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The Adomian Decomposition Method For Solvinga Generalized Black-scholes Equation

Posted on:2015-02-23Degree:MasterType:Thesis
Country:ChinaCandidate:Z ZhuFull Text:PDF
GTID:2309330422971906Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
With the gradual development of the financial markets and the economy, theendless variety of financial innovations, effective control and reasonable pricing&riskfinancial assets has become a timeless research. Many scholars have conducted anin-depth research and achieved fruitful results. Last year’s "China Aunt Gold rush"gives the ordinary people a chance to experience the financial risks. In order to feed thedevelopment of the Internet finance, the financial theory should be developing rapidly.The high risk of Local government financing platform and Real Estate Industry made itto be an essential.Based on the core tools of financial asset pricing and risk management, the optionpricing model, we present a numerical method for solving the generalizedBlack-Scholes option pricing equation. This paper outlines the basic ideas and the basictheories of option pricing theory. Then we presented a review of derivation of B-Sequation based on the no-arbitrage principle and describes a general pricing methods forthe derivative products in which the underlying asset price is fitted the Wiener process.In this paper, we mainly used the Adomain decomposition method to solve thegeneralized Black-Scholes option pricing equation. The Adomian decompositionmethod has been proposed since the early eighties of last century. After it, Adomian andRach&Cherruault have committed to the further research of this decompositionmethod. They discussed many problems of the decomposition method such as thepolynomial coefficient calculation method, convergence problems, noise problems andthe equivalence of some solutions. This method is also widely applied to solve thoseproblems like algebraic equations, differential equations, integral equations andstochastic equations. This method has the solution obtained in the form of series. Andwe could get a rapidly convergence speed, and high precision. After all, this method isease of calculation, it can be used to solve the initial boundary value problem. In theprocess of solving the generalized B-S equation by the Adomain decomposition method,we obtained a factor recursive series solution represented by an integral equation. Thenwe used the trapezoidal rule to iteratively calculate the series solution coefficients, andwe proved the convergence of this method. Some Numerical experiments have beencarried out by comparing the results of the decomposition method and the exactly valueof the numerical solution. We obtained a minimal error value by this method. The decomposition method has proved to be an effective method in dealing with similarinitial boundary value problem.
Keywords/Search Tags:Option Pricing, Black-Scholes equation, Adomian decomposition, Numerical computation
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