Postal: |
Phone: (02) 24 09 51 11
Fax: (02) 24 22 06 57
Web page: http://www.vse.cz/
More information through EDIRC
|Order Information:|| Postal: Editorial office Prague Economic Papers, University of Economics, nám. W. Churchilla 4, 130 67 Praha 3, Czech Republic|
Web: http://www.vse.cz/pep/ Email:
References listed on IDEAS
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.:
- 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.
- Martin Vojtek, 2004.
"Calibration of Interest Rate Models - Transition Market Case,"
- Martin Vojtek, 2004. "Calibration of Interest Rate Models - Transition Market Case," CERGE-EI Working Papers wp237, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
- Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
- Eric Benhamou, 2000. "Pricing Convexity Adjustment with Wiener Chaos," FMG Discussion Papers dp351, Financial Markets Group.
- Eric Benhamou, 2002. "A Martingale Result for Convexity Adjustment in the Black Pricing Model," Finance 0212005, EconWPA.
When requesting a correction, please mention this item's handle: RePEc:prg:jnlpep:v:2009:y:2009:i:4:id:356:p:309-326. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Vaclav Subrta)
If references are entirely missing, you can add them using this form.