Option Greeks: Higher Order Sensitivities

While the basic greeks, delta, theta, vega, and rho describe the way in which an option price changes for changes in the basic input factors, there are other sensitivities which measure the relative change in the option value to changes in the greeks themselves. Gamma is technically one of these higher order sensitivities as it based on the change in delta. We explore some other higher order sensitivities, discuss the greeks when applied to the real world, and introduce the concept of shadow gamma.