Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

Milev, Mariyan, and Tagliani, Aldo. "Low Volatility Options and Numerical Diffusion of Finite Difference Schemes." Serdica Mathematical Journal 35.3 (2010): 223-236. <http://eudml.org/doc/281441>.

@article{Milev2010,
abstract = {2000 Mathematics Subject Classification: 65M06, 65M12.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.},
author = {Milev, Mariyan, Tagliani, Aldo},
journal = {Serdica Mathematical Journal},
keywords = {Numerical Diffusion; Spurious Oscillations; Black-Scholes Equation; Low Volatility Options; Finite Difference Schemes; Non-Smooth Initial Conditions; numerical diffusion; spurious oscillations; Black-Scholes equation; low volatility options; finite difference schemes; non-smooth initial conditions; option pricing; exponential fitting; Milev-Tagliani method; Crank-Nicolson method; discounted payoff options; low volatility options},
language = {eng},
number = {3},
pages = {223-236},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Low Volatility Options and Numerical Diffusion of Finite Difference Schemes},
url = {http://eudml.org/doc/281441},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Milev, Mariyan
AU - Tagliani, Aldo
TI - Low Volatility Options and Numerical Diffusion of Finite Difference Schemes
JO - Serdica Mathematical Journal
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 3
SP - 223
EP - 236
AB - 2000 Mathematics Subject Classification: 65M06, 65M12.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.
LA - eng
KW - Numerical Diffusion; Spurious Oscillations; Black-Scholes Equation; Low Volatility Options; Finite Difference Schemes; Non-Smooth Initial Conditions; numerical diffusion; spurious oscillations; Black-Scholes equation; low volatility options; finite difference schemes; non-smooth initial conditions; option pricing; exponential fitting; Milev-Tagliani method; Crank-Nicolson method; discounted payoff options; low volatility options
UR - http://eudml.org/doc/281441
ER -