Work out options premium (black scholes) instantly with clear inputs, formula shown and shareable results.
Black-Scholes prices an option as the discounted expected payoff under a lognormal price distribution, using a 6% risk-free rate here. The premium splits into intrinsic value — what it is worth exercised now — and time value, which decays to zero at expiry.
Black-Scholes
C = S·N(d₁) - Ke^(-rT)·N(d₂), d₁ = [ln(S/K) + (r + σ²/2)T]/(σ√T)
Figures are estimates for planning only. Market returns are not guaranteed, and rates, limits and tax rules change. This is not financial or tax advice — speak to a qualified adviser before acting.
It is the only input not directly observable, and the premium is highly sensitive to it — which is why options are quoted in volatility terms.
It assumes constant volatility, no jumps and continuous hedging. Real markets violate all three, hence the volatility smile.