Options 2.0 – Part 4. Options Greeks.

The original column has been published in Dutch on July 18 at Telegraaf's DFT.nl / Goeroes / Opties 2.0 – deel 4. De Optie Grieken

The Greeks

In my previous article of July 18th, "The Valuation of Options", you read about the influence of the basic attributes and changing parameters that affect the formation of an option’s premium. Today I’m going to explain the Greeks.

But, first things first. Before we begin with the Greeks, let’s look at Moneyness.

Moneyness

Moneyness is a term that is frequently associated with options. Moneyness indicates the extent to which an option has intrinsic value.

There are three stages of moneyness:

• In-The-Money (ITM)

• At-The-Money (ATM)

• Out-Of-The-Money (OTM)

In-The-Money (ITM)
A Call option is in-the-money if the market price of the underlying asset is higher than the strike price of the Call option.

A Put option is in-the-money if the market price of the underlying asset is lower than the strike price of the Put Option.

These in-the-money options have both an intrinsic value plus a (limited) expected value.

At-The-Money (ATM)
An option is at-the-money if the market price of the underlying asset is (approximately) equal to the strike price of the option. This applies to both Call and Put options.

So, these at-the-money options have (virtually) no intrinsic value, but (almost) exclusively an expected value. At-the-money options have the highest expected value.

Out-Of-The-Money (OTM)
A Call option is out-of-the-money if the market price of the underlying asset is lower than the strike price of the Call option.

A Put option is out-of-the-money if the market price of the underlying asset is higher than the strike price of the Put option.

These out-of-the-money options have no intrinsic value, but rather an expected value only.

This completes our brief explanation of an option’s moneyness. It’s been conveniently summarised in the table below:

Now, moving swiftly onto the Greeks. What are they exactly? And how can I, as an option’s investor, make best use of them?

Options Greeks

Options are sensitive to changes in parameters that affect premium formation (please refer to my previous article). What makes this even more interesting, is that with options, you can actually calculate these sensitivity factors. This means that you can look ahead and analyse how an option’s value will react to certain changes in the parameters that affect premium formation.

We call these sensitivity factors the Greeks. They are:

- Delta

- Gamma

- Theta

- Vega

- Rho

I’ll take you through these Greeks one by one. And I’ll demonstrate what they can do for you. Of course, it‘s this latter point that’s counts, as after all, you’ll want to know "what's in it for me?"

Delta
Delta indicates the sensitivity of an option to a change in the price of the underlying asset.

A more simple definition is, that the Delta of an option represents the theoretical change in the option’s value if there is a point change in the price of the underlying asset.

For example:

Share XYZ is written at 52.0. Option XYZ has a value of 4.50 and a Delta of 0.62.

The Delta indicates that if share XYZ has as a one point increase, say from 52.0 to 53.0, then the value of the Delta option will also change. So, from 4.50 with 0.62 it increases to 5.12.

Call Delta
Call options have a positive Delta. Call options are worth more as the price of the underlying asset increases.

A Call option’s Delta is between 0 and 100.

A deep in-the-money Call option has a Delta of 100. These move almost 1:1 with a price change in the underlying asset.

An at-the-money Call option has a Delta of around 50. These move by around 0.50 with a 1.0 point increase in value.

A far-out-of-the-money Call option has a Delta of approximately 0. This barely moves with a price change in the underlying asset.

Put Delta

Put options have a negative Delta. Put options are worth more as the price of the underlying asset decreases.

A Put option’s Delta is between 0 and -100.

A deep in-the-money Put option has a Delta of -100. These move almost 1: -1 with a price change in the underlying asset.

An at-the-money Put option has a Delta of around -50. These move about 0.50 with a 1.0 point price drop.

A far-out-of-the-money Put option has a Delta of approximately -0. These barely move with a price change in the underlying asset.

How can I make use of Delta?

The added value of Delta is that it actually allows you to predict the price of an option, should the price of the underlying asset change!

This is a tremendous help when you are presented with an options screen that offers a dizzying selection of hundreds of options series. By looking at the Delta per option series, you'll gain a valuable insight into how the option will react to a change in the underlying asset. So, essentially you can look into the future. You need to consider this before you start investing in options.

Note that there is also a difference in the Delta’s of options with the same strike price but different maturities.

The back of a cigarette packet calculation

We can calculate this on the ‘back of a cigarette packet’ in the following way. Suppose that share XYZ is written at 52.0. You expect the price of XYZ to reach 54.5, which is an increase of 2.5 points. On the back of your cigarette pack, you can therefore multiply the Delta by the 2.5 price difference. Suppose an option with a value of 4.50 has a Delta of 0.62. By using the same cigarette packet method, the option will increase in value by 2.5 x Delta = 2.5 x 0.62 = +1.55. So, from 4.50 it increases by 1.55 to 6.05.

You can calculate various options quickly and easily using this simple technique. And ultimately select your desired option.

But be careful. Delta is not a flat, straight line. This ‘back of a cigarette packet’ method is not exact, although it does provide a good indication.

If you need a more precise calculation, then use an online Options Calculator.

Gamma

Gamma indicates the sensitivity of an option’s Delta to a change in the price of the underlying asset. Gamma is the derivative of the Delta.

A more simple definition is, that the Gamma of an option reflects a theoretical change in the option’s Delta value if there is a 1 point change in the price of the underlying asset.

For example:

Share XYZ is written at 52.0. Option XYZ has a value of 4.50, a Delta of 0.62 and a Gamma of 0.04.

The Gamma indicates that if share XYZ has a one point increase, say from 52.0 to 53.0, the Delta value of the Gamma option will also change. So, from 0.62 with 0.04 it increases to 0.66.

Gamma always has a positive value.

Theta
Theta indicates the sensitivity of an option to a change in the maturity of the option.

A more simple definition is, that the Theta of an option indicates the theoretical change in the option’s value when the remaining term of the option decreases by 1 day.

For example:

Share XYZ is written as 52.0. Option XYZ has a value of 4.50 and a Theta of -0.02.

The Theta indicates that, as the maturity decreases by 1 day, the value of the Theta option will also change. So, from 4.50 with -0.02 it decreases to 4.48.

Theta always has a negative value. An option loses expected value every day. As the remaining maturity decreases per day, so the Theta increases and the option’s value decreases. Right up until expiration, when an option will only have intrinsic value.

Vega
Vega indicates the sensitivity of an option to a change in the Volatility of the option.

A more simple definition is, that the Vega of an option reflects the theoretical change in the option’s value if there is a 1 percent point change in the option’s Volatility.

For example:

Share XYZ is written as 52.0. Option XYZ has a value of 4.50, a Volatility of 33% and a Vega of 0.10.

The Vega indicates that if the Volatility increases by 1 percentage point, say from 33% to 34%, the value of the Vega option will also change. So, from 4.50 with 0.10 it increases to 4.60.

Vega always has a positive value. The Vega of both Call and Put options, with the same maturity and strike price, is equal. As the option’s maturity decreases, the Vega becomes smaller.

Rho
Rho indicates the sensitivity of an option to a change in interest rates.

A more simple definition is, that the Rho of an option represents the theoretical change in the option’s value if there is a 1 percent point change in interest rates.

For example:

Share XYZ is written as 52.0. Option XYZ has a value of 4.50 and a Rho of 0.06. The interest rate is noted as 0.7%.

The Rho indicates that if the interest rate increases by 1.0 percentage point, say from 0.7% to 1.7%, then the Rho option’s value will also change. So, from 4.50 with 0.06 it increases to 4.56.

In the case of Call options, Rho has a positive value. With Put options, Rho has a negative value. As the option’s maturity decreases, so the Rho becomes smaller and heads towards zero.

This completes our explanation of Options Greeks. It’s conveniently summarised in the table below:

Options ... Basic Option Strategies

In this article we have outlined what the Greeks can do for you, as an options investor. We can now look ahead and, within reason, predict the future behaviour of options prices. In the next article we’ll cover basic options strategies. In other words, how we can cleverly combine options and what the advantages and drawbacks of this are.

Herbert Robijn is founder and director of FINODEX (www.finodex.com). FINODEX develops innovative online investment tools for private equity and options investors. These cutting-edge tools allow investors to make a comprehensive market analysis, complex calculations and appropriate selections, at just the touch of a button.