David Hobson1, L. C. G. Rogers1
1School of Mathematical Sciences, University of Bath
Tóm tắt
The paper proposes an original class of models for the continuous‐time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log‐price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference‐independent options prices.We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.
