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

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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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Date of creation: 01 Mar 1997
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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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Cited by:
  1. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
  2. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
  3. Sella Lisa, 2008. "Old and New Spectral Techniques for Economic Time Series," Department of Economics and Statistics Cognetti de Martiis. Working Papers 200809, University of Turin.
  4. Carl Chiarella & Nadima El-Hassan, 1999. "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines," Research Paper Series 12, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
  6. Andrew Matacz, 2000. "Path dependent option pricing: the path integral partial averaging method," Science & Finance (CFM) working paper archive 500034, Science & Finance, Capital Fund Management.
  7. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
  8. Ramaprasad Bhar, 2010. "Stochastic Filtering With Applications In Finance:," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.

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