On a pricing problem for a multi-asset option with general transaction costs

2017/04/06 by Amster, Pablo, Mogni, Andres P.
#35K20 #35K55 #91G20 #91G60 #Analysis of PDEs (math.AP) #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.02036

Abstract

We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is multi-dimensional since it involves different underlying assets; on the other hand, the transaction costs are not assumed to be constant (i.e. a fixed proportion of the traded quantity). In this work, we generalize Leland's condition and prove the existence of a viscosity solution for the corresponding fully nonlinear initial value problem using Perron method. Moreover, we develop a numerical ADI scheme to find an approximated solution. We apply this method on a specific multi-asset derivative and we obtain the option price under different pricing scenarios.

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