Qualitative phase portrait of modified Black Scholes model

Abstract

A qualitative model is based on only three values - positive (increasing), zero (constant) and negative (decreasing). This paper gives a simplified interpretation of some basic concepts, to eliminate the necessity of an extensive study of qualitative reasoning. The generally accepted theory of option pricing is based on the Black-Scholes model. The Black-Scholes model is transferred into a set of qualitative relations and two additional variables. Mood on stock market and risk aversion are incorporated into the qualitative model. The resulting model has 1250 solutions, and there are 16 416 transitions among them. A Chaos related interpretation of the results is presented. An example of a prediction based on modified Black-Scholes model is demonstrated below.