Recreating a Share Position From Two Options
Long call, short put, same strike. Put-call parity says it is stock, almost.
Worth reading first: Why Selling an Option Is Not Just Buying in Reverse
Course catalogue99 lessons
Buy a call and sell a put at the same strike and expiration, and you have built something that behaves almost exactly like owning 100 shares, for a fraction of the cash.
This is not a clever trick. It is a direct consequence of put-call parity, and understanding it makes several other things in this course click into place.
Two contracts, one share position
Toggle between the synthetic and 100 actual shares. The payoff line barely changes. What changes is the capital, the expiry, and the dividends.
Toggle between the two and the payoff line barely changes shape, a long call and a short put at the same strike replicate owning the shares. What differs is the capital, the expiration date, and the dividends.
Why it works
Put-call parity is the relationship that keeps calls, puts and the underlying consistently priced. Rearranged, it says a long call plus a short put at the same strike equals long stock plus a bit of financing.
Call − Put = Stock − Strike × e−rTPut-call parity. The left side is the synthetic; the right is stock and a discounted strike.
The intuition without the algebra: above the strike your call gains dollar for dollar and the put is worthless. Below the strike your call is worthless and the short put loses dollar for dollar. Either way you move exactly with the stock, which is what owning it means.
Delta confirms it. A long at-the-money call has delta around +0.50 and a short at-the-money put around +0.50, summing to roughly 1.00. One hundred shares of exposure.
Three real differences
| 100 shares | Synthetic | |
|---|---|---|
| Cash required | $10,000 | Small net debit, plus put collateral |
| Expires | Never | On a date you chose |
| Dividends | Received | None |
| Voting rights | Yes | No |
| Directional exposure | 100 shares | ≈100 shares |
100 shares at $100 against a synthetic at the $100 strike.
The capital line is the appeal and it comes with an asterisk: the short put still needs securing. If you cash-secure it properly, the capital advantage largely evaporates, the saving only exists on margin, which means the saving is leverage.
Why this is worth knowing even if you never trade one
The synthetic relationship explains several things you have already met.
Why a covered call and a cash-secured put have the same payoff shape. Long stock plus short call, versus short put. Rearrange parity and they are the same position, which is why the two lessons produced identical-looking charts.
Why a poor man's covered call works. A deep in-the-money call approximates stock, so selling a call against it approximates a covered call.
Why arbitrage keeps chains coherent. If the synthetic and the stock diverged in price, someone would buy the cheap one and sell the dear one until they did not. That pressure is why option prices behave predictably relative to each other.
Legitimate uses
Capital efficiency on margin, where you accept the leverage deliberately.
Positions in expensive underlyings that would otherwise be unreachable in round lots.
Short-term exposure where you actively want the position to expire rather than needing to remember to close it.
A synthetic short (short call, long put) is the mirror, and it is generally worse than shorting the stock for retail purposes because the short call carries unlimited risk.
What can go wrong
Sizing on the entry cost. It is near zero and the exposure is not.
Forgetting the expiration. Stock is permanent; this is not.
Expecting dividends. Option holders do not receive them.
Not securing the short put. The obligation is the full strike regardless of what the broker holds.
Key takeaways
- A long call and a short put at the same strike replicate 100 shares. Put-call parity, not a trick.
- The deltas sum to roughly 1.00, which is what makes the payoff line nearly identical to stock.
- It differs in three ways: it expires, it pays no dividends, and it costs almost nothing to open.
- That last point is the danger. Size on the exposure, never on the entry cost.
- The same relationship explains why a covered call and a cash-secured put share a payoff shape.
Check your understanding
1. Long a $100 call and short a $100 put. What is your directional exposure?
2. What is the main risk of building a synthetic instead of buying shares?
3. What else does put-call parity explain?
Related lessons
Track what you have worked through. No account needed. View transcript
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