Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2007:10: Option Pricing by Mathematical Programming

Sjur Flåm ()
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Sjur Flåm: Economics Department, Bergen University, Postal: Economics Department, Bergen University, 5007 Bergen , Norway

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 bound or identify option prices. When the asset market is incomplete, the bounds stem from nonlinear pricing functionals.

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.

JEL-codes: C61; G12

20 pages, June 4, 2007

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