The rule that two packages with identical payoffs must cost the same; the foundation under every option pricing relationship.
Every structural fact about options descends from this one idea. put-call-parity holds because violating it would let someone build a risk-free profit. A box-spread must price near its discounted width. Call prices must decline as strikes rise, and spreads cannot be worth more than their width.
Real markets permit small violations, bounded by transaction costs, borrow rates and margin. Those bounds are wider than textbooks suggest, which is why apparent free money on a retail screen is almost always a stale quote, an unlisted dividend, or an early-assignment risk you had not priced.
Example: XYZ $50 call at $2.30, $50 put at $2.02, spot $50.00, 45 days, 4% rates, no dividend. Parity says call minus put should be about $0.25. It is $0.28. The three-cent gap will not survive one bid-ask-spread, which is exactly why it exists.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Buying a call: payoff at expiry. A 105-strike call bought for 3 loses that whole 3 if the price finishes at or below 105, breaks even at 108, then gains a dollar for every dollar higher. The loss is capped at the premium; the upside is not capped.The bid-ask spread. Buy orders sit below, sell orders above, and the gap between the best bid (50.01) and best ask (50.04) is the spread you pay to cross. Bar length shows the size resting at each price.
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