Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm

Jun-ya Gotoh () and Hiroshi Konno ()
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Jun-ya Gotoh: Institute of Policy and Planning Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8573, Japan
Hiroshi Konno: Department of Industrial and Systems Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan

Management Science, 2002, vol. 48, issue 5, 665-678

Abstract: In a recent article, Bertsimas and Popescu showed that a tight upper bound on a Europeantype call option price, given the first n moments of the distribution of the underlying security price, can be obtained by solving an associated semidefinite programming problem (SDP). The purpose of this paper is to improve and extend their results. We will show that a tight lower bound can be calculated by solving another SDP. Also, we will show that these problems can be solved very quickly by a newly developed cutting plane algorithm when n is less than six or seven.

Keywords: bounds on option prices; semidefinite programming problem; cutting plane algorithm (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (8)

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