Abstract
We present a model-independent method for calculating delta, vega and rho based on a comparison of the sensitivities of any derivative payoff with those of its underlying observables. In doing so, we obtain generic definitions for these greeks with an intuitive geometric interpretation. By means of examples, we show how our definitions reduce to standard formulae for familiar special cases. For pure delta hedging of quanto options, we show that the standard formula for delta should be corrected to account for the convexity adjustment in the underlying forward. Finally, by applying the technique to physical and cash-settled swaptions, we illustrate that a systematic approach for calculating delta and vega ensures that contributions from the annuity are captured in a consistent manner.
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