Construct implied PDF of returns from implied volatilities?
Alright nerds, help out a finance noob.
I have a feeling that it should be possible to reconstruct an implied PDF (or at least N moments) of returns for an asset given it's implied volatilities. I have some ideas about how one could do this, but it would be awesome if someone smarter than me has already put some though into this.
It's easier to do it directly from prices than from implied vols.
Given a range of (say) call prices C(K,T) at various strikes K, the implied pdf is simply the second derivative of call price with respect to strike divided by the price of the zero coupon bond B(0,T)
(the only modeling assumption here is that the underlier price is independent of interest rates)
Because there are only finitely many option prices available and because there is a bid-ask spread you cannot imply all pdfs exactly; instead you must make some kind of numerical approximation/interpolation...
this.
use Adobe?
Look up the following paper:
"Recovering Probability Distributions from Option Prices" by Jackwerth and Rubinstein
There's a decent example in the paper you can reconstruct. You could also just email Rubinstein directly at Berkeley and see if he'll give you an ad hoc homework assignment.
Yep, that's actually a trivial result. Thanks to BB Quant and android.
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