
Chapter 7
Forward variance models
We catch up to where we left o, at the end of Chapter 4. We examine diusive
stochastic volatility models built on the dynamics of continuous forward VS vari-
ances – they are exactly calibrated to an initial term structure of VS volatilities, by
construction. They can alternatively be calibrated to a term structure of implied
volatilities of other payos, for example ATMF vanilla options, or power payos.
We concentrate on the control of the term structure of volatility of volatility,
the term structure of the ATMF skew, the smile of volatility of volatility and cover
options on realized variance and VIX instruments. ...