The Greeks

It is important to understand the Greeks before taking an option position. I will explain each of these measures, and then I will touch on some aspects of their relationship to each other. Since the Greeks are actually represented by letters of the Greek language alphabet, let’s take them in alphabetical order.

Delta

Delta is a measure of the change in an option's price (premium of an option) resulting from a change in the underlying security (i.e., stock) or commodity (i.e., futures contract). The value of Delta ranges from –1 to 0 for puts and 0 to 1 for calls. Puts have a negative delta because they have what is called a "negative relationship" to the underlying: put premiums rise when the underlying rises, and vice versa. Call options, on the other hand, have a positive relationship to the price of the underlying: if the underlying rises, so does the premium on the call, provided there are no changes in other variables like implied volatility and time remaining until expiration. And if the price of the underlying falls, the premium on a call option, provided all other things remain constant, will decline. An at-the-money option has Delta a value of approximately 0.5, which means the premium will rise or fall by half a point with a 1 point move up or down in the underlying. For example, if an at-the-money wheat call option has a Delta of 0.5, and if wheat makes a 10-cent move higher (which is a large move), the premium on the option will increase approximately by 5 cents (.5 x 10 = 5), or $250 (each cent in premium is worth $50).

As the option gets farther in the money, Delta approaches 1 on a call and –1 on a put, which means that at these extremes there is a one-for-one relationship between changes in the option price and changes in the price of the underlying. In effect, at Delta values of –1 and 1, the option behaves like the underlying in terms of price changes. This occurs with little or no time-value, as most of the value of the option is intrinsic. I will come back to the concept of time-value below when we discuss Theta.

Three things to keep in mind with Delta: (1) Delta tends to increase as you get closer to expiration for near or at-the-money options; (2) Delta is not a constant, a concept related to Gamma, our next risk measurement, which is a measure of the rate of change of Delta given a move by the underlying; and (3) Delta is subject to change given changes in implied volatility.

Gamma

Gamma, also known as the first derivative of delta, measures the rate of change of Delta. Our presentation below shows how much Delta changes following a one-point change in the price of the underlying. This is a simple concept to grasp. When call options are deep out of the money, they generally have a small Delta. This is because changes in the underlying bring about only tiny changes in the price of the option. But as the call option gets closer to the money, resulting from a continued rise in the price of the underlying, the Delta gets larger

There are some additional points to keep in mind about Gamma:
(1) Gamma is smallest for deep out-of-the-money and deep in-the money options
(2) Gamma is highest when the option gets near the money; and
(3) Gamma is positive for long options and negative for short options

Theta

Theta is not used much by traders, but it is an important conceptual dimension. Theta measures the rate of decline of time-premium resulting from the passage of time. In other words, an option premium that is not intrinsic value will decline at an increasing rate as expiration nears.

Some additional points about Theta to consider when trading:
(1) Theta can be very high for out-of-the- money options if they contain a lot of implied volatility
(2) Theta is typically highest for at the money options
(3) Theta will increase sharply in the last few weeks of trading and can severely undermine a long option holder's position, especially if implied volatility, which we turn to next, is on the decline at the same time.

Vega

Vega, our fourth and final risk measure, quantifies risk exposure to implied volatility changes. Vega tells us approximately how much an option price will increase or decrease given an increase or decrease in the level of implied volatility. Option sellers benefit from a fall in implied volatility, and it's just the reverse for option buyers.

Additional points to keep in mind regarding Vega include the following:
(1) Vega can increase or decrease even without price changes of the underlying because implied volatility is the level of expected volatility
(2) Vega can increase from quick moves of the underlying, especially if there is a big drop in the stock market, or if there is a sudden upwards burst in a commodity like coffee after a reported frost in Brazil
(3) Vega falls as the option gets closer to expiration.