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Lookback option pricing using the Fourier transform B-spline method

Haslip, G. G. and Kaishev, V. K. (2014). Lookback option pricing using the Fourier transform B-spline method. Quantitative Finance, 14(5), pp. 789-803. doi: 10.1080/14697688.2014.882010

Abstract

We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes (jump) diffusions, Lévy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides lookback option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods. We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications in which the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete lookback options under Brownian motion, jump diffusion models, and the variance gamma process.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 27 Mar 2014, available online: http://wwww.tandfonline.com/10.1080/14697688.2014.882010
Publisher Keywords: Lookback option pricing, Fourier transform, B-spline interpolation, Spitzer formula, jump diffusion, variance gamma
Subjects: H Social Sciences > HB Economic Theory
Departments: Cass Business School > Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/11975
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