Computational methods for option replication

Abstract

A computational method is described for option replication. In particular, a procedure is provided for computing the projection basis that corresponds to a positive basis of ℝ ^m . Application of this procedure in order to compute maximal submarkets that replicate any option is demonstrated. Specifically, we provide a computational study for the replication of options in security markets with a finite number of states and a finite number of primitive assets with payoffs given by linearly independent vectors of ℝ ^m . The theoretical background of this work follows the results in Polyrakis and Xanthos [Maximal submarkets that replicate any option, Ann. Finance, DOI: 10.1007/s10436-009-0143-9]. Our goal is to make option replication computationally tractable and hence more viable as a financial tool.

Keywords:

• option replication
• computational methods
• projection bases
• maximal replicated subspaces
• vector sublattice

2010 AMS Subject Classifications :

• 90C90
• 91B99

Acknowledgements

The author would like to thank two anonymous referees for their remarks and suggestions which improved significantly this article.

Notes

Copyright (c) 2009 Bruno Luong, http://www.mathworks.com/matlabcentral/fileexchange/24133-set-partition.