Predicting the value of an option base on an option price

Abstract

The movement of the price of the stock (up or down) has a direct –although not equal- effect on the price of the option. As the price of a stock rises, the more likely the price of a call option rise and the price of a put will fall. The value of an option (and hence value the portfolio of an investor) decreases (or increases depending whether option is call or put) as its expiration date approaches and becomes worthless (or full of gain). The value of an option consists of intrinsic values. A careful projection of the value of options starting a few from a few years in the past up to the present will be a good way of predicting in future the portfolio of investor. In this paper, we predict the value of an investor’s portfolio by solving a second order linear partial differential equation. We first describe the evolution of price of an option as stochastic volatility based and further derived a model equation for predicting the values of option based on the price.