Derivatives and advanced market conceptsModule 3, lesson 15 of 21
Theta, time decay and vega
Theta and accelerating time decay, vega and implied volatility, and how the Greeks combine so a buyer can be right on direction and still lose money.
In this lesson
- Explain theta and why time decay accelerates near expiry.
- Explain vega as an option's sensitivity to implied volatility.
- Combine delta, theta and vega to estimate an option's price change over a few days.
- Explain who benefits from time decay and who is hurt by it.
Builds on
- Options Greeks: delta and gammaThis lesson adds theta and vega to the delta and gamma explained there.
On this page
In simple terms
Delta and gamma describe how an option responds to price moves, as the delta and gamma lesson explains. Two other forces move option prices even when the share price stands still:
- Time: measured by theta. Options lose time value as expiry approaches.
- Implied volatility: measured by vega. Options gain or lose value as expected volatility changes.
Theta and time decay
Theta is roughly the change in an option's price over one day from the passage of time, all else equal. For a buyer it is usually negative: the option loses a little value every day.
Worked example: Time decay of a made-up at-the-money option
| Days to expiry | Time value | Average daily decay over the period |
|---|---|---|
| 30 | ₹40 | |
| 15 | ₹28 | about ₹0.80 a day |
| 5 | ₹16 | about ₹1.20 a day |
| 1 | ₹7 | about ₹2.25 a day |
| 0 | ₹0 | ₹7 in the last day |
Decay speeds up as expiry approaches. The last week costs more than the previous two.
Time decay helps option sellers and hurts buyers. That is why selling options can produce steady small gains, and why those gains are payment for taking on large risks, as the buyers and sellers lesson explains.
Vega and implied volatility
Vega is roughly the change in an option's price for a 1-percentage-point change in implied volatility.
| Vega | ₹2 per point |
|---|---|
| Implied volatility rises 5 points | +₹10 |
| Implied volatility falls 8 points | −₹16 |
Vega is largest for at-the-money options with plenty of time left. Implied volatility often falls sharply after scheduled events such as results, as the volatility lesson explains, so an option bought before an event can lose much of its value overnight even if the share moves.
The Greeks together
Over a short period, an option's price change is roughly the sum of the effects:
Change ≈ delta × price move + ½ × gamma × (price move)² + theta × days + vega × change in implied volatility
Worked example: Right on direction, still losing
A trader buys a call with delta 0.5, theta −₹3 a day and vega ₹2, before a company's results. Over two days, the share rises ₹20 and implied volatility falls 5 points after the results.
| From delta: 0.5 × 20 | +₹10 |
|---|---|
| From theta: 2 × (−3) | −₹6 |
| From vega: 2 × (−5) | −₹10 |
| Approximate change, ignoring gamma | −₹6 |
The share went up, as the trader expected, and the option still lost value.
The seller's side
Sellers collect theta every day, but they are short gamma and vega:
- A sudden large move hurts them more than delta suggests, because of gamma.
- A rise in implied volatility, which often comes with falling markets, raises the value of the options they have sold, increasing their losses and margin.
These risks tend to arrive together in market stress, as the derivative risks lesson explains.
Why it matters
Theta and vega explain most of the surprises option traders face: losing money while being right about direction, options becoming worthless faster than expected, and seller losses that grow in market panics. Understanding them is essential before taking any option position.
Limitations
Greeks come from models and change constantly. The approximations hold for small changes over short periods; large moves, gaps and changes in several inputs at once can produce quite different results.
Common mistakes
- Assuming time decay is even across every day.
- Buying options before events without allowing for the fall in implied volatility.
- Looking only at delta when judging a position.
- Selling options for theta without respecting gamma and vega risk.
Try it yourself
- For a made-up put with delta −0.4, theta −₹2 a day and vega ₹1.5, estimate the price change over three days if the share falls ₹15 and implied volatility rises 4 points.
- Repeat if implied volatility instead falls 6 points.
- Explain which Greek mattered most in each case.
Key takeaways
- Theta is roughly how much an option's price falls each day from the passage of time alone. It is usually negative for buyers.
- Time decay is not even. It is slow when expiry is far away and accelerates in the final days, especially for at-the-money options.
- Vega is how much an option's price changes for a 1-point change in implied volatility. Falls in implied volatility hurt buyers and help sellers.
- The Greeks act together. A buyer can be right on direction and still lose if time decay and a fall in implied volatility outweigh the gain from delta.
- Sellers collect time decay but carry gamma and vega risk, which can produce large losses in sudden moves.
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Terms used in this lesson
- Theta
- Roughly how much an option's price falls each day from the passage of time alone.
- Vega
- Roughly how much an option's price changes for a 1-percentage-point change in implied volatility.
- Time value
- The part of an option's premium above its intrinsic value, paying for the chance of a favourable move before expiry.
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This lesson is general education, not investment advice. Examples use made-up or clearly dated figures to explain ideas; they are not recommendations. Read the disclaimer.