MathFinance Share Simulation tool by Tino Kluge

Share Simulation

by Tino Kluge

The share simulator creates sample paths of stochastic processes commonly used to model 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 Merton Jump-Diffusion model are two of them.

Black Scholes Model

In this 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 Cox-Ingersoll-Ross 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 this model can be found on the homepage of Gunter Winkler and in the formula catalogue.

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 this model can be found on the homepage of Dana Uhlig-Düvelmeyer (in German only).































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