The Mathematical Theory Of The Price Density Function Of European Call Options

The disadvantages of classical B-S model is the stochastic of volatility, and it has not been solved effectively. To overcome this difficulties, volatility should be seen as a random variable. At the same time, information and experience are important in estimating and predicting volatility and they should be thought into the study of volatility.European call option is researched in the framework of Black-Scholes Option Pricing Model. Return on assets has the character of Fat-tail distribution, and supposing it subject to student(t)-distribution, so the prior distribution function be confirmed; Joint distribution function of return on assets and volatility is cleared by a priori information matrix; Prior probability density functions are also confirmed combining with the theorem of Bayesian statistical. At last, deriving the prior density distribution function and posterior density distribution function of European call option.Some financial derivatives, such as stocks, funds, stock dividend ought to be thought in computing option valuation. This moment, the classic option pricing mode need to be revised. European call option is taken for instance, we can construct simulation models based on building new provided simulation objects. Using the same method to inferring the new distribution functions when the European call option has the fixed dividend.