What the Synthetic Put Position Contains
A synthetic long put combines short shares with a long call on the same underlying. This calculator matches 100 short shares to each standard call contract. It does not model adjusted deliverables. The call limits the expiration price exposure above its strike while the short shares gain from a decline.
The Options Industry Council strategy description explains this combination and the possibility that borrowed stock must be returned. A put-like curve does not eliminate the stock loan, collateral or exercise decisions.
Expiration Formula and Boundary Cases
Let A be the short sale price, C the premium per call share, K its strike, S the expiration stock price and N = contracts × 100.
P/L = [A − S + max(S − K, 0) − C] × N
With B = A − C, the payoff is (B − S) × N below K and (B − K) × N at or above K. The best terminal P/L is B × N at S = 0; the worst is (B − K) × N. Max Profit displays max(0, B × N) and Max Loss displays max(0, (K − B) × N). These nonnegative labels do not imply a zero-P/L outcome is available in an all-loss or all-profit input scenario.
- If 0 ≤ B < K, the only breakeven is S = B.
- If B = K, the payoff is zero for every S ≥ K.
- If B < 0, all nonnegative prices produce losses; if B > K, all produce profits in this cost-free input model. Neither case establishes that the entered premiums can be executed.
A Reproducible Manual Example
The initial values are hypothetical: short entry $150, strike $155, call premium $5 and one 100-share contract. Expiration P/L is $14,500 at S = 0, zero at S = $145, and −$1,000 for any S ≥ $155. The $14,500 initial net credit is not freely spendable cash: short-sale proceeds can be restricted as collateral. Costs are excluded.
Importing Call Assumptions
- Enter a ticker and load the available snapshot. At most 250 calls are retrieved; a missing expiry does not establish that no contracts exist.
- Select an expiration and call. Auto-fill uses day close, not the bid/ask midpoint or a promised fill. Missing premium or IV needs manual input.
- Check the share multiplier, expiry and exercise style with the broker. This page filters to standard 100-share calls.
- Review short entry, remaining days, IV, rate and chart bounds. All results are assumptions; a fetched stock price does not confirm an available short sale at that price.
Model Curve and Greeks
The expiration curve uses intrinsic value. The other curve values the long call with European Black-Scholes, a zero dividend yield, constant IV and the entered continuous annual rate. The OIC model overview describes the model context. This implementation does not model American early exercise, discrete dividends or a stock-loan market.
Greeks are position totals: call delta minus one for each short share, then multiplied by N; gamma, theta, vega and rho come from the call and are also multiplied by N. Theta is per calendar day; vega and rho are per one percentage-point change. They describe this unfinanced stock-plus-call model, not the full cash ledger of a long put. At zero time or zero volatility, regular Greeks are not displayed.
Comparing With a Purchased Put
The identity −S + max(S − K, 0) = max(K − S, 0) − K shows the cash offset between terminal shapes. Compare full financing, premiums, dividend compensation and borrow costs on compatible dates. A volatility skew across strikes does not by itself show that a same-strike call plus short shares is cheaper than a put.
Short-sale rebates depend on broker terms and may be absent; borrow charges can outweigh them. Collateral, recall risk and dividend payments remain relevant even with call protection. Choosing an ATM, ITM or OTM call changes both strike and premium: use the payoff formula rather than assuming one moneyness is always cheapest or most protective.
The scenario percentage is P/L divided by call cost, not return on total capital or margin. No historical performance, probability of profit, stock-borrow availability or execution is calculated here.