# Introduction to Options Greeks

While many highly mathematical textbooks have been written about Options Greeks, a trader does not have to be a mathematical genius to understand the basics of the Greeks. And such an understanding will greatly enhance any trader’s ability to trade options profitably.

There are five Greeks: Delta, Gamma, Rho, Theta and Vega. They were first identified by Professors Black and Scholes in their ground-breaking model for which they later received the Nobel Prize for economics.

The Greeks measure sensitivity of stock options to changes in a number of factors. We will briefly explain each one below.

**Delta **measures the rate of change in the price of an option in response to a $1 change in the price of the underlying trading asset, whether that be a share, currency or commodity. A Delta of 15% simply means that for every $1 increase in the price of the underlying asset, the option will increase in value by $0.15. A Delta of -15% or -0.15 conversely means that for every $1 drop in the price of the underlying, the option’s value will drop by $0.15.

At the Money options have a Delta of close to 0.5. The deeper In the Money an option becomes, the closer to 1 its Delta will move. Far Out of the Money options have a Delta of well below 0.5, which means they do not respond much to changes in the price of the underlying asset.

**Gamma **is related to Delta. It measures the rate of change in Delta for a $1 change in the price of the underlying asset. The Delta of an ATM option will for example be 0.5. Let us assume that this option has a Gamma of 0.20 or 20%. That means if the price of the underlying goes up by $1, the Delta of that option will go up by 20%.

**Theta **measures the rate of change in the price of an option in response to time decay. In laymen’s terms this simply means that for every day that passes, the value of an option will drop by an amount equal to Theta. An important fact to remember is that Theta also plays a role even when markets are closed, e.g. over weekends.

An option with a Theta of 0.20 will decline in value with $0.20 every day. This is why Theta is often called an option buyer’s enemy and an option seller’s friend.

**Vega **measures the effect of Volatility on the value of an option. An option with a Vega of 0.10 will become $0.10 more expensive if the implied volatility goes up by 1 percent. Theta is at its highest for At the Money options. Both In the Money and Out of the Money options have lower Theta rates.

Option buyers usually look for high Theta values and option sellers generally prefer options with low Thetas – unless they are trading on expectations of a so-called ‘volatility collapse’.

**Rho **measures movement in options prices as a result of changes in the risk-free interest rate. This variable usually does not play a significant role with short-term options, e.g. the new 1-week options. The longer the time until expiration, the bigger role Rho would play.

**Advanced:**

For those who want the complete formula for the Black-Scholes model and the Greeks:

C_{0} = S_{0}N(d_{1}) – Xe^{-rT}N(d_{2})

Where:

d_{1} = [ln(S_{0}/X) + (r + σ^{2}/2)T]/ σ √T

And:

d_{2} = d_{1} – σ √T

And where:

S_{0} = current stock price

C_{0} = current option value

X = exercise price

N(d) = the probability that a random draw from a standard normal distribution will be less than (d).

r = risk-free interest rate (annualized continuously compounded rate on a safe asset with the same maturity as the expiration of the option; usually the money market rate for a maturity equal to the option’s maturity.)

e = 2.71828, the base of the natural log function

ln = natural logarithm function

σ = standard deviation of the annualized continuously compounded rate of return on the stock

T = time to option’s maturity, in years