 Lookback option pricing using the Fourier transform B-spline methodGareth G. Haslip and Vladimir Kaishev Quantitative Finance, 2014, vol. 14, issue 5, 789-803 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, L�vy 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. Date: 2014 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:14:y:2014:i:5:p:789-803 Ordering information: This journal article can be ordered from DOI: 10.1080/14697688.2014.882010 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
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