Numerical Valuation of American Options under Exponential Levy
Processes
Xinzheng Huang
Site of the project:
TU Delft
start of the project: February 2005
The Master project has been finished in August 2005
( Masters Thesis). This master project leads to
a journal article.
Summary of the master project:
The valuation of American options is of practical importance because
the majority of exchange-traded options is American. We focus on
numerical
issues related to American options since there are no closed form
solutions
available. We investigate the option price, the optimal exercise
boundary and
the Greeks (partial derivatives of the option prices).
Two models for the dynamics of stock prices are considered: the
Black-Scholes
model and the variance gamma model. The Black-Scholes model, which
marks the
beginning of the modern era of financial derivatives and remains
dominant in
option trading assumes that the log-price of stocks follows a
geometric
Brownian motion. The variance gamma model is a three parameters model
that is
obtained by evaluating a Brownian motion at random times given by a
gamma
process. We deal with the numerical evaluation of partial
differential
equations and partial integro-differential equations with a coordinate
transformation that can be made time-dependent in order to follow the
optimal
exercise boundary.
Contact information:
Kees
Vuik
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