# Deriving the put-call parity

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 quant.stackexchange.comApr 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