AI-Explained Option Pricing

• Start with a quick demo scenario or enter your own parameters.
• Click Explain Option to calculate price and Greeks and generate an AI explanation.
• Review the Pricing Summary and Greeks on the right to understand the risk profile.
• Use the payoff chart and slider on the left to see how the option responds to moves in the underlying.
• Read the AI explanation as a narrative you can use with clients or stakeholders.

European Call Option (Black–Scholes)

C = S₀N(d₁) − K e^−rT N(d₂)

European Put Option (Black–Scholes)

P = K e^−rT N(−d₂) − S₀ N(−d₁)

d₁ and d₂

d₁ = [ln(S₀/K) + (r + ½σ²)T] / (σ√T)
d₂ = d₁ − σ√T

Where

• S₀ = current underlying price
• K = strike price
• r = risk-free rate (continuous)
• T = time to maturity (years)
• σ = volatility
• N(·) = standard normal CDF

Equity options use Black–Scholes; futures options apply Black–76 conventions.

Core Greeks (under Black–Scholes)

• Delta (Δ) — Call: Δ = N(d₁), Put: Δ = N(d₁) − 1
• Gamma (Γ) — Γ = N'(d₁) / (S₀ σ √T)
• Vega — Vega = S₀ N'(d₁) √T
• Theta (per year) — Call and put formulas use combinations of N(d₁), N(d₂), r, and σ
• Rho (ρ) — Sensitivity of option value to a 1-unit change in interest rate r