Getting to Know the Greeks

An option's price can be influenced by a number of factors. These factors can either help or hurt traders, depending on the type of options positions they have established. To become a successful option trader, it is essential to understand what factors influence the price of an option, which requires learning about the so-called "Greeks" – a set of risk measures that indicate how exposed an option is to time-value decay, implied volatility and changes in the underlying price of the commodity. In this section, we'll look at four "Greek" risk measures - delta, theta, vega and gamma- and explain their importance. But first, let's review some related option characteristics that will help you better understand the Greeks.

The Greeks

Below are the four major risk measures – our so-called Greeks – all of which a trader should take into account before taking any option position.

  • Vega: Measures Impact of a Change in Volatility
  • Theta: Measures Impact of a Change in Time Remaining
  • Delta: Measures Impact of a Change in the Price of Underlying
  • Gamma: Measures the Rate of Change of Delta

Because 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). The value of delta ranges from -100 to 0 for puts and 0 to 100 for calls (here delta has been multiplied by 100 to shift the decimal). Puts have a negative delta because they have what is called a "negative relationship" to the underlying: put premiums fall 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 a delta value of approximately 50 (0.5 without the decimal shift), which means the premium will rise or fall by half a point with a one-point move up or down in the underlying. For example, if an at-the-money stock call option has a delta of 0.5, and if the stock goes up $1.00, the premium on the option will increase by approximately 50 cents (0.5 x 1.00 = .50), or $50 per contract (each contract controls 100 shares).

As the option gets further in the money, delta approaches 100 on a call and -100 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 -100 and 100, the option behaves like the underlying security in terms of price changes. This occurs with little or no time value, as most of the value of the option is intrinsic. We'll 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 fact related to gamma, our next risk measurement, which is a measure of the rate of change of delta given a move by the underlying.
  3. Delta is subject to change given changes in implied volatility.
  4. Delta can also be used to determine the market maker's probability of an option expiring in-the-money. That's why most options which are at-the-money have a delta of 50, meaning a 50% change of expiring in-the-money.

Gamma

Gamma, also known as the "first derivative of delta", measures delta's rate of change. 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. 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
  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 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.
  3. Vega falls as the option gets closer to expiration.

Conclusion

While this overview is only an intermediate-level discussion of delta, gamma, theta and vega (an advanced level analysis would involve mathematical nuances which are not practical in terms of trading), it should nonetheless help clarify not only how the price of an option is influenced by changes in the underlying, the time to expiration and the implied volatility, but also how we measure the impact of these variables on an option's price.

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