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Option pricing by mathematical programming

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Abstract

Financial options typically incorporate times of exercise. Alternatively, they embody set-up costs or indivisibilities. Such features lead to planning problems with integer decision variables. Provided the sample space be finite, it is shown here that integrality constraints can often be relaxed. In fact, simple mathematical programming, aimed at arbitrage or replication, may find optimal exercise, and bound or identify option prices. When the asset market is incomplete, the bounds stem from nonlinear pricing functionals.

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  • Flåm, Sjur Didrik, 2007. "Option pricing by mathematical programming," Working Papers in Economics 08/07, University of Bergen, Department of Economics.
    • Handle: RePEc:hhs:bergec:2007_008
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    More about this item

    Keywords

    asset pricing; arbitrage; options; finite sample space; scenario tree; equivalent martingale measures; bid-ask intervals; incomplete market; linear programming; combinatorial optimization; totally unimodular matrices.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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