On the difference between volatility swaps and the ATM implied volatility

Prof. Elisa Alos (University Pompeu Fabra-Barcelona) will be presenting this Probability and Financial Mathematics seminar.

This talk focuses on the difference between the fair strike of a volatility swap and the at-the-money implied volatility (ATMI) of a European call option. It is well known that the difference between these two quantities converges to zero as the time to maturity decreases.

In this talk, we make use of a Malliavin calculus approach to derive an exact expression for this difference. This representation allows us to establish that the order of convergence is different in the correlated and uncorrelated cases, and that it depends on the behavior of the Malliavin derivative of the volatility process. In particular, we see that for volatilities driven by a fractional Brownian motion, this order depends on the corresponding Hurst parameter H. 

Moreover, in the case H ≥ 1/2, we develop a model-free approximation formula for the volatility swap in terms of the ATMI and its skew.

(Joint work with Kenichiro Shiraya)

If you are interested to join this talk, please contact Dr Miryana Grigorova at m.r.grigorova@leeds.ac.uk for the Zoom details.