Arbitrage-Free Interpolation Of The Swap Curve
AbstractWe suggest an arbitrage free interpolation method for pricing zero-coupon bonds of arbitrary maturities from a model of the market data that typically underlies the swap curve; that is short term, future and swap rates. This is done first within the context of the Libor or the swap market model. We do so by introducing an independent stochastic process which plays the role of a short term yield, in which case we obtain an approximate closed-form solution to the term structure while preserving a stochastic implied short rate. This will be discontinuous but it can be turned into a continuous process (however at the expense of closed-form solutions to bond prices). We then relax the assumption of a complete set of initial swap rates and look at the more realistic case where the initial data consists of fewer swap rates than tenor dates and show that a particular interpolation of the missing swaps in the tenor structure will determine the volatility of the resulting interpolated swaps. We give conditions under which the problem can be solved in closed-form therefore providing a consistent arbitrage-free method for yield curve generation.
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 InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.
Volume (Year): 12 (2009)
Issue (Month): 07 ()
Contact details of provider:
Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml
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.:
- Carl Chiarella & Oh-Kang Kwon, 1999.
"Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model,"
Research Paper Series
5, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Tomas Björk & Bent Jesper Christensen, 1999.
"Interest Rate Dynamics and Consistent Forward Rate Curves,"
Wiley Blackwell, vol. 9(4), pages 323-348.
- Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
- 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.
- 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, 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.
- 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.
- Mark Davis & Vicente Mataix-Pastor, 2007. "Negative Libor rates in the swap market model," Finance and Stochastics, Springer, vol. 11(2), pages 181-193, April.
- repec:aah:aarmng:1999-4 is not listed on IDEAS
- Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
- Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim).
If references are entirely missing, you can add them using this form.