Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition

15

Option Sensitivities: The ‘Greeks’

INTRODUCTION

Chapter 13 showed that, according to the Black-Scholes pricing model, the value of a European option on a share is determined by only five factors. The model inputs and the output are shown again in Figure 15.1.

Users of options are also interested in the sensitivities of the model. In other words, they are concerned with how changes to the inputs to the model affect the output value that is calculated.

This is what the ‘Greeks’ delta, theta, vega (or kappa) and rho measure. Technically speaking, they are partial derivatives of the option pricing model. This means that they measure the change in the calculated option value for a given change in one of the inputs to the model, all the other inputs remaining constant.

The most important ‘Greek’ is the delta. It measures the sensitivity of the option value to a small change in the price of the underlying. However, as discussed in Chapter 13, delta is not just a sensitivity number. It tells a dealer how much of the underlying to trade to hedge the risks involved in taking an option position.

Chapter 13 also showed that delta is not a constant. Given this fact, traders also use a ‘second-order’ Greek called gamma. This measures the change in delta for a given change in the spot price of the underlying.

DELTA (Δ OR δ)

Delta measures the change in the option value for a small change in the price of the underlying asset, assuming all other inputs to the model are held constant. ...