Chaos Theory Applied To Option Pricing

Option has the functions in venture evading,venture investment and value detection etc . It has the properties of agility and diversity as well. Therefore,since the 1990s, it has become one of the most energetic financial derivatives and has been applied broadly and rapidly. In this paper, based on chaos theory;from the perspective of chaos theory of option pricing rules and methodology. Chaos theory's is a new analysis method that is from rationality to bounded rationality,from linear to nonlinear,from the external mechanism to internal mechanism ,It breaks through traditional finance theory's external and will certainly change the development of finance theory Profoundly.Several fruitful results in this paper are as follows:First, introduced the research background and significance, briefly summarized the chaos theory, the application of the situation in the economy.Second, from the traditional definition of chaos, scientific interpretation, and the non-linear relationship between done are described. The fundamental nature of the chaotic motion provided a detailed description.Third, focused on the Brown movement and the Ito formula, arrived at the classic Black-Scholes of European call option pricing model and the Asian call option pricing model .Fourth, described in detail the chaotic points, as well as its statistical nature, focused on analyzing the efficient market hypothesis and the Fractal Market Hypothesis of the similarities and differences. Combined with the nature of option pricing, the bulldozing of a chaotic dynamical system, the central limit theorem, and chaotic market, the statistical nature of the point process discussed.Fifth, Option Pricing with ideas and knowledge of Chaos Theory is derived European option pricing formula for chaos and chaos Asian option pricing formula.Sixth, for the simple European call option pricing, respectively, with Black-Scholes option pricing formula, the chaotic introduction of this option pricing formula and Carlo simulation model, the pricing of three methods results obtained very similar.And finally, present this thesis's summary and the direction for deeper study.