The Option Pricing Model Based On Neural Network

The option pricing and volatility estimate is financial project ,financial mathematics problem of leading edge as well as a hot one at present. To the pricing question of the option, this text uses the neural network to set up a parameter to predict the non-linear model with the change of the environment changes at the same time. Because volatility has an important influence in the price of option, this text have the detailed discussion of volatility change, and carry on emulation, predict to the volatility with the neural network The part of this text introduction has done the reviewing of generality to the financial derivative and pricing theory. At the second chapter, the article studies the classical Black-Scholes option model and concludes the B-S option pricing formula. The article transforms the solving problem of partial differential equation for the American put price into a standard initial and boundary value problem of Parabolic Type by making some transformation. A finite difference method is supplied, and compared with the improved difference method by using numerical examples. The experimental result of numerical indicates these methods are effective and practical. At the third chapter of the article, assets price movement of the option have carried on new improvement with a mixture normal distribution model replaces the traditional pricing model, a new option pricing model is given. The parameter of mixture gaussian distribute model is given by using the neural network B-P algorithm and a new option pricing mode is provided. The results of numerical method indicate this one is effective and pricing accurate gets more promotion. Volatility smiles and term structure are calculated through index matrix of volatility in the fourth chapter detailed introduction. Introduce the volatility index VIX of CBOE, is predicted by the network model on this basis. Using VIX data proved predict algorithm and the result indicates predict algorithms are effectual.