# Put Gamma in Binary Options – Definition & Example

The Put Gamma in Binary Options measures how much the delta of a put option changes with respect to movements in the underlying asset’s price. It is also the first derivative of the delta of a binary put option.

Put Gamma in a nutshell

• Put Gamma measures delta change in put options relative to asset price.
• It is derived from the option price’s second derivative.
• Expiration time significantly influences gamma’s absolute value.

## Understanding Put Gamma Dynamics in Binary Options

Gamma indicates the rate of change of the exposure to the underlying asset, regardless of whether it is a binary or conventional option.

### Fluctuations in Put Gamma

The gamma of binary put options fluctuates based on their status in relation to the strike price and underlying asset movement. When in-the-money, gamma is zero, shifting between long and short gamma as the asset moves beyond the strike price. Conversely, out-of-the-money puts have positive gamma, while in-the-money puts have negative gamma. At-the-money, gamma is zero, similar to binary call options.

### Impact of Expiration Time

The time to expiration significantly impacts the absolute value of the gamma, with very short-term options usually having a gamma that tends toward zero. In contrast, it is common to see examples where the gamma for a 25-day 25% option is essentially flat at zero.

The absolute value of the gamma of binary put options remains constant, mainly across the implied volatility range. The peak and trough values of the options approach the strike as implied volatility decreases, reflecting the steepening of the delta.

## Calculation & Example

The put gamma for binary options is calculated by taking the second derivative of the option price in relation to the price changes of the underlying asset. Below, you find the formula to calculate the put gamma:

where:

• γput​: Put gamma, measuring put option’s sensitivity
• V: Option price
• S: Price of the underlying asset

For example, if a put option has a gamma of -0.03, it implies that the option’s delta will decrease by 0.03 for every one-point increase in the underlying asset’s price, illustrating the option’s sensitivity to market movements.

## Wrapping it up! – Gamma is a vital trading indicator for binary options traders

In options trading, gamma is a vital trading indicator. Traders refer to themselves as long or short gamma players, depending on their feelings about the current market situation. It may sound crazy, but shouldn’t a short-gamma trader become a long-gamma trader to deal with volatile markets? Possibly. But you will never find evidence of the rational expectations’ theory! As a long-time “local” options trader, I can confidently say that market rationality has never existed and most likely never will.

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