Fourier Transformation, Martingale, and the Pricing of Average-Rate Derivatives

36 Pages Posted: 28 Nov 1997

See all articles by Nengjiu Ju

Nengjiu Ju

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF)

Date Written: August 22, 1997

Abstract

In this paper, a general way to compute the density of the arithmetic average of a Markov process is proposed. This approach is then applied to the pricing of average rate options (Asian options). It is demonstrated that as long as a closed form formula is available for the discount bond price when the underlying process is treated as the riskless interest rate, analytical formulas for the density function of the arithmetic average and the Asian option price can be derived. This includes the affine class of term-structure models. The CIR (1985) square-root interest rate process is used as an example. When the underlying process follows a geometric Brownian motion, a very efficient numerical method is proposed for computing the density function of the average. Extensions of the techniques to the cases of multiple state variables are also discussed.

JEL Classification: G13

Suggested Citation

Ju, Nengjiu, Fourier Transformation, Martingale, and the Pricing of Average-Rate Derivatives (August 22, 1997). Available at SSRN: https://ssrn.com/abstract=39936 or http://dx.doi.org/10.2139/ssrn.39936

Nengjiu Ju (Contact Author)

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF) ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

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