Green, Ross and Abrahams, I. David and Fusai, Gianluca
(2007)
*Pricing financial claims contingent upon an underlying asset monitored at discrete times.*
Journal of Engineering Mathematics, 59 (4).
pp. 373-384.
ISSN 1573-2703
(In Press)

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## Abstract

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-transform in time and a Fourier transform in the logarithm of asset prices. The Wiener–Hopf technique is used to obtain probabilistic identities for the related random walks killed by an absorbing boundary. An accurate and efficient approximation is obtained using Padé approximants and an approximate inverse z-transform based on the trapezoidal rule. For simplicity, European barrier options in a Gaussian Black–Scholes framework are used to exemplify the technique (for which exact analytic expressions are obtained). Extensions to different option contracts and options driven by other Lévy processes are discussed.

Item Type: | Article |
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Uncontrolled Keywords: | Discrete monitoring - Fourier transform - Option pricing - Padé approximants - Wiener–Hopf technique - z-transform |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 26 Nov 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/961 |

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