Due to the complexity of deriving a closed-from solution, the Greeks are evaluated by computing a discrete approximation of the partial derivative. That is, the option is revalued with a fractional change for each relevant parameter (e.g. Spot for Delta, Volatility for Vega, etc) and the change in the option value divided by the increment is the approximated Greek.

OV = option value.

OV₁ = option value derived from using the incremented parameter.

S = spot price of the underlying asset.

S₁ = S + I

I = an incremental change of 0.00001.

r = risk-free interest rate, expressed with continuous compounding.

r₁ = r + I.

b = cost of carry for the underlying asset, expressed with continuous compounding.

b₁ = b + I.

vol = volatility of the relative price change of the underlying asset.

vol₁= vol + I.

T = time to maturity measured in years (actual/365 basis).

T₁ = T - I.

= Delta of OV_1.