Two dimensional COS method for pricing early-exercise and discrete barrier options under the Heston Model

Moir, Richard

Two dimensional COS method for pricing early-exercise and discrete barrier options under the Heston Model

Master Thesis

2014

Publisher

University of Cape Town

Department

Division of Actuarial Science

Faculty

Faculty of Commerce

Abstract

We focus on the pricing of Bermudan and barrier options under the dynamics of the Heston stochastic volatility model. The two-dimensional nature of the Heston model makes the pricing of these options problematic, as the risk-neutral expectations need to be calculated at each exercise/observation date along a continuum of the two state spaces. We examine the 2D-COS method, which makes use of Fourier-cosine expansions in each of the two dimensions in order to approximate the integrals. Using the fast Fourier transform, we are able to efficiently calculate the cosine series coefficients at each exercise/observation date. A construction of this method is provided and we conduct numerical experiments to evaluate its speed and accuracy.

Description

Includes bibliographical references.

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