APPLICATIONS OF REALIZED VOLATITILY, LOCAL VOLATILITY AND IMPLIED VOLATILITY SURFACE IN ACCURACY ENHANCEMENT OF DERIVATIVE PRICING MODEL

In this research paper, a pricing method on derivatives, here taking European options on Dow Jones index as an example, is put forth with higher level of precision. This method is able to price options with a narrower deviation scope from intrinsic value of options. The finding of this pricing method starts with testing the features of implied volatility surface. Two of three axles in constructed three-dimensional surface are respectively dynamic strike price at a given time point and the decreasing time to maturity within the life duration of one strike-specified option. General features of implied volatility surface are justified by the real trading data. With the dynamic strike price and variable volatility, option price is assumed to reflect the market expectation towards the performance of underlying asset and accompanied uncertainty when approaching the maturity. Therefore, the applications of implied volatility, local volatility and realized volatility are involved in the pricing of derivatives, because of their respective compatibilities of the forward-looking expectation, the stochastic parameter and the tight fit to the real return distribution. In the researching and analysing process, it is found that the realized volatility and the real return distribution are the derivative pricing combination with highest accuracy in the three categories of volatility. The implied volatility fails to fit the derivative price for its emphasis on market expectation and lack of independence from existing model, at the meantime, the local volatility loses its ground in practical application in pricing derivatives, with insufficient small-interval data of transactions.