Synthetic Long Stock Calculator

Synthetic Long Stock at a glance

How a synthetic long stock works

Synthetic long stock, often called a synthetic long or long combo, follows directly from put call parity: a call minus a put at the same strike equals the stock price minus the present value of the strike, adjusted for dividends. Because of that relationship, the two options together track the share price almost one for one. The net cost is usually small. When interest on the strike outweighs the expected dividends, the at the money call typically costs a bit more than the put, so the combo opens for a modest debit.

At expiration the payoff is a straight diagonal line, the same shape as owning 100 shares. Above the strike, the long call is in the money and the short put expires worthless, so you gain one for one with the stock. Below the strike, the call expires worthless and the short put loses one for one. The only differences from real stock are the breakeven, which shifts by the net debit or credit, and the fact that the position ends at expiration unless you roll it or take delivery.

Before expiration, time decay on the long call is largely offset by time decay collected on the short put, and their vegas also mostly cancel, so changes in implied volatility have little net effect. What remains is carry: you have effectively borrowed the strike price, and the option prices build in that interest along with the dividends you give up. A change in interest rates or in the expected dividend can therefore move the position slightly even when the stock is unchanged.

Synthetic Long Stock example with real numbers

With the stock at $100, implied volatility at 30%, a 4.1% risk free rate and no dividend, you would buy 1 100 call (32 days) at $3.73, sell 1 100 put (32 days) at $3.39. That is a net debit of $34. At expiration a maximum profit of unlimited and a maximum loss of $10,034, with a breakeven at $100.34. The lognormal chance of profit is 48%.

These are theoretical American option prices from the Bjerksund and Stensland model, not live quotes. Load any ticker in the synthetic long stock calculator above to run the same math on real market prices.

When to use a synthetic long stock

• You want stock like exposure without committing the full cash needed for 100 shares.
• You are bullish on a stock that pays little or no dividend, so giving up dividends costs little.
• You want to replace a stock position temporarily while keeping the same directional exposure.
• You want to compare the financing cost implied by option prices with the cost of buying shares on margin.

Max profit, max loss and breakeven

Maximum profit

Unlimited. Above the breakeven, profit equals the stock price minus the strike minus the net debit (or plus the net credit), times 100, and grows with no ceiling as the stock rises.

Maximum loss

Strike plus net debit (or minus net credit), times 100, if the stock falls to zero. That is limited in theory but comparable to the loss on owning the shares outright, so treat it as full stock risk.

Breakeven

Breakeven = strike plus net debit, or strike minus net credit if the combo was opened for a credit.

Synthetic Long Stock Greeks

• Delta: Delta is close to +100 per combo, because the call delta and the absolute put delta at the same strike add up to roughly one, so the position moves like 100 shares.
• Gamma: Gamma is close to zero, since the long call and short put at the same strike have nearly equal gamma that cancels.
• Theta: Theta is small, because decay on the long call is mostly offset by decay on the short put, with any remainder reflecting interest and dividends.
• Vega: Vega is close to zero, because the call and put vegas at the same strike largely offset each other.

See the live numbers for your position in the Greeks tab of the calculator, or explore a single option in the options Greeks calculator.

Early exercise and assignment risk

The short put is the leg to watch. If the stock falls well below the strike, the put becomes deep in the money, its time value shrinks, and the holder may exercise early to receive the strike price now and earn interest on it. Assignment means you buy 100 shares at the strike, so you need the cash or margin to hold them. Your position becomes real long stock plus an out of the money long call: the downside exposure is about the same, but the capital tied up is now much larger.

Dividends matter on both sides. A synthetic long never receives dividends, and option prices already discount the expected payouts, so the combo is not a free substitute for owning shares of a dividend stock. If the stock rallies and your long call goes deep in the money ahead of an ex dividend date, exercising it to collect the dividend can make sense when the dividend is larger than the call's remaining time value. Large special dividends usually trigger an OCC contract adjustment, but ordinary dividend changes do not.

The calculator's Early exercise risk tab flags short legs that are likely to be assigned. For a single option, use the early exercise calculator or read how early exercise and assignment work.

Pros and cons

How to manage a synthetic long stock

• Size the position as if you owned 100 shares per combo, not by the small net premium.
• Roll both legs together to a later expiration before the front month expires if you want to keep the exposure.
• Keep enough buying power to take delivery if the short put is assigned.
• Compare the combo's implied financing rate with your margin rate before choosing it over shares.

Synthetic Long Stock FAQ

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Educational tool, not financial advice. Calculations are theoretical and depend on your inputs; real fills, fees, early assignment and dividends can change results. Options involve risk and are not suitable for every investor.