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

Chapter 14. Option Sensitivities: The 'Greeks'

INTRODUCTION

In Chapter 13 we saw that, according to the standard pricing model, the value of an option on a share is determined by five factors. (Appendix A shows how to set the model up on an Excel spreadsheet.)

• The spot or cash price of the underlying

• The strike or exercise price of the option

• Time to expiry

• The volatility of the underlying share

• The cost of carry – the interest rate to the expiry of the option less any dividend income received on the share over that period.

Dealers and investors in options are also interested in the sensitivities of the model. In other words, they are concerned with how changes to the inputs will affect the output value that is calculated. The sensitivities most commonly used in the market are known collectively as the 'Greeks': delta, gamma, theta, vega and rho. As vega is not actually a Greek letter, kappa is occasionally used instead. Technically speaking these 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, all other inputs remaining constant.

The most important of the 'Greeks' is the option delta. This measures the sensitivity of the option value to a given small change in the price of the underlying. A bought call has positive delta. This means that the value of the contract increases as the share price rises. To that extent it is rather like a long or 'bull' position in the underlying. ...