# Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

Milev, Mariyan; Tagliani, Aldo

Serdica Mathematical Journal (2010)

- Volume: 35, Issue: 3, page 223-236
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topMilev, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.