## Understanding the Option Greeks

### What are Option Greeks?

Delta, Gamma, Vega, and Theta

### What do they do?

Option Greeks measure the sensitivity of an option contract’s price relative to the underlying’s performance and time.

More importantly, the Option Greeks measure the risk of a contract and almost exclusively how the option contract is priced.

### What is Delta?

Delta measures the sensitivity of change in the underlying’s price to the change of the option contract’s price relative to expiration. Put very simply, Delta represents the probability that the contract will become profitable before and at expiration.

If a put option contract has a Delta of 0.30, it means it has a 30% chance of becoming profitable before and/or at expiration.

Another thing to consider is how the price of the underlying affects the Delta of a contract.

If our put option contract has a Delta of 0.30 and the price of the underlying decreases by \$1 then the total value of the contract will increase by \$0.30.

### What is Gamma?

Gamma is the rate of change for an option’s Delta based on a single-point move in the Delta’s price. In other words, if the Gamma on our put contract is 0.05 and the underlying’s price decreases by \$1, then our contract will increase by \$0.05 value.

I like to think of Gamma as the bonus multiplier. For every \$1 increase or decrease to the underlying’s price, Gamma will increase or decrease the value by the Gamma value on the contract.

Gamma is often the highest At-The-Money (ATM) and tapers off in either direction. That is because the rate of change for an option’s Delta based on a single-point move in the Delta’s price is expected to be greatest ATM.

Another important thing to consider is how Gamma changes over the life of the contract. Gamma tends to increase as we get closer to expiration and the reason why is because the sensitivity of change increases greatly the closer we get to expiration.

Put simply, if the price of the underlying is at \$300, we would expect a larger trading range 30 days from now vs 7 days from now. Therefore, the Delta, or sensitivity to change should be sharper 7 days from now vs 30 days from now. Because of this the Gamma will be higher the closer we get to expiration.

Gamma is one of the most important factors for an options price and as we’ll get in to, Short Gamma is one of the most telling factors to gauge expected trading ranges on expiration.

### What is Vega?

Vega is the measurement of an option’s price sensitivity to changes in the volatility of the underlying asset. It measures the amount that an option contract’s price changes in reaction to a 1% change in the implied volatility of the underlying asset.

### What is Implied Volatility?

Implied Volatility represents the perceived market forecast for the security’s price. It is the most important factor to pricing an option and the biggest unknown factor since volatility is ever changing.

### So how does Vega affect an Option Price?

This is where it gets a little complicated as we use Vega and Implied Volatility to calculate the change in price of an option contract.

For our Put contract with a Delta of 0.30 and Gamma of 0.05, if the Vega on the contract is 0.20 and the IV is 25% we can calculate the change in the Option Contract price based on Vega.

Let’s say Implied Volatility increases from 25% to 30% while the underlying’s price stays the same. Then the value of the contract should increase by (5 x 0.20) since there was a 5% increase to IV and the contract has a Vega of 0.20. So, if the Put Option Contract trades at \$1.50 and we have a 5% move to IV while the underlying remains the same, the new price should be \$1.50 + (5 x 0.20) = \$2.5.

Something else to consider is that contrary to Gamma, Vega tends to decrease the closer we get to expiration. That is, Vega 7 days from now should be less than Vega 30 days from now. This is because Implied Volatility, or the market’s perceived forecast, leads to a greater trading range 30 days from now vs 7 days from now.

### What is Theta?

Theta refers to the rate of decline in the value of an option due to the pass of time. Since Option Contracts are decaying assets, the total value of the Option Contract will decrease in value the closer we get to expiration.

Theta is our best friend as Option Sellers because it is the amount we can expect the contract to decay every day we hold the Option Contract short.

For our put contract, let’s say the Theta on the contract is 0.10 and we have 30 days to go until expiration. If we paid \$1.50 for the contract and price of the underlying remained neutral for 5 days, we would expect the value of the Option Contract to have decreased by \$0.50 (0.10 x 5).

Another important thing to consider is that Theta increases exponentially the closer we get to expiration. This is because the closer we get to expiration, the chance of the contract becoming profitable is running out rapidly. As we get closer to expiration, the Delta ranges taper off as the expected trading range tightens. Therefore, the chance for the contract to make a drastic move 7 days before expiration is significantly less than 30 days before expiration.A