Put-Call Parity

A European call and a European put are written on the same non-dividend-paying stock $S$, with identical strike $K$ and maturity $T$. The continuously compounded risk-free rate is $r$.

The Task

Derive the put-call parity relation

$c-p=S-K{e}^{-rT}$

using a no-arbitrage argument, and explain the arbitrage trade if the market violates it.