CostOfCarry

The generalised Black-Scholes-Merton price for a European option under a lognormal underlying with a continuous cost of carry b:

d1 = (ln(S/K) + (b + sigma^2/2) T) / (sigma sqrt(T))
d2 = d1 - sigma sqrt(T)
call = S e^{(b-r)T} N(d1) - K e^{-rT} N(d2)
put  = K e^{-rT} N(-d2) - S e^{(b-r)T} N(-d1)

The single carry parameter recovers the whole vanilla family:

• b = r — Black-Scholes on a non-dividend stock;
• b = r - q — a stock or index with continuous dividend yield q (GeneralizedBsm);
• b = r - r_f — an FX rate with foreign rate r_f (GarmanKohlhagen);
• b = 0 — an option on a forward or futures price (Black76).

This class exposes the raw price function; the public wrappers add the AnalyticGreeks for their own parameterisation (which fixes how the carry moves with r).