Isolating a risk premium on the volatility of volatility

Lorenzo Ravagli shows a risk premium could be embodied in the price of out-of-the-money options. He demonstrates that in a family of stochastic volatility models, and under some limits, this premium is related to the overvaluation of implied volatility of volatility compared to the realised volatility of implied volatility. He carries out a numerical analysis on foreign exchange options to support his findings

Volatility arrows

The author finds that for a class of stochastic volatility models, under the limits of zero skew, short maturity and near-the money, the implied lognormal volvol enters the dynamics of an option as a breakeven term corresponding to theVolga axis of risk: a non-zero Volga term monetises a P&L that is proportional to the differential of the squared values of implied and realised volvol.


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