Arbitrage-Free Interpolation in Models of Market Observable Interest Rates
AbstractModels which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.
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 Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 71.
Date of creation: 01 Dec 2001
Date of revision:
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.:
- Erik Schlögl, 1999.
"A Multicurrency Extension of the Lognormal Interest Rate Market Models,"
Research Paper Series
20, Quantitative Finance Research Centre, University of Technology, Sydney.
- Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
- 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.
- 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.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
- Sandmann,Klaus & Sondermann,Dieter, . "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
- 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.
- 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.
- Lech A. Grzelak & Cornelis W. Oosterlee, 2012.
"On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates,"
Applied Mathematical Finance,
Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
- Grzelak, Lech & Oosterlee, Kees, 2010. "On cross-currency models with stochastic volatility and correlated interest rates," MPRA Paper 23020, University Library of Munich, Germany.
- Mark H. A. Davis & Vicente Mataix-Pastor, 2009. "Arbitrage-Free Interpolation Of The Swap Curve," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 969-1005.
- Grzelak, Lech & Oosterlee, Kees, 2010. "An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile," MPRA Paper 20574, University Library of Munich, Germany.
- Erik Schlögl, 2002. "Extracting the Joint Volatility Structure of Foreign Exchange and Interest Rates from Option Prices," Research Paper Series 79, Quantitative Finance Research Centre, University of Technology, Sydney.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford).
If references are entirely missing, you can add them using this form.