UTS Business School

University of Technology, Sydney

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

Author(s): |
Carl Chiarella & Nadima El-Hassan |

Date of publication: |
March 1997 |

Working paper number: |
72 |

Abstract: |
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. |

Paper: |
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Comments: |
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. |

Known citations: |
Baaqule, B. E., 2001, "Quantum Field Theory of Treasury Bonds", Baaqule, B. E., 2004, Baaqule, B. E., Srikant, M. and Warachka, M., "A Quantum Field Theory Term Structure Model Applied to Hedging", Bhar, R., 2010, Bhar, R. andl Chiarella, C., 1997, "Interest Rate Futures: Estimation of Volatility Parameters in an Arbitrage-Free Framework", Bormetti, G. and Cazzaniga, S., 2011, "Multiplicative Noise, Fast Convolution, and Pricing", Paper: 1107.1451, arXiv.org. Černý, A., 2004, "Fourie Transform", Černý, A., 2004, "Introduction to Fast Fourier Transform in Finance", Chiarella, C. and El-Hassan, N., 1999, "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines", Research Paper: 12, Quantitative Finance Research Centre, University of Technology, Sydney. Chiarella, C., El-Hassan, N. and Kucera, A., 1999, "Evaluation of American Option Prices in a Path Integral Framework Using Fourier-Hermite Series Expansions", Chiarella, C., El-Hassan, N. and Kucera, A., 2008, "The Evaluation of Discrete Barrier Options in a Path Integral Framework", In Erricos J. Kontoghiorghes, Berç Rustem and Peter Winker (eds) Duffie, D, 2001, Lin, J. and Ritchken, P., 2001, "On Pricing Derivatives in the Presence of Auxiliary State Variables", Working Paper. Matacz, A., 2000, "Path Dependent Option Pricing: The Path Integral Partial Averaging Method", Working Paper. Rosa-Clot, M. and Taddei, S., 2002, "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods", Sella, L., 2008. "Old and New Spectral Techniques for Economic Time Series", Working Paper: 200809, Department of Economics and Statistics Cognetti de Martiis, University of Turin. |