Questions for the reader:
Easy) What's this a chart of?
Medium) Notice anything weird happening earlier today? Explain why it's weird using a first principles argument.
Hard) Why might have this weird thing happened?
Mar 16, 2024 • 8 tweets • 2 min read
Alright let's tackle these one by one.
1) So we want to minimize C(k)+P(k). So C'(k)+P'(k) = 0. But C'(k) = [C(k+h) - C(k)]/h for very small h. This is a very tight call spread and is thus effectively a binary option scaled by h. Its price should simply be the probability...
... that it expires in the money. So if C'(k) = - P'(k) we are basically choosing the strike where we are just as likely to expire above as below. That is the *median* of the distribution.
