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# 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.

Theta (θ) is a measure of the sensitivity of the option price relative to the option’s time to maturity. If the option’s time to maturity decreases by one day, the option’s price will change by the theta amount. The Theta option Greek is also referred to as time decay.

##### Formula for Theta

Where

∂ – the first derivative

V – The option’s price (theoretical value)

τ – The option’s time to maturity

In most cases, theta is negative for options. However, it may be positive for some European options. Theta shows the most negative amount when the option is at-the-money.

Example

In March, a September option will have a daily time decay of .02. By August, the daily decay will increase to .06 and the option more quickly decays.

Time decay is not linear, and moreover, for ATM strikes decay continually accelerates into option expiration.

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.

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.”