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Niklasson, V. och Tivedal, F. (2018) Multi-asset options: a numerical study. Göteborg : Chalmers University of Technology
BibTeX
@mastersthesis{
Niklasson2018,
author={Niklasson, Vilhelm and Tivedal, Frida},
title={Multi-asset options: a numerical study},
abstract={This thesis compares three methods for numerically pricing multi-asset options, as-
suming the underlying assets follow a multi-dimensional geometric Brownian motion
with constant coeffcients. The considered methods are the binomial pricing model,
the Monte Carlo method, and the finite element method (FEM) applied to the pric-
ing PDE (the PDE method). It is shown that the binomial model can be used to
price both European and American multi-asset options. It is also concluded that
the binomial model has a rather fast convergence rate and the results can be fur-
ther improved by using adaptive mesh refinements. However, the binomial model
performs worse for large volatilities. Furthermore, it is found that the Monte Carlo
method converges very fast and that the results can be improved by using variance
reduction techniques. This method also works well for pricing Asian options due to
its simple formula. Even though the Monte Carlo method is shown to be the fastest
and most reliable out of the three methods, it does not perform well for larger
volatilities. While the binomial pricing model and the Monte Carlo method seem to
underestimate the price for large volatilities, the PDE method is shown to be the
only method out of the three that gives reliable estimates. However, the method
also has the slowest convergence rate out of the three methods when the volatilities
are low. This method also needs the most adaptation for each new option.},
publisher={Institutionen för matematiska vetenskaper, Chalmers tekniska högskola},
place={Göteborg},
year={2018},
}
RefWorks
RT Generic
SR Electronic
ID 255030
A1 Niklasson, Vilhelm
A1 Tivedal, Frida
T1 Multi-asset options: a numerical study
YR 2018
AB This thesis compares three methods for numerically pricing multi-asset options, as-
suming the underlying assets follow a multi-dimensional geometric Brownian motion
with constant coeffcients. The considered methods are the binomial pricing model,
the Monte Carlo method, and the finite element method (FEM) applied to the pric-
ing PDE (the PDE method). It is shown that the binomial model can be used to
price both European and American multi-asset options. It is also concluded that
the binomial model has a rather fast convergence rate and the results can be fur-
ther improved by using adaptive mesh refinements. However, the binomial model
performs worse for large volatilities. Furthermore, it is found that the Monte Carlo
method converges very fast and that the results can be improved by using variance
reduction techniques. This method also works well for pricing Asian options due to
its simple formula. Even though the Monte Carlo method is shown to be the fastest
and most reliable out of the three methods, it does not perform well for larger
volatilities. While the binomial pricing model and the Monte Carlo method seem to
underestimate the price for large volatilities, the PDE method is shown to be the
only method out of the three that gives reliable estimates. However, the method
also has the slowest convergence rate out of the three methods when the volatilities
are low. This method also needs the most adaptation for each new option.
PB Institutionen för matematiska vetenskaper, Chalmers tekniska högskola,PB Institutionen för matematiska vetenskaper, Chalmers tekniska högskola,
LA eng
LK http://publications.lib.chalmers.se/records/fulltext/255030/255030.pdf
OL 30
