Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two payoff curves intersect on the x-axis, i.e. $K_1+c=K_2-p$. Then, wouldn't the ensuing portfolio always have a non-negative payoff? Is there some theoretical justification to prevent this from happening?
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$\begingroup$ A nonnegative payoff alone isn’t sufficient for an arbitrage, for example: a straddle. The portfolio must be zero cost as well. $\endgroup$– Bob Jansen ♦Commented Jun 22 at 8:21
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$\begingroup$ I am accounting for the cost in the payoff, so for example the payoff for the call is $-c$ till the stock price reaches $K_1$ and increasing linearly thereafter, and so on. $\endgroup$– Ambitious-Walk3171Commented Jun 22 at 13:05
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The ‘pure payoff” diagram (excluding option premia) for this structure shows that the payoff is always at least $K_2 - K_1 $ Therefore the total premium $c+p$ must be at least $K_2 -K_1$ so yes, a simple arbitrage argument shows this condition should not occur.
