Dichotomous Rate in Stock-Price Process

This paper identifies the “good news” and “bad news” in the generalization of classical market model with a new source of uncertainty — the dichotomous process, and studies a model with dichotomous expected rate of return. Both the dichotomous and integrated dichotomous process are described, including derivation of exact form of their distribution. The pricing of an European stock option is examined and the first steps to derive a Black-Scholes formula were done. The analytical results are compared both with computer simulations and data from the Prague stock exchange. The analysis of a stock index shows, that the gain is a sum of dichotomous process and some noise. This fact is important especially for forecasting and measuring the risk.