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A survey of some modern fast Fourier Transform-based methods to value vanilla early-exercise options

Authors
Publisher
University of Cape Town
Publication Date
Keywords
  • Mathematical Finance
Disciplines
  • Computer Science
  • Mathematics

Abstract

The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non- commercial research purposes only. Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. Un ive rsi ty of Ca pe To wn Un ive rsi ty of Ca pe To wn University of Cape Town A survey of some modern fast Fourier Transform-based methods to value vanilla early-exercise options Author: Paolo Innocenzi Supervisor: Adj. A/Prof. Graeme West February 11, 2011 Submitted in partial fulfilment of the M.Phil degree in Mathematical Finance in the Department of Economics The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions ar- rived at are those of the author, and are not necessarily to be attributed to the NRF. Abstract Two fast and accurate methods for pricing Bermudan options are surveyed and im- plemented. The need to calculate risk-neutral expectations along a continuum of state spaces at each exercise date to price these options is problematic. The CONV method we consider identifies these expectations as convolution integrals, and estimates them using the fast Fourier transform to achieve O(MN log2N) complexity, for pricing an M -times exercisable Bermudan option with N grid-points of the underlying asset. We also consider the COS method, which uses Fourier-cosine series expansions to approxi- mate the convolution integrals with remarkable accuracy for small N . The cosine series coefficients at each exercise date can be calculated using the fast Fourier transform, reducing computational complexity considerably. Both of these methods are applicable to any independent increment asset process model for w

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