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I am looking at the proof of the put-call parity, $P+S=C+Ee^{-rT}$

The proof begins by defining two portfolios with same strike price $E$ and time to expiry $T$:
1. A call $C(E,T)$ plus cash $Ee^{-rT}$
2. A put $P(E,T)$ plus stock $S$.

We want to make it so that arbitrage is not possible, so $\forall T$, the put-call parity holds: $P+S=C+Ee^{-rT}$.

The above is what I would have considered an adequate proof. However, in my course notes it says that at the expiry time the value of the both portfolios is $max(E,S)$, and this is why the portfolios are equal.

Exactly what does my lecturer mean by this? Is the argument I provided an acceptable proof?

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migrated from Apr 12 '12 at 7:42

This question came from our site for finance professionals and academics.

Which curriculum book do you follow ? It is nicely explained in the book by Hull or check out the CFA study material. Both should be easily available if you seem to be doing a finance course. – DumbCoder Apr 12 '12 at 7:47

Think of it this way:

C + (-P) = forward contract.

Work it out from there. Anyways, this stack is meant for professionals, not students, I think.

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