BFS 2002 

Contributed Talk 
Emanuele Amerio, Gianluca Fusai, Antonio Vulcano
In this paper we construct a risk neutral dynamics of the at the money implied volatility to price implied volatility futures and forward starting compound options. These are exotic derivatives contracts whose payoff depends on the future implied volatility. Starting from the description of the real mechanism on the basis of which implied volatilities are actually quoted by option traders in option markets, we derive the risk neutral dynamics for the stochastic implied volatility. In particular we obtain the risk neutral drift restriction that must be satisfied by each single stochastic implied volatility, individually considered, on the volatility surface invariant both to time to maturity and to relative futures prices with the same time to maturity. We show the risk neutral process of the instantaneous spot volatility towards which the risk neutral at the money market implied volatility converges by the absence of maturity arbitrage.