##

#### Option Greeks

Option prices are driven by multiple variables including changes in the underlying price, interest rates, passage of time, and changes in the expected volatility in the market. Collectively, these are called “the Greeks” because the symbols used to represent the sensitivities of these complex derivatives come from calculus and use the Greek Alphabet. Gain a basic understanding of how “the Greeks” are integral to managing a portfolio of options.

Futures contracts can be an effective and efficient risk management or trading tool. Their performance is basically two-dimensional, either you are up money or down depending on the entry price point and whether the market is up or down versus your position.

But with options on futures there are more dimensions, or forces, acting on the price or premium of the option.

There are metrics to measure each of these different impacts on the premium of an options. These metrics are often referred to by their Greek letter symbols and collectively as “the greeks.”

Let’s look at one of the most commonly used Greeks – Delta.

**Delta**

Delta is the change in the option’s price or premium due to the change in the Underlying futures price.

It is some portion of the movement of the underlying. Delta is a percentage measure.

Assume, we have a call option priced at 1.00 and it has a .50 delta. This means whatever the change of the underlying future is, the option will move by 50% of that change. Our underlying futures product moved from 96 to 97.5. This is a 1.5 point move. So, our option’s premium will now change by 50% of 1.5 or .75. Making the option’s new price 1.75

Calls always have positive delta between 0 and 1.00, while puts always have negative delta between 0 and -1.00.

The delta of a futures contract is 1.00.

Traders usually refer to the delta without the decimal point. So, a .40 delta is commonly referred to as a 40 delta.

Being Long a call will result in positive Delta; being short a call results in negative Delta. Conversely, being Long a put results in negative Delta; being short a put results in positive Delta. The absolute value of the Delta also tells the approximate probability that the option will finish in-the-money.

For example, if the option has a delta of 20 it suggests it has a 20% chance of finishing in-the-money. A delta of 50 suggests it has a 50-50 chance of finishing in-the-money.

If an options delta is less than 50 it is said to be out of the-money. If the delta is greater than 50 the option is said to be in-the-money. If the delta is equal or close to 50 the option is said to be at-the-money.

The delta is used in calculating hedge ratios to establish a neutral or delta hedged position using the underlying futures. Let’s say we sold 8 call options that have a 25 delta, we have a delta position of -200. To be delta neutral, we need to buy 2 underlying Futures contract.

Delta is dynamic and changes with movement in the underlying. That means delta neutral ratios and other hedge ratios using options are also dynamic and change too.

Futures contracts can be an effective and efficient risk management or trading tool. Their performance is basically two-dimensional, either you are up money or down depending on the entry price point and whether the market is up or down versus your position.

But with options on futures there are more dimension, or forces, acting on the price or premium of the option.

There are metrics to measure each of these different forces impacts on the premium of an options. These metrics are often referred to by their Greek letter and collectively known as the Greeks.

**Gamma**

We discussed previously that delta is the change in the options price or premium due to the change in the underlying futures contract price.

We will now discuss how delta itself changes with a change in the underlying futures price. This is known as gamma. Think of gamma as the delta of the delta.

Look at it a different way; you are driving a car at 30 miles per hour (mph). If you increase your speed to 40 mph, you have accelerated by 10 miles per hour. If you think of speed as your delta, then the change in your speed is your gamma. In other words, gamma is your acceleration.

Understanding Gamma Movements

Gamma is usually expressed as a change in the delta per one point change in the price of the underlying.

For example, if the futures price is 200, a 220 call has a delta of 30 and a gamma of 2.

If the futures price increases to 201, the delta is now 32. Conversely, if the futures price decreased to 199, the delta is 28.

Just like delta, gamma is dynamic. It is the highest when the underlying price is near the option’s strike price.

As the underlying moves away from the strike price, the gamma decreases. As the underlying moves towards the strike price, the gamma increases.

At the money options have the highest gamma, because their deltas are the most sensitive to underlying price changes.

Futures contracts can be an effective and efficient risk management or trading tool. Their performance is basically two-dimensional, either you are up money or down depending on the entry price point and whether the market is up or down versus your position.

But with options on futures there are more dimensions, or forces, acting on the price or premium of the option.

There are metrics to measure each of these different forces impacts on the premium of an option. These metrics are often referred to by their Greek letter, and collectively known as “the Greeks.”

**Theta**

Delta and gamma measure the effect of price movement of the underlying on the option premium. As we demonstrated in previous videos, both are dynamic as to the option being out-the-money (OTM), at-the-money (ATM), or in-the-money (ITM).

Now we will investigate the effects of time on an option. The Greek that measures an option’s sensitivity to time is theta. Theta is usually expressed as a negative number. Be careful to always make sure what time is referenced in the model you are using.

For example, if the value of an option is 7.50 and the option has a theta of .02. After one day, the option’s value will be 7.48, 2 days 7.46. etc.

Theta is highest for at-the-money (ATM) options and lower the further out-the-money or in-the-money the option is. The absolute value of theta of an option that is at- or near-the-money rises as the option approaches expiration. Theta for an option that is deep in- or out- the-money falls as the option approaches expiration.

In the prior example, theta was a constant value of .02 for all three days. In reality, the theta loss increases as the option approaches expiration.

**Vega**

Vega is the Greek that measures an option’s sensitivity to implied volatility.

It is the change in the option’s price for a one-point change in implied volatility. Traders usually refer to the volatility without the decimal point.

For example, volatility at 14% would commonly be referred to as “vol at 14.”

Volatility should not be confused with Vega. Volatility is either the historical or expected bounciness of the underlying future. Historical volatility is volatility in the past and is therefore known. Expected volatility is unknown volatility in the futures contract that feeds into the option price as implied volatility.

Whereas, Vega is the sensitivity of a particular option to changes in implied volatility.

For example, if the value of an option is 7.50, implied volatility is at 20 and the option has a Vega of .12.

Assume that implied volatility moves from 20 to 21.5. This is a 1.5 volatility increase. The option price will increase by 1.5 x .12 = .18 to 7.68.