The no-arbitrage relationship linking a call, a put, the stock and a bond: call minus put equals stock minus discounted strike.
For European options on a non-dividend stock, C − P = S − K·e^(−rt). It is not a model or a forecast; it is an accounting identity enforced by arbitrage. If it breaks, a riskless profit exists and someone takes it in seconds.
Everything about synthetics follows from rearranging it. Long call plus short put equals long stock. Long stock plus long put equals long call. This is why conversion, reversal-arbitrage and the box-spread work.
Example: XYZ at $50, the $50 call at $2.30, the $50 put at $2.10, 90 days, rates near 1.6%. C − P = $0.20. S − K·e^(−rt) ≈ $50 − $49.80 = $0.20. The relationship holds, so no free money — and if the put were quoted at $1.60 instead, it would not.
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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