# Put Theta in Binary Options – Definition & Example

Put Theta in binary options is the rate at which the price of a put option in binary trading decreases each day until expiry. It indicates the first derivative of the fair value of binary put options with respect to a change in time to expiration.

Put Theta in a nutshell

• Put Theta measures the daily decline rate of binary put option prices until expiry.
• Trading binary puts involves considering changes in theta position relative to the option’s moneyness and expiration.

## Understanding Put Theta in Binary Options

Put Theta is a ratio that describes the difference in the fair value of put options due to a time change. The Theta of binary put options is negative when they are out-of-the-money and positive when they are in-the-money, just like the Theta of binary call options. Time to expiration significantly impacts the absolute value of the Theta, with very short-term options having theta values well above the amount of premium that can genuinely devalue.

The Theta decreases rapidly as expiration approaches, often peaking as low as 0.5 ticks for 25-day binary put options. Across the spectrum of implied volatility, the Theta of binary put options typically maintains a fairly constant absolute value. However, the high and low values of the options approach the strike price as implied volatility decreases. This enlarges the probability that the binary option will expire at 0 or 100.

## Calculation of Put Theta in Binary Options

Put Theta, denoted as Θ, represents the rate of change in the price of a put option concerning time decay. The formula for Put Theta can be expressed as:

Where:

• Θ: Put Theta
• V: Price of the put option
• t: Time until expiration

### Example

Imagine you hold a binary put option for a binary asset with a strike price of \$100 and an expiration time set 30 days from now. The Theta for this option is -0.03. Now, if we’re five days into the option’s life, applying the Theta value tells us that the option’s value would decrease by \$0.15 (\$0.03 * 5 days). This means that with each passing day, the option loses \$0.15 in value due to time decay.