Generally, sensitivity analysis is an attempt to study how the price of an instrument responds in a change of one of the parameters which affect it. In options, first order sensitivity analysis studies the change in the price of a call or put if the value of one of the parameters that affect this price change.

First order Greek letters

Another phrase for sensitivity analysis is ”Greek letters” or ”Greeks” due to their symbols, which have been taken from the Greek alphabet. First order Greek letters measure the effect that a change in the value of various factors has in the price of the option. These factors and their corresponding Greek letters are:

1. Price of the underline security (Delta)

2. Volatility (Vega)

3. Time to maturity (Theta)

4. Interest rates (Rho)

Second and third order Greek letters

Second order Greeks measure the change of the first order Greeks relatively to a factor that affects them and third order Greeks measure the change of the second order Greeks relatively to a factor that affects them. The most important second order Greek is Gamma, which measures the change of delta relatively to a dollar change of the underline security. Our primary focus will be on the first order Greeks as they are more important.

Sensitivity factors are a good approximation of reality but not 100% accurate. They constantly changing due to the dynamic nature of financial markets. Their usefulness lies on the fact that they provide option traders with a measure of risk and benefit relatively to a certain options strategy. For example, $1 price advance in a stock will not cause an $1 advance in the price of an ATM call option but far less. We want to know the exact amount in order to have a clear view about the potential benefit if we are long calls or the potential risk of such an advance in the stock price if we are call writers.