Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 35, No 3, (2010), 223p-236p
In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant scheme of Milev-Tagliani. We present a short survey of these two schemes, investigate the origin of the respective artificial numerical diffusion and demonstrate how it could be diminished.