I recently received an analytical expression for a volatility swap as a variance swap and have been (spared) the mathematical proof but cannot tie the relationship with the results. The first segment claims that the corresponding volatility strike (Kvolswap) can be expressed as a function of the variance swap strike (Kvarswap) and the vol of vol (VoV).Kvolswap = Kvarswap * (1 - VoV^2/8*T)therefore VarSwap - VolSwap = (RVol - Kvarswap)^2/(2* Kvarswap) - Kvarswap * (1 - VoV^2/8*T)When applying this in the model I cannot replicate the Volswap payoff as a functional transformation of the Variance Swap. Is anyone familiar with this? If so is the RVol referring to the realized vol component of the total volatility calculation and is the VoV expressed as a percentage, annualized? Any help greatly appreciated.

vol of vol is just some parameter of some model. you need to specify what the model is.there is no static replication of vol swap.what are you going to use the result for?

The model being used to price the variance swap is Gatheral. Unfortunately I'm using limited information sent to me but I've been told that there is a functional transformation to represent a volatility swap from outputs from a variance swap with the above formula. The purpose is to see if in fact I can use a variance swap model (which I have) to approximate a vol swap (for which I do not have a model). Thanks