Geodesic
Low Volatility Options and Numerical Diffusion of Finite Difference Schemes
Serdica Mathematical Journal, Tome 35 (2010) no. 3, pp. 223-236

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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.
Keywords: Numerical Diffusion, Spurious Oscillations, Black-Scholes Equation, Low Volatility Options, Finite Difference Schemes, Non-Smooth Initial Conditions 
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     title = {Low {Volatility} {Options} and {Numerical} {Diffusion} of {Finite} {Difference} {Schemes}},
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Milev, Mariyan; Tagliani, Aldo. Low Volatility Options and Numerical Diffusion of Finite Difference Schemes. Serdica Mathematical Journal, Tome 35 (2010) no. 3, pp. 223-236. http://geodesic.mathdoc.fr/item/SMJ2_2010_35_3_a1/