-1
$\begingroup$

The second derivative of the call price at K gives the probability of that strike (implied probability density).

In practice, what adjustments or acknowledgements (if any) need to be made to produce a IPD with puts?

$\endgroup$
2
$\begingroup$

By call-put parity, the second derivative of a European call option price with respect to strike is strictly equivalent to that of a European put.

So, yes: the result, known as the Breeden-Litzenberger identity, stays unchanged.

$\endgroup$
  • $\begingroup$ Are there any results for American options? $\endgroup$ – Jared Oct 22 '16 at 19:46
  • $\begingroup$ No, because an American option does not only depend on a terminal probability density. $\endgroup$ – Quantuple Oct 22 '16 at 19:50
  • $\begingroup$ Is it actually the same for both? Normally you see different implied forwards from p/c parity at different strikes (I believe due to different margining costs for puts and calls, but not totally sure). $\endgroup$ – will Oct 23 '16 at 22:12
  • $\begingroup$ Theoretically (under the usual assumptions) then yes it should. There is only one conditional pdf $q(s)=d\Bbb{Q}(S_T\leq s)/ds$ after all. $\endgroup$ – Quantuple Oct 24 '16 at 7:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.