What are the option Greeks?

By , CEO of Volcube.

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The Greeks are a collective set of risk metrics that give us information about the risk to an option or to an option portfolio. Many of these Greeks have well-known names, such delta, vega, gamma and theta. Others such as vomma and vanna are less well-known, but are still useful for option risk management.

Let’s consider what the option Greeks really mean by considering an analogy. Imagine you have just bought a shiny new car. This car is an asset and it has a value. So what is your risk as the owner of the car? Your risk is that its value declines. Now, what might cause this to happen? Lots of factors. The mileage you drive for example. The more miles you put on the clock, the less the car is worth. What about the car simply getting older? Generally, older cars are worth less than newer cars, so as time passes, your car will lose value. What about the price of fuelling the car? If gasoline/petrol rise in price, cars in general may be less attractive compared to say bicycles or taking the train. There are many factors like this that affect the value of your car and you could maybe come up with a formula that tells you how each of these factors would affect the value. For example, maybe your car loses $1000 in value for every 25,000 miles you drive? That’s a useful metric if you are concerned about the ‘risk’ to the value of your car from driving it.

For options, the Greeks serve a similar purpose. The basic Greeks tell you how much your options will alter in value when something else changes. For example, option delta tells you much an option’s value alters when the underlying product price changes. Do you see how this compares to the car value ‘Greek’ that tells us the change in the car’s value for a change in the car’s mileage? Another basic option Greek is the vega which tells us how much the option value changes for a change in the level of implied volatility (another factor that affects option value).

The basic, or 1st order, Greeks tell us how option value changes for a change in one of the factors that affects option values. However, there are plenty of other useful Greeks. What do they do? Well 2nd order or higher order Greeks tell us how other option Greeks change when something else changes. What does this mean? Think about the car ‘mileage Greek’ again which told us the car lost $1000 for every 25,000 miles driven. What if this mileage Greek changed depending on the miles the car had already driven? So maybe it is $1000 for the first 25,000 miles, but increases to $2000 for the next 25,000 miles and then increases again to $3000 for the next 25,000 miles etc etc. What we are saying here is that the mileage Greek is not a constant; it is affected by the miles driven. Similarly with options, the basic Greeks such as delta and vega might not be constant numbers. Rather, they can (and do) change when something else changes. The higher order Greeks tell us by how much the lower order Greeks change when something else changes. For example option gamma tells us by how much an option’s delta changes when the underlying product price moves. So we have a hierarchy of Greeks. We have our option value and then an option Greek that will tell us how this value changes when a certain factor changes. Then we have a higher order Greek telling us how much the lower order Greek changes when the same (or even a different) factor changes.

OPTION VALUE

1st ORDER GREEK : Says how option value changes for a change in a risk factor.

2nd ORDER GREEK : Says how 1st order Greek changes for a change in a risk factor.

3rd ORDER GREEK: Says how 2nd order Greek changes…etc

So how are the option Greeks useful? Well, primarily they are used for hedging as well understanding the amount of risk an option trader has. He can use his portfolio delta for example to tell him how to delta hedge and become delta neutral, thus ‘eliminating’ the delta risk to the portfolio. The portfolio gamma then tells us by how much the portfolio delta is going to change when the price of the underlying changes. So the delta Greek gives one risk metric and the gamma Greek shows how this delta Greek could change. Also, if the trader knows how much his option portfolio will change in value for a change in some factor or other, then if he has an opinion about this other factor, he has a handle on the amount of risk. For example, the vega of the portfolio tells the trader how much his portfolio will change in value if implied volatility changes. So if the trader has a good idea of how much the implied volatility is likely to move, then through the vega he knows how much in $ his portfolio’s value is likely to change. In other words, he can quantify his risk that is due to changes in implied volatility, because he knows the portfolio vega. Nice!

In summary, option Greeks help option traders to quantify their option risk, which means telling them how the value of their options will change when certain other things change. They also tell them how these risk measures themselves will change. There is precious little about options that is constant and this is half the fun! Understanding option Greeks is fundamental to learning to trade options effectively and of course Volcube’s option market simulator is a great place to begin.

 Read more Volcube option articles here

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Volcube is an options education technology company, used by option traders around the world to practise and learn option trading techniques.

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