I've heard that you can convert lognormal vols to normal vols using the approximation NVol = LNVol x sqrt( ATM Fwd x Strike)Can someone hlep me in understanding this approximation?Many thanks!!-Raph

This makes no sense, I'm not even sure what the variables mean.I assume NVol is the volatility of the underlying return, and LNVol is the volatility of the underlying log return. But are these implied or actual volatilities?What is ATM Fwd? The forward price of the underlying? The strike price that makes makes puts and calls equally valuable?The use of strike implies you are talking about a specific option, in which case I assume you are working with implied volatilities. But then everything is model and market dependent.Perhaps if you gave more context to this problem, we could help. I'm probably misunderstanding you entirely.

As an approx Nvol = LNvol x FwdYou can check this easily using a one step monte carlo for whatever time period you are interested in.For the reason. Calculate the Taylor expansion of Ln(y) about a start point of 1. You are looking for Ln((S+dx)/S) which is the same as Ln(1+dx/S). You then put the dx/S into your Taylor series and calculate second moment. Compare to what you would get for a normal assumption.Anyway, the first term in the Taylor expansion for Ln(y) around start point of 1 is (y-1), putting y = 1+dx/S the result is (ignoring higher order terms i.e. the rest of the Taylor expansion) dx/S. For a more accurate translation price an option using a lognormal model, get a normal model and see what the implied vol is to give the same price.