The Market Model of Interest Rate Dynamics
A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates. Copyright Blackwell Publishers Inc. 1997.
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Volume (Year): 7 (1997)
Issue (Month): 2 ()
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References listed on IDEAS
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- D. Sondermann & K. Miltersen, 1994. "Closed Form Term Structure Derivatives in a Heath-Jarrow- Morton Model with Log-Normal Annually Compounded Interest Rates," Discussion Paper Serie B 285, University of Bonn, Germany.
- Musiela, Marek & Dieter Sondermann, 1993. "Different Dynamical Specifications of the Term Structure of Interest Rates and their Implications," Discussion Paper Serie B 260, University of Bonn, Germany.
- Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
- 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.
- Musiela, Marek, 1995. "General framework for pricing derivative securities," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 227-251, February.
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