AnalyticGreeks

A closed-form price and its first- and second-order sensitivities — the reference an adjoint Monte-Carlo run is checked against.

Sign conventions match BlackScholes and the gradient carrier EquityMarket:

• delta is dV/dS (spot delta of the primary underlying);
• gamma is d^2V/dS^2;
• vega is dV/dsigma, per unit volatility (not per 1%);
• theta is dV/dT, the derivative with respect to the time to expiry — the same convention as EquityMarket.maturity() as a gradient slot, so it is the negative of the calendar-time theta usually quoted in textbooks;
• rho is the total dV/dr in the pricer's own parameterisation (for a dividend-yield or foreign-rate model the carry moves with r);
• strikeSensitivity is dV/dK.

Every pricer in this package computes price in closed form and the six sensitivities by central differencing of that closed form (see Greeking); the differences carry no Monte-Carlo noise and only ~1e-7 truncation error, which is what makes the record usable as an oracle.