Title:  Computational methods for Levy-driven Russian options

Abstract:

In this master thesis we present some computational methods for the
Russian option, where the price process of the underlying stock is
modeled as an exponential L\'evy process with phase--type distributed
jumps. In addition, we derive an analytic expression for the expected
waiting time of the optimal stopping strategy of the Russian option in
the case of general phase--type jumps. By using the denseness property
of phase--type distributions, we obtain an approximate value of the
expected waiting time of a Russian option driven by an arbitrary
L\'evy process in the following way: By minimizing the distance
between the first cumulants of the given L\'evy model, in our case a
normal inverse Gaussian L\'evy model, and a phase--type L\'evy model
in the sense of least squares, we transfer the properties of the given
L\'evy model to the phase--type model. The derived expression for the
waiting time is then evaluated with the adjusted phase--type L\'evy
model parameters, and by comparing the obtained value with values
comming from simulation we study the efficiency of the method.