
Hi all,
I have a serious doubt about volatility, let me explain here.
My coworkers are calculating return of a IR serie, as RdRd1 (they call it, absolute return), and then they are calculating volatility using this “absolute return”. My point is that this volatility is not comparable between nodes because of the “absolute return” and no even right.
Then they argue that they are calculating volatility points, and the volatility calculated with “absolute returns” is the same as volatility calculate with log returns multiplied by the average price.
To be specific, im using the 1M libor rate, if I compute the log return, and then standard deviation, I have 2.52% daily volatility.
If I compute absolute return, and then standard deviation is 0.05%.
What they say is, that if I take my log volatility (2.52%) and multiply for the average price of the serie (in this case rate because is libor, which is 2.29%) I get their volatility 2.52%*2.29%=0.05% they call it volatility basis points
I don’t see this explanation to be right. Can you help me here? 



Strange


Total Posts: 1677 
Joined: Jun 2004 


Your coworkers are right :) It's a matter of distributional assumption, you can assume normal or lognormal and the two are converted as normal_vol = lognormal_vol * forward. 
'Progress just means
bad things happen faster.’


vertigo


Total Posts: 9 
Joined: Dec 2015 


let z have lognormal dynamics dz/z=v*dw, then (dz * dz / dt)^0.5 = v^2 z^2. let z have normal dynamics dz=n*dw, then (dz*dz/dt)^0.5 = n^2. matching these quadratic variation terms gives us (v*z)^2 = n^2, equivalently n = v*z, where n is the basis point volatility, v is the black volatility and z is the forward 
... maybe one day ... 

