Lognormality of Rates and Term Structure Models
AbstractA term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain positive. They are bounded from below and above by lognormal processes. The model can be used to price and hedge caps, swaptions and other interest rate and currency derivatives including the Eurodollar futures contract, which requires integrability of one over zero coupon bond. This extends results obtained by Sandmann and Sondermann (1993), (1994) for Markovian lognormal short rates to (non-Markovian) lognormal forward 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 University of Bonn, Germany in its series Discussion Paper Serie B with number 394.
Date of creation: Nov 1996
Date of revision:
Contact details of provider:
Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de/index.php?id=517
Term structure of interest rates; lognormal volatility structure; Heath; Jarrow and Morton models.;
Find related papers by JEL classification:
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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.:
- Farshid Jamshidian, 1993. "Option and Futures Evaluation With Deterministic Volatilities," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 149-159.
- 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.
- K. Sandmann & Sondermann, D., 1993. "A Term Structure Model and the Pricing of Interest Rate Derivative," Discussion Paper Serie B 180, University of Bonn, Germany.
- D. Sondermann & Sandmann, K., 1994. "On the Stability of Log-Normal Interest Rate Models and the Pricing of Eurodollar Futures," Discussion Paper Serie B 263, University of Bonn, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (BGSE Office).
If references are entirely missing, you can add them using this form.