ATM vanilla, 1 year
Spot 100, strike 100, 30% volatility, 1% rate, 365 days. This is the default form.
- Call price
- 12.368
- Put price
- 11.373
- Call delta
- 0.57273
0DTE options calculator
Same Black-Scholes calculator as the vanilla and binary option tool, opened in minutes for same-day expiry. The form starts at 390 minutes — one U.S. regular session of clock time (9:30–16:00) — not a multi-day tenor.
Spot, strike, volatility, the risk-free rate, and time to expiry are enough for a closed-form price. Time is calendar days by default, or minutes when you select that unit. Choose vanilla for the usual call or put payoff, or binary for a cash-or-nothing that pays one unit if the option finishes in the money. Figures are theoretical and for information only.
How the Black-Scholes price is calculated
Black-Scholes assumes the underlier follows a geometric Brownian motion with constant volatility and a constant risk-free rate, and that the option can be exercised only at expiry. There is no dividend yield in this implementation.
Time is a year-fraction T. In days (the default), T is days until expiration divided by 365, so 365 days is one year. In minutes, T is minutes divided by 365.25 × 24 × 60: calendar minutes in a mean Gregorian year, not a trading-session clock. Volatility and the risk-free rate are entered as percentages and converted to decimals. N is the standard normal cumulative distribution:
C = S N(d1) − K e−rT N(d2)
P = K e−rT N(−d2) − S N(−d1)
d1 = [ln(S / K) + (r + σ2 / 2) T] / (σ √T)
d2 = d1 − σ √T
- S — spot price
- K — strike price
- σ — volatility (decimal)
- r — risk-free rate (decimal)
- T — time to expiry in years (days ÷ 365, or minutes ÷ (365.25 × 24 × 60))
A cash-or-nothing binary that pays one unit if it finishes in the money uses the same d2 but a simpler payoff: the call is e−rT N(d2) and the put is e−rT N(−d2). Option prices are rounded to three decimals. Vega and rho are reported per one percentage point; theta is per calendar day.
Worked examples
These three cases use the same formula and rounding as the calculator above. Type the inputs in and you should get the same call and put prices.
ATM vanilla, 90 days
Same spot, strike, vol, and rate, but only 90 days to expiry. Less time means a lower premium.
- Call price
- 6.054
- Put price
- 5.808
- Call delta
- 0.53627
ATM vanilla, 390 minutes
Same spot, strike, vol, and rate, with the maturity unit set to minutes and 390 minutes left (one U.S. regular session). That is the 0DTE preset.
- Call price
- 0.326
- Put price
- 0.326
- Call delta
- 0.50199
ATM binary, 1 year
Same market as the first example, with type set to binary (cash or nothing). The payoff is one unit of cash, not the vanilla difference.
- Call price
- 0.449
- Put price
- 0.541
- Call delta
- 0.01308
Related calculators on this site
Black-Scholes is the closed-form equity-style case. FX options use two interest rates, implied volatility inverts the same vanilla formula, and the converter rescales a vol number before you type it in here. Path-dependent Asians and lookbacks, and a long call or put payoff chart, sit next to that vanilla engine.
Option pricing FAQ
It uses the Black-Scholes closed-form for a European call or put. Spot, strike, volatility, the risk-free rate, and time to expiry (days divided by 365, or minutes divided by 365.25 × 24 × 60) go into d1 and d2. The call is spot times N(d1) minus the discounted strike times N(d2). The put uses the complementary terms. Prices are rounded to three decimals, matching the results panel.
A vanilla call pays the difference between spot and strike if that difference is positive; a vanilla put pays the opposite difference. A cash-or-nothing binary here pays one unit of cash if the option finishes in the money, and nothing otherwise. The binary price is therefore the discounted risk-neutral probability of finishing in the money, not a share of the underlier.
European only. Exercise is assumed at expiry, which is what the Black-Scholes formula prices. Early exercise (American style) is not modelled, and there is no dividend yield on the underlier.
Put-call parity says call minus put equals spot minus the discounted strike. With a positive risk-free rate the discounted strike is below spot, so the call is slightly more valuable than the put at the same strike. The default one-year example (call 12.368, put 11.373) shows that gap.
Delta is the change in option value for a one-unit move in spot. Gamma is the change in delta for that same spot move. Vega and rho are scaled per one percentage point of volatility or rate. Theta is the change in value per calendar day. Call and put gamma and vega are the same for a vanilla option.
Choose days or minutes. Days are the default when the unit is left unset, and convert to a year-fraction by dividing by 365, so 365 days is exactly one year. Minutes use calendar time, not a trading session: divide by 365.25 × 24 × 60, the number of minutes in a mean Gregorian year. One calendar day is 1,440 minutes on that clock (1/365.25 year), which is close to but not the same as entering 1 day. There is no business-day calendar. Theta stays the change in value per calendar day in both modes.
Live quotes include bid-ask spreads, dividends, borrow, early-exercise premia, and a volatility smile that Black-Scholes (a single flat vol) does not capture. Rounding and the 365-day year can also differ. Figures here are theoretical and for information only.
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.