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.

Black Scholes Model

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

Heston Model

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.

Jump-Diffusion Model

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).