Option Pricing by Mathematical Programming - Sjur Flåm (Lund University, School of Economics and Management, Department of Economics, 2007)
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: C61; G12; 330; asset pricing; arbitrage; options; finite sample space; scenario tree; equivalent martingale measures; bid-ask intervals; incomplete market; linear programming; combinatorial optimization; totally unimodular matrices.