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Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques

This paper considers the evaluation of derivative security prices within the Heath-Jarrow-Morton framework of stochastic interest rates, such as bond options. Within this framework, the stochastic dynamics driving prices are in general non-Markovian. Hence, in principle the partial differential equations governing prices require an infinite dimensinal state space. We discuss a class of forward rate volatility functions which allow the stochastic dynamics to be expressed in Markovian form and hence obtain a finite dimensional state space for the partial differential equations governing prices. By applying to the Markovian form, the transformed suggested by Eydeland (1994), the pricing problem can be set up as a path integral in function space. These integrals are evaluated using fast fourier transform techniques. We apply the technique to the pricing of American bond options and compare the computational time with other methods currently employed such as the method of lines and more traditional partial differential equation solution techniques.

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Paper provided by Finance Discipline Group, UTS Business School, University of Technology, Sydney in its series Working Paper Series with number 72.

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Length: 33 pages
Date of creation: 01 Mar 1997
Date of revision:
Publication status: Published as: Chiarella, C. and El-Hassan, N., 1997, "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques", Journal of Financial Engineering, 6(2), 121-147.
Handle: RePEc:uts:wpaper:72
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Web page: http://www.uts.edu.au/about/uts-business-school/finance

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  1. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. " Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-37, June.
  2. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
  3. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(03), pages 461-474, September.
  4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  5. Carl Chiarella & Nadima El-Hassan, 1996. "A Preference Free Partial Differential Equation for the Term Structure of Interest Rates," Working Paper Series 63, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  7. Eydeland, A, 1994. "A Fast Algorithm for Computing Integrals in Function Spaces: Financial Applications," Computational Economics, Society for Computational Economics, vol. 7(4), pages 277-85.
  8. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
  9. Bhar, R. & Hunt, D.F., 1993. "Predicting the Short Term Forward Interest Rate Structure Using a Parsimonious Model," Papers e9307, Western Sydney - School of Business And Technology.
  10. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 619-642, December.
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