## Share Simulation

The share simulator creates sample paths of stochastic processes
which are believed to approximate the share price development.
The classical model was examined by Black and Scholes in order
to evaluate derivatives. There exists a diversity of tailored
models of the Black Scholes model. The Heston- and the
Jump-Diffusion model are two of them.

In that model the stochastic process is a geometric Brownian
motion.

This model is based on the Black Scholes Model but with the
assumption that the square volatility is a stochastic process itself.
The square of volatility is assumed to be a so called mean reversion
process, i.e. a process which is fluctuating about a mean
value. More details about this process and ways to price
derivatives with that model can be found on the homepage of

Gunter Winkler and in the formula catalogue of the

MathFinance portal.

This model is based on the Black Scholes Model with an additional
jump process. The time gap between two jumps are exponentially
distributed and the hight of each jump is proportional to the
current share price and to a lognormal distributed random variable.
More details about this process and a discussion of anti trend
strategies in that model can be found on the homepage of

Dana Düvelmeyer (in German only).