Decreasing absolute risk aversion and option pricing bounds
Management Science
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
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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.