Expires at the strike
Spot finishes at the 100 strike. The put expires worthless and you lose the premium. That premium is the maximum loss.
- Expiry P&L
- −10
- Implied vol (from 10)
- 26.51%
Long Put Calculator
A long put is the right to sell at a fixed strike. This long put calculator charts the expiry payoff, the breakeven, and live P&L before expiry.
The most you can lose is the premium. The put pays off if the underlying falls below the strike. Click Calculate to solve implied vol, then use the sliders. Figures are theoretical and for information only. For a bullish view, open the long call calculator.
Type a symbol, then Load or leave the field. Spot, ~30-day historical realized vol, and a US risk-free proxy are filled when the ticker is found. Strikes and target are recentered near the new spot.
Delayed/free data. Historical realized vol is not implied vol from an options chain. Not investment advice.
New Option Price:
What a long put is
A long put is the purchase of a put option. You pay a premium up front for the right, not the obligation, to sell the underlying at the strike price. At expiry the put is worth the greater of strike minus spot, and zero. Your profit is that amount minus the premium you paid, times the number of options.
This long put calculator opens with Type set to Long Put. Spot 100, strike 100, premium 10, rate 1%, and 365 days are the defaults — the same market as the long call page, so you can compare the two payoffs. Click Calculate to solve implied volatility, then move the sliders to reprice the put before expiry.
How the long put payoff is calculated
At expiry the chart uses the put payoff minus the premium. Before expiry, the sliders reprice the same vanilla Black-Scholes put used on the option calculator and subtract the original premium.
Expiry P&L = Q × [max(K − S, 0) − V]
- V — premium paid per put
- K — strike
- S — underlying price at expiry
- Q — quantity (positive long)
- Breakeven: S = K − V
- Max loss: Q × V. Max gain: Q × (K − V), if the underlying goes to zero.
- Live P&L = Q × (new Black-Scholes put − V), using the slider spot, remaining time, and implied vol. Remaining time stays in the unit chosen at Calculate (days or minutes).
After you click Calculate, implied volatility is solved from V with the same bisection as the implied-vol page, rounded to two decimals. Default inputs (put, V = 10, S = K = 100, 1% rate, 365 days) imply 26.51%. The matching long call at a premium of 10 implies 23.97%, because a positive interest rate makes the at-the-money call worth more than the at-the-money put.
Worked examples
These expiry P&L figures use the same payoff the chart draws for a one-lot long put with premium 10 and strike 100. Type those defaults, leave Type on Long Put, and the line should pass through these points.
Breakeven at 90
Put payoff is 10, which exactly offsets the 10 premium. Below 90 the long put is profitable.
- Expiry P&L
- 0
- Breakeven
- K − V = 90
Spot at 70
Intrinsic is 30, net of the 10 premium. If spot went to zero the put would pay 100, and profit would be 90: strike minus premium.
- Expiry P&L
- 20
- Max gain (spot at 0)
- 90
When to use a long put
A long put fits a view that the underlying will fall below the breakeven before expiry, when you want the loss on the option capped at the premium. Holders of the shares sometimes buy a put as insurance: the put sets a floor near the strike, and the premium is the cost of that floor. This page charts the put on its own, not the shares plus the put.
- You want a payoff that grows as the price falls, down to a maximum of strike minus premium if the underlying goes to zero.
- You know the most the option itself can lose: the premium times quantity.
- A strike further below the market is cheaper and needs a larger drop to break even.
If the view is that the price will rise, use the long call calculator. If you expect only a modest drop, a bear put spread on the options spread calculator costs less and caps the gain. A straddle is the chart for a large move when you do not pick a direction. Invert a market price first with the implied volatility calculator if you have a quote and want the vol this page will solve.
Related calculators on this site
The long call is the other single-option purchase. A put spread caps both sides. Implied vol is the same solver this page uses after Calculate.
Long put FAQ
A long put is a purchased put. You pay a premium for the right to sell the underlying at the strike. If the put expires unused, the most you lose is the premium. The seller of the put is the short side, charted on the short put page.
For each underlying price on the x-axis, expiry P&L is quantity times (max(strike − spot, 0) minus premium). That is the grey payoff line at maturity. The coloured line is the live Black-Scholes P&L from the sliders.
Breakeven at expiry is strike minus premium. On the default inputs (premium 10, strike 100) that is 90. At that spot, expiry P&L is zero. Above 90 you have not earned back the premium.
Maximum loss is the premium times quantity: 10 on the one-lot default. Maximum gain, if the underlying goes to zero, is quantity times (strike minus premium): 90 on the defaults.
When you expect the underlying to fall below the breakeven, or you want insurance on shares you already hold. This chart is the put by itself, not the shares plus the put. A bear put spread on the options spread calculator costs less if you only expect a modest drop, and it caps the gain.
The same premium of 10 is inverted on a put, not a call. With a positive interest rate the at-the-money call is worth more than the at-the-money put, so a price of 10 implies 23.97% on the long call and 26.51% on the put. The solver is the same bisection as the implied volatility calculator. The price has to sit strictly above intrinsic or the search stops.
Disclaimer: the contents of this website are for informational purposes only and do not constitute any investment recommendation. The visitor acts at his own risk.