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

Chiarella, Carl; El‐Hassan, Nadima

doi:10.2139/ssrn.882009

Cited by 14 publications

(10 citation statements)

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“…For t 1 < t < t 2 , the probability distribution function for the paths of the Gaussian process equals The term DW denotes path integration over all the random variables W (t) which appear in the problem. A path integral approach to the HJM model has been discussed in Chiarella and El-Hassan [7] although the action derived is different than the one given above since a different set of variables were involved. A formula for the generating function of forward rates driven by a Gaussian process is given by the path integral This path integral is crucial for applications involving the pricing of derivatives as demonstrated in Sec.…”

Section: A1 Restatement Of Hjmmentioning

confidence: 99%

A Quantum Field Theory Term Structure Model Applied to Hedging

Baaquie

Srikant

Warachka

2003

Int. J. Theor. Appl. Finan.

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A quantum field theory generalization, Baaquie [1], of the Heath, Jarrow and Morton (HJM) [10] term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.

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Section: A1 Restatement Of Hjmmentioning

confidence: 99%

A Quantum Field Theory Term Structure Model Applied to Hedging

Baaquie

Srikant

Warachka

2003

Int. J. Theor. Appl. Finan.

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“…A path integral approach to the HJM-model has been discussed in [14]; the action they derive is different than the one given above since they use a different set of variables and end up with an action involving the time derivatives of their variables.…”

Section: Path Integral Formulation Of the Hjm-modelmentioning

confidence: 99%

Quantum field theory of treasury bonds

Baaquie

2001

Phys. Rev. E

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The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM-model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract. PACS:02.50.-r Probability theory, stochastic processes 05.40.+j Fluctuation phenomena, random processes and Brownian motion 03.05.-w Quantum mechanics

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“…One can quite easily extend the Fourier pricing formula from binomial lattice of Part I to multinomial lattices, see µ Cerný [2004, Chapter 12]. Further applications of FFT appear in Albanese et al [2004], Andreas et al [2002], Benhamou [2002], Chiarella and El-Hassan [1997], Dempster and Hong [2002], and Rebonato and Cooper [1998]. For the most up-to-date developments in option pricing using (continuous) Fourier transform see Carr and Wu [2004], and for evalution of hedging errors refer to µ Cerný [2003] and Hubalek et al [2004].…”

Section: Discussionmentioning

confidence: 99%

Introduction to Fast Fourier Transform in Finance

Cerný

2006

SSRN Journal

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The Fourier transform is an important tool in Financial Economics. It delivers real time pricing while allowing for a realistic structure of asset returns, taking into account excess kurtosis and stochastic volatility. Fourier transform is also rather abstract and therefore o¤-putting to many practitioners. The purpose of this paper is to explain the working of the fast Fourier transform in the familiar binomial option pricing model. We argue that a good understanding of FFT requires no more than some high school mathematics and familiarity with roulette, bicycle wheel, or a similar circular object divided into equally sized segments. The returns to such a small intellectual investment are overwhelming.

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

Cited by 14 publications

References 0 publications

A Quantum Field Theory Term Structure Model Applied to Hedging

A Quantum Field Theory Term Structure Model Applied to Hedging

Quantum field theory of treasury bonds

Introduction to Fast Fourier Transform in Finance

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