Binary Options Put Theta definition


Put Theta indicates the first derivative of the fair value of binary put options with respect to a change in time to expiration. It is a ratio that describes the difference in the fair-value of put options due to a time change.

Put Theta can be represented as:


Properties of Put Theta


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.

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The position changes from a short theta position to a long theta position or vice versa when the underlying passes the strike since Theta is zero when it is in the money.

Since selling an out-of-the-money put would lose money when it falls through the strike, it is clear that this feature of vanilla binary options makes them not ideal for taking advantage of time decay by selling out-of-the-money puts.

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