# The Greeks: From Past to Present by Tyler Curtis

by Tom Doan

When people mention the Greeks, images of Zeus, Athena, and Hercules may come to mind.  However, in the finance industry, the Greeks are a set of variables used as measures of risk sensitivity.  The Greeks consist of delta, theta, gamma, vega, and rho.  This article will provide an overview of each variable and what they represent.

Delta (∆) – Delta represents the price sensitivity of an option.  In other words, it is the rate which an option’s price changes as the underlying asset’s price increases \$1.  If a call option for XYZ has a delta of .6, then for every \$1 XYZ increases, the call option for XYZ will increase by \$.60.  The delta is also a rough estimate of the probability the option will expire in-the-money.  According to equal probability, there’s a 50% chance a stock will increase in value and a 50% chance a stock will decrease in value.  As a result, the delta will approach .5 as a call option approaches closer to the strike price.  In addition, as a call option nears expiration, in-the-money calls will approach a delta of 1 and out-of-the money options will move towards 0.  Since premiums for put options have an inverse relationship with the stock price, the delta is negative for put options.

Gamma (Γ) – This variable is a derivative of delta.  Gamma is the rate of which delta changes for each dollar the underlying stock increases.  If a long XYZ 30 call option has a gamma of .62, then the delta for the long XYZ 30 call will increase by .62 for each dollar XYZ increases.  Long options have a positive gamma and short options will have a negative gamma.

Rho (Ρ) – Rho measures the change in option value based on changes in interest rates.  For example, if an option has a rho of .1043, then for every 1% increase in the risk-free interest rate, the value of the option will increase by 10.43%.  Although in theory a risk-free investment does not exist, the three month U.S. Treasury bill is typically used as the risk-free interest rate in the finance industry.

Theta (Θ) – As expiration nears, the time value of an option declines.  Theta measures the rate of which an option’s value declines each day.  Since the last 30 days before expiration is when time value decreases at the greatest rate, the theta is usually highest during that time frame.  If an option has a theta of .3421, then with all other factors remaining the same outside of time, the option will lose \$.3421 per day.

Vega – Option premiums are heavily influenced by implied volatility.  When implied volatility of a stock changes, the value of the option associated with the stock also change.  Vega is a variable that shows the extent of which an option’s value will change for every percentage point change in implied volatility.  Since option sellers benefit from decreased volatility while option buyers benefit from increased volatility, a short call will have a negative vega and a long call will have a positive vega.  If a short XYZ 30 call has a vega of -.6719, then for every 1% increase in implied volatility for XYZ, the short XYZ 30 call will lose \$.6719.

The Greeks help us evaluate options and other derivatives by giving us data on its price, time, and volatility sensitivity.  Understanding these variables allow us to better evaluate how derivatives react as market conditions change.