Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model
In this paper, a class of forward rate dependent Markovian transformations of the Heth-Jarrow-Morton [HJM92] term structure model are obtained by considering volatility processes that are solutions of linear ordinary differential equations. These transformations generalise the Markovian system obtained by Carverhill [Car94], Ritchken and Sankarasubramanian [RS95], Bhar and Chiarella [BC97], and Inui and Kijima [IK98], and also generalise the bond price formulae obtained therin.
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- Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- Ram Bhar & Carl Chiarella, 1995.
"Transformation of Heath-Jarrow-Morton Models to Markovian Systems,"
Working Paper Series
53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26.
- Tomas BjÃrk & Andrea Gombani, 1999. "Minimal realizations of interest rate models," Finance and Stochastics, Springer, vol. 3(4), pages 413-432.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Björk, Tomas & Svensson, Lars, 1999. "On the Existence of Finite Dimensional Realizations for Nonlinear Forward Rate Models," SSE/EFI Working Paper Series in Economics and Finance 338, Stockholm School of Economics.
- Carl Chiarella & Oh-Kang Kwon, 2000. "A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility," Research Paper Series 34, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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.
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