The mathematical characteristics of the Black-Scholes model are named after the greek letters used to represent them in equations.
These are known as the "Greeks". These Greeks measure the movement characteristics of every option contract traded in an exchange.
For the general investor and retail options trader, knowing the delta of your options position gives you an indication of how your options value will change with movements in the underlying stock price - all other variables remaining the same. Knowing your time decay (theta) gives you an indication of how much time value your option position is losing each day - all other variables remaining the same. Other measures are explained below.
The professionals use the Greeks to measure exactly how much they need to hedge their portfolio. The Greeks also enable the measurement of how much risk the portfolio is exposed to, and where that risk lies (with movements in interest rates or volatility, for example).
A by-product of the Black Scholes model is the calculation of delta: the degree to which an option price will move given a change in the underlying stock price, all else being equal. For example, an option with a delta of 0.5 will move half a cent for every one cent movement in the underlying stock.
A far out-of-the-money call will have a delta very close to zero; an at-the-money call a delta of 0.5; a deeply in-the-money call will have a delta close to 1.
Call deltas are positive; put deltas are negative, reflecting the fact that the put option price and the underlying stock price are inversely related. The put delta equals the call delta minus 1.
The delta is often called the neutral hedge ratio. For example if you have a portfolio of n shares of a stock then n divided by the delta gives you the number of calls you would need to write to create a neutral hedge - i.e. a portfolio which would be worth the same whether the stock price rose by a small amount or fell by a small amount. In such a "delta neutral" portfolio any gain in the value of the shares held due to a rise in the share price should be exactly offset by a loss on the value of the calls written, and vice versa.
Note that as the delta changes with movements in the stock price and time to expiration the position would need to be continually adjusted to maintain the hedge.
How quickly the delta changes with the stock price is given by gamma
The gamma of an option indicates how the delta of an option will change relative to a 1 point move in the underlying asset. In other words, the Gamma shows the option delta's sensitivity to market price changes.
Gamma is important because it shows us how fast our position delta will change as the market price of the underlying asset changes.
The Vega of an option indicates how much, theoretically at least, the price of the option will change as the volatility of the underlying asset changes.
Vega is quoted to show the theoretical price change for every 1 percentage point change in volatility. For example, if the theoretical price is 2.5 and the Vega is showing 0.25, then if the volatility moves from 20% to 21% the theoretical price will increase to 2.75.
Vega is most sensitive when the option is at-the-money and tapers off either side as the market trades above/below the strike.
To completely understand this, you will need to understand how stock options are priced and how volatility is factored into it.
Theta measures how fast the premium of an option decay with time. The nearer the expiration date, the higher the theta and the farther away the expiration date, the lower the theta.
To completely understand what the premium of an option is, you need to understand how stock options are priced.
Rho measures the sensitivity of an option or options portfolio to a change in interest rate.
For example, if an option or options portfolio has a rho of 12.124, then for every percentage-point increase in interest rates, the value of the option increases 12.124%.
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