Fractional-order Equation In The Financial Model Of The Application And Numerical Solution

Fractional equation in physics, engineering, finance and other areas and research on environ -mental issues is widely used. This paper, the fractional equation applied to the finance to get some resultsThe Black- Scholes-Merton formula has become the most popular method for option pricing. Since then, its generalized version has provided mathematically beautiful and powerful results on option pricing. However, they are still theoretically adoptions and not necessary consistent with empirical features of financial return series.Empirical tests indicate that the actual prices at which options are bought and sold deviate in certain systematic ways from the values predicated by the formula. Option buyers pay pices that are consistently higher than those predicated by formula. Option writers, There are large transaction costs in the option market, all of which are effectively paid by option buyer.This dissertation is divided into four chapters . In the first chapter, the article mainly introduces the research background and related prior knowledge. Introduced the options and option pricing formula, fractional equation of state and foreign researchers Moreover, focuses on the definition of fractional equations, nature and fractal part. In the second chapter, it considers the change of option price in the financial market as a fractal transmission systerm, and reference to the history of the diffusion process of the option price on the fractal structure .Using the transmission fraction on the underlying fractal ,and the option price current rateY(S,t),from the start-terminal t=T, which is given by the Black-Scholes equation,we obtain the time–fractional Black-Scholes-Merton different equation. By applying laplace transform, the theorem of conjugate of Reimann-Liouville fractional integrals and derivatives and the operator method of ordinary differential equation, we get the solution of the equation. Using example, the result shows that the time-fractional Black-Scholes option price formula for European call option is more suitable for actual situation. In the three chapter,at first,we use levy process,risk-free rate to analyze this model,and then get a solution ,then use laplace transform and the solution which got from this model to express the equation which satisfies to the European-style;After that , analyze this diffusion equation with the property of fraction calculus and the fraction calculus called Granwald-Letnikov to get the numerical solution. In the four chapter ,use both time and space to analyze the option price .Try to get better result.