Spectral Method In The Application Of Pricing Options

Financial mathematics,financial engineering and financial management is among the most important projects of the National Natural Science Foundation of China.At the same time,option pricing theory is a forefront and hot issues of the Financial mathematics and Financial engineering.However,option pricing of the classical Black- S choles equation ignore transaction costs and the risks of unprotected portfolio.Therefore,in considering the transaction costs such as buyer's bid and the seller's asking price,classical Black-S choles theory no longer applies.The RAPM model Considers transaction costs and the risk of instability.It has a wide range of applications in practice.In this paper we improve the model of RAPM,assume the total risk premium is the Linear combination of risk cost from the unprotected Volatile portfolio and the transaction costs.In this way,it will closer to reality and Other effects can also be integrated into the the risk cost from the unprotected volatile portfolio,then can get more reasonable and accurate option prices.At the same time,as a differential equation solving numerical method,spectral method, with the finite difference method and the finite element method constitute the basic of solving partial differential equations.This paper gives the characteristics of options,give a spectral collocation method for the price which meet the RAPM model,and Summed up the options market,give prospects.