# Potential arbitrage opportunity or fallacy?

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?

• A nonnegative payoff alone isn’t sufficient for an arbitrage, for example: a straddle. The portfolio must be zero cost as well. Commented Jun 22 at 8:21
• 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. Commented Jun 22 at 13:05

## 1 Answer

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.