Digital Options Calculator

Concept:
Digital (binary) options pay a fixed amount if the option finishes in-the-money at maturity.

Pricing Formula:
$$V_\text{call} = e^{-rT} N(d_2), \quad V_\text{put} = e^{-rT} N(-d_2)$$

Where:
$$d_2 = \frac{\ln(S_0/X) + (r - 0.5\sigma^2)T}{\sigma \sqrt{T}}$$

Spot Price S₀: Strike Price X: Risk-Free Rate r (decimal): Time to Maturity T (years): Volatility σ (decimal):

Interpretation

The price is the discounted expected payoff under the risk-neutral measure.
Digital options are sensitive to volatility, spot price, and time to maturity.
Unlike vanilla options, delta is not used directly for pricing; instead, d₂ captures the probability of finishing in-the-money.

Black–Scholes assumptions apply: no arbitrage, frictionless market, lognormal underlying, constant volatility, and constant risk-free rate.
Payoff occurs only at maturity (European-style).
Continuous compounding is used for discounting.