Option theta — how time decay works

What this lesson explains and for whom

This lesson shows how to calculate daily theta cost in PLN (Polish złoty) and as a percentage of the premium paid, why decay accelerates before expiry, and how to match an option series to the horizon of your thesis. It is for a reader who already understands the components of the premium but picks a contract by price rather than by the relation of time to the expected move. All numbers in the examples are illustrative, and you should confirm the multiplier, commissions, and session calendar with your broker.

What theta is and why decay is not linear

An option is a right with a finite term: it expires on the date determined by the series. Theta measures how much time value it loses each day. The most important practical observation: decay is not linear. It accelerates as expiry approaches and is fastest for ATM options, that is, those whose strike sits close to the current price of the underlying.

That is why two options on the same instrument can behave completely differently. A series with 60 days to expiry gives up time value slowly; a series with 7 days loses it every day. The premium consists of intrinsic value and time value, and theta eats the second part.

Daily theta as a percentage of the premium — how to calculate it

Theta in points alone does not say whether the position has time to realise the thesis. Only relating it to the premium gives a number that can be compared across series.

theta cost per day (PLN) = theta × multiplier × number of contracts
theta share of premium (% per day) = theta / premium × 100
cost of holding for X days = daily cost × X   (a lower estimate, because theta accelerates)
number of contracts = (capital × risk per trade) / (premium × multiplier)

Example (illustrative numbers): a series with 30 days, a premium of 4.00, and theta of 0.05 gives up 1.25% of the premium per day. A series with 7 days, a premium of 1.20, and theta of 0.09 gives up 7.5% per day — six times more relative to price. After two weeks the first structure has lost more than a dozen per cent of the premium; the second has nothing left to lose.

One decision rule follows from these formulas. Entering a long option makes sense when this condition holds:

expected move > theta cost over the horizon + spread and commission cost

You estimate the left side from delta and your own scenario, and calculate the right side from the platform. If the inequality does not hold, the structure is mismatched — regardless of how good the chart looks. That is the same calculation described by the definition of a setup.

Who pays theta

• The option buyer pays theta every day: the premium falls even when the underlying price stands still. You are buying time and volatility, so you must know what can outweigh them: a price move and a rise in implied volatility.
• The option seller collects theta, but accepts the risk of a delta jump, a demand for additional deposit, and a loss larger than the premium collected. That is trading risk, not free income.

The choice is not a judgment about which side is better — it is a decision about the result profile: you earn either from movement and volatility, or from the passage of time. The links between the Greeks are described in a separate lesson, and the volatility side in IV crush after earnings.

How to choose a series relative to the horizon

Comparing IV with realised volatility helps decide whether you are paying expensively or cheaply for time at a given moment. The level of IV alone does not settle it, because it needs a reference point.

The cost of time for your position: table to fill in

Complete it for each series you consider, and compare the rows with each other before choosing one.

When theta says do not trade

1. Theta cost over the planned horizon exceeds the expected move. Then you are not trading a thesis, you are paying for time you will not use.
2. You choose a series with only days left, without a plan for those final days. The fastest decay then coincides with the most uncertain decision.
3. The only argument for entry is a low premium. A low premium can be the result of a short time to expiry, not an opportunity.
4. You justify holding on by how much you have already paid. A sunk cost is not an argument for keeping a position; the current relation of theta to the expected move decides.

Typical mistakes

• The option is cheap, so I will buy it — a low premium often means near expiry and high theta relative to price.
• Holding until expiry on a sure thing — the final days are the fastest decay; the exit plan is set earlier, as the lesson managing an option position explains.
• Mixing horizons — day trading an option with three days to expiry is a game in theta, not in price movement.
• Ignoring vega — theta and implied volatility can pull the result in opposite directions, especially around calendar events.
• Comparing theta in points across series with different premiums — without reference to the premium, those numbers are not comparable.

Measurable exercise

Take two options on the same instrument: one with about 30 days and one with about 7 days to expiry. Record the premiums and daily theta, calculate theta cost in zloty and its share of the premium, and then the cost of holding for five days. Complete the table from the lesson and check the inequality: does the expected move exceed the cost of time and spread. Goal: two calculated series and one decision — which of them fits your horizon and why.

Common questions

Is theta always unfavorable for the buyer?

Yes — by buying an option, you pay for time every day. Whether the position makes sense depends on whether the expected move and the rise in volatility outweigh that cost. In other words: theta does not rule out entry, but it sets the minimum move that must happen.

How do I calculate how much theta eats?

Multiply daily theta by the multiplier and the number of contracts to get the cost in zloty, then divide theta by the premium to get the percentage share. That second number is comparable across series, the first across positions of different size.

Does the option seller bear no costs?

The seller bears other risk: a delta jump, a demand for additional deposit, and a loss larger than the premium collected on a naked position. Theta is payment for accepting that risk, not income without cost.

Why calculate theta's share of the premium instead of looking at theta alone?

Because theta quoted in points says nothing about how long the position can live. Only dividing it by the premium shows what percentage of value the option gives up each day — and that is the number that decides whether the thesis horizon even fits within the life of the series. At theta 0.09 and premium 1.20, the option gives up 7.5% of value per day, so a week of delay costs more than half the premium, before any price move at all.