Lesson 10
Theta: Time Decay & The Trade Life Cycle
Understand what time changes in an option, what Theta estimates and why the next price can tell a different story.
Time passes. Decay speeds up.
Days left to expiry
Move across the chart, or drag on a phone, to read each line.
Hypothetical NIFTY 50 ATM Call · strike 25,000 · 18% IV, 6% rate, 1% yield · spot unchanged · ₹ per unit
Let’s separate the clock from the market
Mr. Chartist will follow one NIFTY example as its remaining time shrinks. We will compare a daily estimate with a full repricing, then see why a theta sign cannot tell us whether a trade will make money.
By the end you will be able to answer
- What does theta actually measure?
- Is daily theta tomorrow’s price change?
- Does every option decay faster near expiry?
You check a NIFTY Call on two mornings. The index is at nearly the same level, yet the premium is lower. One day passed. Is that the whole story? Not quite. The quote may also carry a different implied volatility (IV), the volatility figure that a pricing model reads from the premium. Theta separates out what the clock alone does, so you do not blame every price change on time decay.
The premium is the option’s price. Expiry is when the contract ends. Theta is the model’s estimate of how the premium changes as time passes, with every other input held still. It is quoted in rupees per unit per day. It is a rate, not a daily fee, not a cash payment between traders and not a forecast of tomorrow’s quote.
One example runs through the Greeks lessons (Delta, Theta, Vega, Gamma): NIFTY 50 with spot and strike both at 25,000 points, 30 calendar days left, interest 6% a year, dividend yield 1% a year, volatility 18% a year. The European Black–Scholes–Merton price is ₹565.99 per unit for the Call and ₹463.55 for the Put. Prices, quantities and costs are teaching assumptions, not live quotes.
Updated
What does theta actually measure?
The clock’s effect on the premium alone
NIFTY is at nearly the same level as yesterday, but my call is cheaper. Is that just time decay?
Not quite the whole story. The quote may also carry a different implied volatility. Theta separates out what the clock alone does.
So what is theta, exactly?
The model’s estimate of how the premium changes as time passes, with every other input held still. It is quoted in rupees per unit per day.
For our 30-day call it is about minus ₹10.285. So I lose that every day?
No. It is a rate, not a daily fee, not a payment between traders, and not a forecast of tomorrow’s quote.
And the minus sign?
It says the model value falls as time passes, with spot, volatility, interest and dividend unchanged.
A Greek is a sensitivity: how much the model value moves when one input moves. Delta, from the last lesson, is about the underlying’s price. Theta is about time passing. A Call (C or CE) and a Put (P or PE) each have a theta. Keep two things apart: the option’s own theta, and the signed exposure of a long or short position in it.
For our 30-day Call, theta is about −₹10.285 per unit per calendar day. The minus sign says the model value falls as time passes, with spot, volatility, interest and dividend unchanged. The Put’s theta is about −₹6.880. These are rates at today’s inputs, so a full day of repricing need not lose exactly these amounts. The next chapter shows why.
The daily rate grows as the clock runs down
Each rung is the same at-the-money Call with less time left. The bar is that day’s theta; the last column is that one day’s theta as a share of what the Call is worth.
Call · CE · NIFTY 50 · 25,000 CE · same Call, fewer days left
European BSM · 18% annual volatility · NIFTY held at 25,000 · ₹ per unit per calendar day · teaching values, not quotes
In symbols, theta is Θ = ∂V/∂t: the change in option value V as calendar time t advances. If τ is the time left to expiry, the same thing is Θ = −∂V/∂τ, because the clock moving forward shrinks what is left. You do not need calculus to use it. Move time a tiny step, hold the other inputs, and see how the premium responds.
The model counts time in years, T = 30/365, so the formula first gives theta per year. Dividing by 365 gives the per-calendar-day figure used here. Some screens divide by 252 trading days instead. Check the convention, the sign and the quantity multiplier before comparing screens. The display scale does not change the contract’s real expiry.
Theta applies to the whole model premium, including the effects of discounting and dividends, not just the chance of a favourable move. It is called time decay because most bought options have negative theta. That is common, not universal: later in this lesson a European Put gains value as expiry nears.
Is daily theta tomorrow’s price change?
Why a rate is not a forecast
The quick estimate is today’s daily theta times the days that pass. For the Call, one day gives −₹10.285. The full repricing changes the time left from 30/365 to 29/365 and recalculates the premium: ₹555.64, down ₹10.36 from ₹565.99. Both are fine for their purpose. The small gap appears because the rate itself changes as time passes.
The gap grows with the interval. After seven days, with all else fixed, the Call at 23 days left is worth ₹490.01, a fall of ₹75.98. Seven times the starting theta gives only ₹71.99. For the Put, repricing gives −₹52.13 and seven times theta gives −₹48.16. Theta is a changing rate, not a fixed daily deduction.
With one day left, the same at-the-money Call is worth ₹95.68 and its theta is −₹48.70. If NIFTY does not move, the last day takes the value to zero at expiry: a fall of ₹95.68, not ₹48.70. One day is too large a share of the contract’s remaining life for a local rate to be accurate.
A daily rate and a full day differ
Compare today’s local theta estimate with a full one-day repricing. The distinction is small at 30 days and large when only one day remains.
Call · CE · NIFTY 50 · 25,000 CE
30 → 29 calendar days left
- Local estimated change
- −₹10.28
- Local estimated value after
- ₹555.71
- Exact frozen-input change
- −₹10.36
- Exact model value after
- ₹555.64
- Exact change − local estimate
- −₹0.07
1 → 0 calendar days left
- Local estimated change
- −₹48.70
- Local estimated value after
- ₹46.98
- Exact frozen-input change
- −₹95.68
- Exact model value after
- ₹0.00
- Exact change − local estimate
- −₹46.98
Hypothetical European model · calendar days · other inputs held fixed
Use theta to feel the sensitivity over a small step. Use a full repricing for a stated interval. Neither is a market quote. At expiry, use the payoff and the settlement rules. Close to expiry the at-the-money theta grows without limit in the model, so multiplying a one-day theta by the days left is meaningless.
Does every option decay faster near expiry?
Time decay is not the same everywhere
Moneyness is the strike compared with the underlying. With NIFTY at 25,000, a 24,000 Call is in the money, a 25,000 Call is at the money and a 26,000 Call is out of the money. At an unchanged NIFTY their expiry payoffs per unit are ₹1,000, zero and zero. Different starting points give different time paths.
Follow the at-the-money 25,000 Call first. Its premium at 30, 15, 7 and 1 day left is ₹565.99, ₹389.61, ₹260.60 and ₹95.68, and zero at expiry. Its daily theta grows from −₹10.28 at 30 days to −₹19.47 at 7 days and −₹48.70 at 1 day. This is the familiar speeding-up of decay near the money.
Three strikes, three time paths
The at-the-money Call’s theta becomes more negative near expiry. The other two Calls do not follow the same accelerating pattern at this fixed spot.
Call · CE · NIFTY held at 25,000 points
| Call strike | 30 days left | 7 days left | 1 day left |
|---|---|---|---|
| In the money24,000 strike | −₹8.32 | −₹7.37 | −₹3.26 |
| At the money25,000 strike | −₹10.28 | −₹19.47 | −₹48.70 |
| Out of the money26,000 strike | −₹7.76 | −₹5.79 | −₹0.01 |
European BSM · 18% annual volatility · sample days are not actual quotes
The other strikes behave differently. The 26,000 Call’s theta is −₹7.76 at 30 days, −₹5.79 at 7 days and only −₹0.0088 at 1 day: with NIFTY fixed it has almost no premium left to lose. The 24,000 Call’s theta also shrinks, to −₹8.32, −₹7.37 and −₹3.26, as its value heads towards its ₹1,000 payoff. The at-the-money pattern is not a rule for every strike.
In a simple constant-volatility model, an at-the-money premium is roughly proportional to the square root of the time left. That explains the steeper final stretch, though interest, dividends and changing moneyness alter the exact numbers. Do not divide the premium by the days left and call it theta, and do not assume a fixed share of premium disappears each week.
The comparison holds NIFTY and volatility still so that only time acts. In real trading, spot moves, so a contract drifts towards or away from the money and its theta path changes. Near the money, expiry also makes delta swing faster with spot. That is gamma, the subject of lesson 12. A large theta alone does not mean profit for the seller or safety for anyone.
How does theta change for buyer and seller?
The same number seen from both sides
A long position owns the option. A short position owes its payoff. For the same contract and quantity, their theta exposures have opposite signs. Our long Call’s −₹10.285 per unit per day becomes +₹10.285 for the short Call. This says the seller’s liability shrinks on paper as time passes. It is not cash arriving in the account each day.
To scale theta, multiply the unrounded per-unit figure by the signed quantity, then round the total. For an assumed 65 units, the long Call’s daily exposure is about −₹668.52 and the short Call’s +₹668.52. The Put gives −₹447.20 long and +₹447.20 short. The 65 is a teaching quantity, so check the real lot size. A multi-leg position needs the signed exposure of every leg.
The position reverses the theta sign
Long and short positions in the same Call or Put have opposite local time sensitivities. Quantity scales the exposure; it does not turn theta into cash income.
Same pricing inputs · separate positions
65 assumed units in each separate position
Call · CE
Put · PE
Bought · longYou hold the right
Sold · shortYou owe the right
Hypothetical calendar-day exposures · totals use unrounded theta · before costs
The seller receives the premium once, at the sale, and stays obliged until the position is closed or settled. A favourable model value is not a second payment and not a daily earning. A separate example: sell at ₹570, buy back at ₹550. That is ₹20 per unit, or ₹1,300 for 65 units, and ₹1,220 after assumed charges of ₹80. The buyer on the same two fills has −₹1,300, or −₹1,380 after the same charges.
These results come from the two fills, not from adding up theta. The fills already contain the spread, so do not subtract it again. The ₹80 is an example total, not a tax rate or a broker tariff. Model value, unrealised change and realised profit answer different questions.
Both sides carry risk. An uncovered short Call has no upper limit on loss as the underlying rises. A short Put’s loss is large but capped, because the underlying cannot fall below zero: the most it can owe is the strike per unit, less the premium and before costs. A buyer can lose the whole premium. Holding stock options to expiry can also create delivery and funding obligations. Margin is security for the obligation, not a limit on loss. A delta hedge calms small moves, but delta changes as the market moves, and gamma, volatility, gaps, funding and execution risk remain.
Can a negative-theta option rise tomorrow?
Other inputs can outweigh the clock
Theta looks at one input. Real premium changes also come from the underlying, volatility, rates, expected dividends and the quote on screen. A Call with negative theta can still gain if another effect is bigger. A short position with positive theta can lose far more from a spot or volatility move than it gains from time.
Three separate one-day cases from the same ₹565.99 Call. Only time changes (30 to 29 days): the value falls to ₹555.64. NIFTY rises 100 points to 25,100, with the one day passing: ₹611.28, up ₹45.28. NIFTY stays at 25,000 but volatility rises from 18% to 20%, with the one day passing: ₹611.53, up ₹45.54. Negative theta did not stop either rise.
Time is only one pricing input
The Call starts with negative theta. A 100-point rise in NIFTY or a rise in the volatility input can outweigh the one-day time effect in these model scenarios.
Call · CE · Three separate hypothetical one-day reprices
1 calendar day pass in every scenario
- 1
Only time changes
Spot 25,000 · Volatility 18.00% · 29 days left
−₹10.36Model value after ₹555.64 - 2
NIFTY rises 100 points
Spot 25,100 · Volatility 18.00% · 29 days left
+₹45.28Model value after ₹611.28 - 3
Volatility rises to 20%
Spot 25,000 · Volatility 20.00% · 29 days left
+₹45.54Model value after ₹611.53
Only the named input and remaining time change · ₹ per unit · no forecast
These are full reprices, not a breakdown of a real trade, and none predicts the market. Delta is the sensitivity to spot, gamma is how delta changes, and vega is the sensitivity to volatility (lesson 11). Adding starting Greeks works for small moves. For a larger, stated scenario, reprice the whole option.
A positive theta says nothing about direction. Time and spot are different questions. A short Call has positive theta and negative delta. A long Put has negative delta and, in some cases, positive theta. Read each exposure on its own. A plus sign is not a forecast of rising prices and not an assurance of profit.
Can a long option have positive theta?
A case that breaks the usual pattern
Yes. Take a separate European NIFTY Put with spot 22,000 and strike 25,000, and the same 30 days, 6% interest, 1% yield and 18% volatility. It is deep in the money. Its premium is ₹2,898.40 per unit and its long theta is +₹3.008 per day. After one day, other inputs fixed, it reprices to ₹2,901.43, up ₹3.03.
Why? Intrinsic value is not cash you can collect today. The Put’s intrinsic value is max(strike − spot, 0) = ₹3,000. But a European option pays at expiry only, so there is no early exercise to collect it now. That future payment is discounted back to today. As the date comes closer, the discount shrinks, and that gain in present value can outweigh the loss of optionality. Dividends also enter the calculation.
A long Put with positive theta
This model Put rises from ₹2,898.40 to ₹2,901.43 after one frozen-input day. Its future exercise cash flow helps explain both positive theta and a premium below raw current intrinsic.
Put · PE · Separate European NIFTY Put · spot 22,000 · strike 25,000
6.00% annual rate · 1.00% annual yield · 18.00% annual volatility
Separate hypothetical case · European exercise at expiry · ₹ per unit
So the premium sits below intrinsic value here: ₹2,898.40 − ₹3,000 = −₹101.60. It is wrong to picture every European premium as a fixed intrinsic core plus a layer of time value that can only melt. That picture hides this carry effect. With spot fixed, intrinsic value stays at ₹3,000 while the total premium still changes as the discounted payment gets closer. A price below intrinsic does not by itself mean an arbitrage.
This is why theta is defined on the whole model value. Deep in-the-money European Puts can have positive long theta, and a large enough dividend yield can give a long Call positive theta too. “Long options have negative theta” is common, not universal. The matching short Put here has negative theta, and the long Put still has negative delta. Neither sign is a trading recommendation.
What changes over weekends and at expiry?
How closed days and the last day count
Time keeps passing when the market is shut. In our method you take the exact valuation time and the expiry time and reprice for the fraction of a year in between. A weekend or holiday does cut the calendar time left. That does not mean Monday’s quote falls by an exact multiple of Friday’s theta.
Models and traders count time differently, and earlier quotes can already price in a closed stretch. The Options Industry Council says there is no industry-wide method for decaying options, and describes US traders sometimes pricing the weekend during the Friday session. That does not give one fixed Friday adjustment for NSE. News, the opening price, IV and liquidity can matter more.
As expiry nears, keep the contract terms and funding in view. NIFTY index options are European and cash-settled. NSE stock options are also European, but expiry positions create physical delivery obligations. Theta is not a settlement instruction, and holding because theta looks favourable does not remove delivery, margin, price or liquidity risk.
When you analyse a position, write down the contract, how time is counted, spot, volatility, rates, dividends, and the sign and units of theta. For a finished trade use the real fills and costs. At expiry use the payoff and clearing rules. That keeps theta as a sensitivity and stops it being mistaken for a promised daily return.
Next is vega, the premium’s sensitivity to volatility. Our one-day cases already showed why: time passes while the market’s expectations change, and you need to tell the two apart.
Before you go
Check yourself
5 questions from this lesson. Pick an answer to see why, then slide on to the next.
Question 1 of 5
Questions readers ask
Common questions
How do I calculate theta per day for a NIFTY option?
Start with a stated model and consistent spot, strike, expiry time, volatility, rate and dividend assumptions. If analytical theta is measured per year, divide by 365 for the calendar-day convention used here. Our 30-day Call has long theta about −₹10.285 per unit per calendar day. Multiply by signed quantity for position exposure; verify each platform’s convention and contract lot size.
Is one day of theta the same as the actual one-day premium change?
No. Theta is a local rate at the starting inputs. Even a frozen-input full repricing can differ because theta changes over the interval. Our Call’s initial daily theta is −₹10.285, while its 30-to-29-day model change is −₹10.358. Real quotes also respond to spot, IV and execution conditions.
Is theta always negative for an option buyer?
No. European in-the-money Puts can have positive long theta when carry effects outweigh declining optionality. Our separate Put with spot 22,000 and strike 25,000 points has long theta about +₹3.008 per calendar day. High dividend yield can also permit positive long Call theta under suitable assumptions. Typical negative-long examples are not universal rules.
Does every option decay faster as expiry approaches?
No. The accelerating pattern is especially familiar near the money under fixed inputs. Our fixed 25,000-spot at-the-money Call’s theta becomes more negative near expiry, but the 26,000 out-of-the-money Call’s theta approaches zero as almost no premium remains. Moneyness, volatility and carry affect the path.
Does theta decay over weekends and holidays?
Calendar time continues, and our model reduces remaining time for the exact elapsed interval. The next market quote need not lose a fixed number of displayed daily thetas: earlier quotes can anticipate the closed interval, conventions differ, and spot, IV or news can change. No universal NSE Friday deduction time or guaranteed weekend gain follows.
Does positive theta mean option sellers earn money every day?
No. It means the model position benefits locally from time passing with other inputs fixed. Premium is received when an option is sold, not received again daily through theta. Price or volatility moves can outweigh that benefit, and realized results use actual closure fills, charges and settlement obligations.
Can a European option price be below its current intrinsic value?
Yes, under suitable carry assumptions. A European right is exercised at expiry, so its future cash flows are discounted; raw current intrinsic is not an immediate exercise payment. Our separate Put has intrinsic ₹3,000 but model premium ₹2,898.40. The negative difference is not automatically a data error or an arbitrage.
What is the difference between theta, delta and vega?
Theta measures local sensitivity to time passing, delta to spot, and vega to volatility. Each holds other model inputs fixed. Negative theta can coexist with a rising option premium if spot or volatility changes favourably. Positive theta is a time-sensitivity sign, not a view or a promise of profit.