On Estimation of Volatility Surface and Prediction of Future Spot Volatility

A stochastic process v(t) is considered as a model for asset's spot volatility. A new approach is introduced for predicting future spot volatility and future volatility surface using a finite set of observed option prices. When the volatility parameter σ2 in the Black-Scholes formula[image omitted]   is represented by the integrated volatility [image omitted]   , then the local volatility surface can be estimated. The main idea is to linearize the expressions for implied volatility by using a result on Normal correlation. This linearization is obtained by introducing various ad hoc approximations.