wilmott.com

Hi,I used Vasicek model to simulate price.And used GBM model to simulate return.I got two volatility in these two models. Is it possible to compare them?If the volatility of price is fixed, will the return of the volatility fixed?Thanks.

The two vols should essentially follow the relation between BM vols and GBM vols. So vol(Price) = Price x vol(Return)

Thanks for reply. May I know where I could find the formula related with the relation of the vol? I tried, but I could not derive it.And do you mean in GBM model , both vol of price and vol of return are fixed?

What I wrote is just an instantaneous relation. Your price model is Vasicek, sodP = (blah1) dt + sig1 dW , which means E[dP(t)^2]/dt = sig1^2Your return model is GBM, so dP/P = (blah2) dt + sig2 dW, which means E[(dP(t)/P(t))^2]/dt = sig2^2 or E[dP(t)^2] /dt= P(t)^2 sig2^2 So, the noise terms (and ONLY the noise terms) are instantaneously consistent at time t if sig1 = P(t) sig2, which is what I wrote before.But since sig1 and sig2 are constants and P(t) is not, you can really only match things up at a single time,say time-0. To answer your question directly, in the GBM model, the vol of return is fixed, but *not* the vol of price. Apart from the noise terms, your models are not consistent no matter how you line up the vols.You can't even argue that one is objective and the other is risk-neutral. But, that is a separate issue -- I just throw in the thought.