1
$\begingroup$

Okay this is probably going to be an extremely easy/straightforward question but I thought I should post it here just to double check. Suppose I have a payoff $\Phi = (S_{T}-K)^{+}$. Now let's say I now have an equation: $u = s\partial_{s}\Phi - \Phi$, this means that given a payoff $\Phi$ as given above then, substituting this payoff into the equation and assuming $S_T = S_{0}\exp((r-1/2)T+\sigma\sqrt{T}Z_i))$ then I should get:

$u = max(S_{T},0) - max(S_{T}-K,0)$, right?

And from this equation, the possible solutions should be:

If $S_{T} > K$, $u = K$, if $S_{T} < K$ and $S_{T} > 0$, $u = S_{T}$, and if $S_{T} < K$ and $S_{T} < 0$ then $u = 0$.

Is all of this correct? I know this is really trivial but I just thought I should check...

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

$$s\partial_{s}\Phi = S_T I_{S_T>K}.$$ so no.

(I am not absolutely sure whether you want to differentiate wrt S_T or S_0 however.)

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks for that, that helps clear up the issue I had. I knew it was fairly trivial but I didn't think I'd make a mistake like that haha $\endgroup$
    – ThePlowKing
    May 11, 2016 at 8:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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