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 OV1.
Copyright 2013 Hedgebook Ltd.