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USING MODEL-INDEPENDENT LOWER BOUNDS TO IMPROVE PRICING OF ASIAN STYLE OPTIONS IN LÉVY MARKETS

Published online by Cambridge University Press:  19 February 2014

Griselda Deelstra ,
Grégory Rayée ,
Steven Vanduffel  and
Jing Yao
Griselda Deelstra
Affiliation:
Department of Mathematics, Université Libre de Bruxelles, Bruxelles, Belgium E-Mail: griselda.deelstra@ulb.ac.be
Grégory Rayée
Affiliation:
Department of Mathematics, Université Libre de Bruxelles, Bruxelles, Belgium E-Mail: Gregory.Rayee@ulb.ac.be
Steven Vanduffel*
Affiliation:
Department of Economics, Vrije Universiteit Brussel, Bruxelles, Belgium
Jing Yao
Affiliation:
Department of Economics, Vrije Universiteit Brussel, Bruxelles, Belgium E-mail: jingyao@vub.ac.be
*
E-mail: steven.vanduffel@vub.ac.be
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Abstract

Albrecher et al. (Albrecher, H., Mayer Ph., Schoutens, W. (2008) General lower bounds for arithmetic Asian option prices. Applied Mathematical Finance, 15, 123–149) have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

Keywords

Asian-style optionsconditional expectationcontrol variatesstochastic clock
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 2 , May 2014 , pp. 237 - 276
Copyright
Copyright © ASTIN Bulletin 2014 

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