4
$\begingroup$

I am having a tough time conceptualizing this question here: Let $P$= Price of European Option, $S$ = Present Price of Option and $K$ = Strike Price. If $P > K$, why does abritrage exist? Assuming $r = 0$. I really can't figure this out.

I understand that when C(call option) is greater then S abritrage exists because $C - S + K > 0$ and even if you don't execute the option, $C - S > 0$.

Could the same logic be utilized here?

$\endgroup$
  • $\begingroup$ Hi Efrain Olivenhain=) Welcome to quant.SE. To obtain fast and helpful answers to your questions you should clarify it a little bit: What makes you assume that arbitrage exist if $P>K$? Do you already have some ideas on how to solve this question? As a hint: What can you say about the boundaries of option prices? $\endgroup$ – muffin1974 Oct 18 '15 at 11:42
  • $\begingroup$ What is the difference between "Price of European Option" and "Present Price of Option "? $\endgroup$ – Gordon Dec 17 '15 at 19:34
1
$\begingroup$

Assuming S is non-negative, the payoff function of a put at maturity is dominated by K:

$P_T = max(K - S_T, 0) = K + max(-S_T, -K) \leq K$

Under the assumption of a zero risk-free rate, one can write a put and invest K until maturity, for a positive cashflow at initiation ($P - K > 0$) and possibility 1 non-negative cashflow at maturity ($P_T \leq K$).

More generally, any put value above $e^{-rT}K$, $T$ being the time to maturity, yields an arbitrage opportunity, it being the amount necessary to dominate the final payoff function.

$\endgroup$
1
$\begingroup$

Let $P>K$ and $r=0$.

Then you can short the put and receive $P$.

At maturity, the maximum payoff you have to pay from the put is $K$.

Therefore you have a sure profit of at least $P-K>0$, which is an arbitrage.

$\endgroup$
0
$\begingroup$

First, assume r = 0 then Put-Call parity holds: C - P = S - K which can be rewritten as C = S - K + P > S - K + K = S. That's your answer.

$\endgroup$

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.