Bounding Option Prices Using SDP With Change Of Numeraire

Kai Ye, Panos Parpas and Berc Rustem

No 16, Working Papers from COMISEF

Abstract: Recently, given the first few moments, tight upper and lower bounds of the no arbitrage prices can be obtained by solving semidefinite programming (SDP) or linear programming (LP) problems. In this paper, we compare SDP and LP formulations of the European-style options pricing problem and prefer SDP formulations due to the simplicity of moments constraints. We propose to employ the technique of change of numeraire when using SDP to bound the European type of options. In fact, this problem can then be cast as a truncated Hausdorff moment problem which has necessary and sufficient moment conditions expressed by positive semidefinite moment and localizing matrices. With four moments information we show stable numerical results for bounding European call options and exchange options. Moreover, A hedging strategy is also identified by the dual formulation.

Keywords: moments of measures; semidefinite programming; linear programming; options pricing; change of numeraire (search for similar items in EconPapers)
Pages: 23 pages
Date: 2009-06-15
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