POSSIBILITIES OF BROWNIAN MOTION APPLICATION FOR OPTION PRICING

The behaviour of stock prices in a very short period of time is the base for valuing contingent claims, especially those that appear as formalized options, but also in the parameters that define long-term behaviour in stock’s hidden options. Changes in stock prices alter the risk of contingent claims, and because of that, for valuing the most of them it is not possible to apply the economic value concept. One of the possibilities for pricing the options is to rely upon the stochastic behaviour of stock prices or other underlying asset. It is
important to determine the stochastic process that describes this behaviour. The continuous time stochastic process is known as geometric Brownian motion or Wiener process and it is a building block for all kinds of models for options pricing. The best-known model for option pricing is the Black-Scholes model and it assumes that stock prices follow geometric Brownian motion. Despite critics and the existence of alternative models for option pricing,
the Black-Scholes model is widely used and with appropriate adjustments it can be used for pricing of different options and business processes with embedded options.