Programmes de volatilité stochastique et de volatilité implicite : applications Visual Basic (Excel) et Matlab

Abstract

Markets makers quote many option categories in terms of implicit volatility. In doing so, they can reactivate the Black and Scholes model which assumes that the volatility of an option underlying is constant while it is highly variable. First of all, this article, whose purpose is very empirical, presents a simulation of stochastic volatility programmed in Visual Basic (Excel) whose aim is to compute the price of an European option written on a zero coupon bond. We compare this computed price with this one resulting from Black analytical solution and we also show how to compute an interest rate forecast with the help of the simulation model. Then we write many Visual Basic and Matlab programs for the purpose of computing the implicit volatility surface, a three-dimensional surface which can be plotted by using graphical capacities of Excel and Matlab. It remains that the concept of implicit volatility is very criticised because it is computed with the exercise price of an option and not with the price of the underlying, as it should be. Therefore, there are biases in the estimation of the «greeks» computed with implicit volatility.Financial engineering, Monte Carlo simulation, stochastic volatility, implicit volatility.