Convexity adjustment for volatility swaps

In this paper we focus on the convexity adjustment between variance and volatility swaps. It is the difference between the prices that make the two swaps fair. Our aim is to link this adjustment to the implied volatility surface. From practitioners point view this allows to have a first assessment of the volatility swap price without diving into complicated model details. To this aim we look at the SABR model and we use a small time analysis in order to derive such relationship. This technique has been used by various authors to derive extremely accurate approximation of the implied volatility arising from stochastic volatility models.