Lie group analysis of exotic options.
Loading...
Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Exotic options are derivatives which have features that makes them more complex
than vanilla traded products. Thus, finding their fair value is not always an easy
task. We look at a particular example of the exotic options - the power option - whose
payoffs are nonlinear functions of the underlying asset price. Previous analyses of
the power option have only obtained solutions using probability methods for the
case of the constant stock volatility and interest rate. Using Lie symmetry analysis
we obtain an optimal system of the Lie point symmetries of the power option PDE
and demonstrate an algorithmic method for finding solutions to the equation. In
addition, we find a new analytical solution to the asymmetric type of the power
option.
We also focus on the more practical and realistic case of time dependent parameters:
volatility and interest rate. Utilizing Lie symmetries, we are able to provide a new
exact solution for the terminal pay off case.
We also consider the power parameter of the option as a time dependent factor. A
new solution is once again obtained for this scenario.
Description
Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2013.
Keywords
Differential equations., Lie groups., Exotic options (Finance), Derivative securities., Theses--Mathematics.