Theta Decay Curve

The theta decay curve is the shape of how an option’s time value shrinks as expiry gets closer. The decay isn’t a straight line. When expiry is far away, an option loses value slowly. As expiry approaches, the loss speeds up, and in the final days a large part of the remaining time value can disappear within a single session.

Theta is the Greek that measures how much an option loses per day from the passage of time alone. The decay curve is what theta traces out over the option’s life.

The theta decay curve in numbers

Here’s how the premium of an at-the-money call falls as expiry approaches, if the index stays at 20,000 and implied volatility stays at 13% (hypothetical numbers from a pricing model):

Three things stand out:

• The decay speeds up. With a month to go, the option loses about ₹5 a day. With a week to go, it loses about ₹11 a day. On the final day, it loses the last ₹54 in one session.
• Half the value goes in the last quarter of the time. The option still has about half its 30-day value with seven and a half days left. It takes 22 days to lose the first half, and only the last week or so to lose the rest.
• The shape follows the square root of time. An at-the-money option’s time value is roughly proportional to the square root of the days left, which is why the curve is gentle at first and steep at the end.

Decay for in-, at- and out-of-the-money options

The curve isn’t the same for every strike. Here’s how much of each option’s time value is left between seven days and one day before expiry, with the index at 20,000 (hypothetical numbers):

• At-the-money options carry the most time value and lose the most in rupees, with the steepest drop on the very last day.
• Out-of-the-money options lose almost everything in their final days. They have only time value to begin with, so once there isn’t enough time left for the price to reach the strike, the premium collapses towards zero. This is why cheap out-of-the-money options bought close to expiry so often expire worthless.
• In-the-money options keep their intrinsic value. Their small time value disappears fast, but the intrinsic part stays as long as they remain in the money.

What the decay curve means for buyers and sellers

Option buyers are fighting the curve. Even with the right view on direction, a long option held into its final days can lose money because the time value drains away before the move arrives. Many buyers choose expiries with more time left, or plan to exit before the steepest part of the curve.

Option sellers do the opposite. Strategies such as short straddles, short strangles and iron condors are built to collect time decay, usually in the last part of the curve. That’s a theta-positive strategy.

The catch: gamma is highest where decay is fastest

The steep end of the decay curve is also where gamma is highest. Close to expiry, an at-the-money option’s value can swing sharply on a small move in the underlying. For sellers, that means the period with the fastest decay is also the period with the most gamma risk: one sharp move can wipe out many days of collected decay.

Other things that change the curve

• Price moves. The table above assumes the index doesn’t move. In reality, a move in the underlying usually changes the premium far more than a day’s decay.
• Implied volatility. A rise in implied volatility adds to the premium and can more than offset a day’s decay. A fall, such as volatility crush after an event, speeds up the drop.
• Weekends and holidays. Pricing models often count calendar days, so time value keeps decaying over weekends and holidays when the market is shut. Premiums often reflect this before the break.
• Weekly vs monthly options. Weekly index options spend their whole short life on the steep part of the curve, while monthly options spend their early weeks on the flatter part.

How traders use the decay curve

• Picking an expiry. Buyers who need time for a view to play out often choose a later expiry to stay on the flatter part of the curve.
• Timing exits. Buyers often close positions before the final few days, when decay is steepest.
• Timing entries for selling. Sellers often open positions closer to expiry to collect the steepest decay, sized to survive a sharp move.
• Reading premiums on expiry day. Knowing how fast time value is draining helps explain why premiums can fall sharply even on a quiet expiry day.

To watch the decay curve of real options as it plays out through the session, use Stolo’s options premium decay tool, or check theta for every strike with Stolo’s Option Greeks tool.