Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality

$$P(K, t) - P(K + s, t) \geq se^{-rt}$$

holds? I know that for a call option $C(K, t)$, it can be shown that the inequality $C(K, t) - C(K + s, t) \leq se^{-rt}$ must hold, otherwise there is an arbitrage. In particular, this arbitrage can be obtained by selling a call option with strike price $K$ and exercise time $t$, buying a $C(K + s, t)$ call option, and putting the remaining $C(K, t) - C(K + s, t) \geq se^{-rt}$ in a bank.

So, I was wondering whether there is a similar justification for the inequality I mentioned above to hold.

  • 3
    $\begingroup$ No, why? If the put is enough out of the money both puts and the difference will be close enough to zero to make the inequality false. $\endgroup$ – Mats Lind May 20 '19 at 11:13
  • 1
    $\begingroup$ Apply the Put Call Parity to the inequality about Calls and see what you get for Puts. $\endgroup$ – noob2 May 20 '19 at 12:26

Your Answer

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

Browse other questions tagged or ask your own question.