Sorrentino, Gabriele (2009) Option pricing in a path integral framework. PhD thesis, Victoria University.

Abstract

This dissertation is an examination of methods for computing an option price using a path integral framework. The framework, developed by Chiarella, El-Hassan and Kucera, is based on the Black and Scholes paradigm. The path integral is backward recursive with the payoff known at expiry and has no closed form solution. Three specific financial derivatives are used in this dissertation, they are, European (call and put), American put and a down and out call (Barrier type) option. The work in this dissertation examines three methods to approximate the option price. The first is a review of the spectral method offered by Chiarella et al. Their method involves the use of a Fourier-Hermite series expansion which represents the option value at each time step. The Hermite orthogonal polynomials and their associated properties are employed to create a set of recurrence relations so that a final option pricing polynomial is formed. A similar approach using normalised Hermite orthogonal polynomials is also presented. Similar methods and techniques are utilised to form a new set of recurrence relations. The accuracy obtained for both types of orthogonal polynomials are of the same magnitude.

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