Dear all,I was asked a question, which I am not sure of the answer. Can someone please help?There are 2 assets priced at S1 and S2 respectively. What would be the volatility of the derivative defined as "S1-S2"? Can someone please tell me what I should be reading to get around such questions.Cheers

Sth like this one?M.

Hi,this should help....MPT

Thanks a lot guys. What would be the solution if the derivative is defined as "S1*S2"?

That's a bit of a trick question (the original one, about S1-S2). That's because if S1 and S2 are lognormally distributed, their difference is not. Neither is their sum, but at least the sum is positive, and a lognormal distribution is not really a terrible approximation. However, for the difference you can have a sign change, so the (lognormal) volatility would explode. The answer to your second question is much simpler; just apply Ito's lemma. Back to the first one. There is another notion of volatility, which is very popular in interest rates: normal volatility. The SDE for an asset is dS = drift + sigma*dW, as opposed to dS = drift + sigma*S*dW. When does it make sense to use normal vol? In interest rates for sure, and that's because rates themselves are not traded assets, bonds are. And since the bond is, roughly speaking, an exponential of some rate, then lognormal bonds means normal rates. Another reason for the use of normal vol in rates is that recently rates have gone very low, and there is nothing to guarantee they won't become negative in the future. Leaving aside the possibility of negative rates, for very low rates the lognormal vols are extremely high (well above 100%), so the models are not stable anymore. Best,V.