UNCERTAINTY IN VOLATILITY. AN APPLICATION TO THE VALUATION OF BARRIER OPTIONS

Some barrier options, such as the down-and-out puts, exhibit a gamma that changes sign. In this article we price this kind of options assuming that there is uncertainty regarding volatility but it is assumed to lie within a certain range. We present the partial differential equation corresponding to the derivative and solve it numerically using the finite difference method. The results show that barrier option prices are quite sensitive to the existence of uncertainty about volatility. We also show that the prices obtained using the uncertain volatility model are consistent with the prices generated under a stochastic volatility framework.