Fitted strong stability-preserving schemes for the Black-Scholes-Barenblatt equation

Abstract

We solve numerically a fully nonlinear Black–Scholes problem of Bellman type. The algorithm is focused on the so-called Delta greek, the first spatial derivative of the option price. Since the elliptic operator degenerates on the boundary we use a fitted finite volume discretization in space. Strong stability-preserving time-marching is further applied in accordance to the nonlinear nature of the differential problem. Numerical experiments validate our considerations.

Keywords:

• Black-Scholes-Barenblatt
• fitted finite volume
• strong stability-preserving
• consistency

2010 AMS Subject Classifications:

• 91G60
• 65M08
• 65M12

Disclosure statement

No potential conflict of interest was reported by the author.

Funding

This research was supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE - Novel Methods in Computational Finance) and by the Bulgarian Fund of Sciences under Grant No. FNI I02/20-2014.