On Estimation of Volatility Surface and Prediction of Future Spot Volatility

Abstract

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

is represented by the integrated volatility , 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.

Acknowledgements

We thank W. Shaw for helpful comments and for bringing the issues of small Vega and model instability to our attention. This research was supported by the Australian Research Council Grant DP0451657 and was a joint‐work with R. Liptser while he was visiting Monash university during year 2005.