Write the Black-Scholes formula for a European call option: C = S·N(d₁) - K·e^(-rT)·N(d₂)

the Black-Scholes formula prices

Black-Scholes formula: C = S*N(d1) - X*e^(-rT)*N(d2), P = X*e^(-rT)*N(-d2) - S*N(-d1)

d₁ and d₂ are in Black-Scholes: d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T

d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T

put-call parity states: C - P = S - K·e^(-rT)

Call price (C) minus Put price (P) equals Stock price (S) minus Strike price (K) multiplied by exponential decay factor (e^(-rT))

Interest

Compound interest formula: A = P(1 + r/n)^(nt)

the Black-Scholes assumptions are

Black-Scholes assumes constant volatility, no dividends, log-normal prices, no transaction costs

Greeks (finance)

Greeks measure sensitivity of option prices to underlying parameters