Continuous-time term structure models: Forward measure approach (*)
The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and spot probability measures are introduced in this general set-up. Two conditions of no-arbitrage between bonds and cash are examined. A process of savings account implied by an arbitrage-free family of bond prices is identified by means of a multiplicative decomposition of semimartingales. The uniqueness of an implied savings account is established under fairly general conditions. The notion of a family of forward processes is introduced, and the existence of an associated arbitrage-free family of bond prices is examined. A straightforward construction of a lognormal model of forward LIBOR rates, based on the backward induction, is presented.
Volume (Year): 1 (1997)
Issue (Month): 4 ()
|Note:||received: July 1996; final version received: October 1996|
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/mathematics/quantitative+finance/journal/780/PS2|
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.:
- Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997.
"Towards a general theory of bond markets (*),"
Finance and Stochastics,
Springer, vol. 1(2), pages 141-174.
- Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
- 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.
- Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- 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.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:261-291. 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: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.