Calendar Spread Calculator

Calculate net debit, theta differential and the value of a calendar spread when the front leg expires.

A calendar spread holds the strike and the option type still and moves only the expiry: sell the near-dated contract, buy the far-dated one at the same strike. Platforms and older options texts file the same structure under time spread and horizontal spread, and this calendar spread calculator treats the three names as one thing. What is left after the two legs offset each other is a position on time and on implied volatility, with very little opinion about direction attached to it.

Formula: value at front expiry = back leg model value - front leg intrinsic - net debit

Your figures

Currency

Option type

Underlying price

Strike price

Both legs share this strike — only the expiry differs.

Days to the front-month expiry

Calendar days to the expiry of the leg you are short.

Days to the back-month expiry

Calendar days to the expiry of the leg you are long. Must be the later date.

Front-month implied volatility

Annualised, from the chain, for the month you are selling.

Back-month implied volatility

Annualised, from the chain, for the month you are buying.

Risk-free rate

Annualised. Roughly the yield on a short government bond.

Dividend yield

Optional — annualised continuous yield on the underlying.

Net debit paid per share

What the spread actually cost, per share as quoted rather than per contract.

Number of contracts

Shares per contract

From your own contract specification. 100 on standard US equity options.

Results

Gain at the front expiry

+US$217.65

with the underlying still at US$100.00 and back-month volatility unchanged

Position theta, per dayBack-month theta less front-month theta, across 100 shares. This is what one calendar day passing is worth to the position.: +US$2.21
Position vega, per 1% of volatilityThe back month has more time for volatility to act on, so a calendar is normally long volatility on balance.: +US$4.65
Model net debit, per shareBack leg less front leg at model value — US$97.62 for the whole position.: US$0.9762
Net debit paidWhat you entered, across every contract.: US$100.00
Paid versus model, per sharePositive means the fill was above what the model values the spread at, on the volatilities entered.: +US$0.0238
Front leg model value, per shareTheta -US$0.0638 a day, vega US$0.1139. The spread is short this leg.: US$3.63
Back leg model value, per shareTheta -US$0.0417 a day, vega US$0.1604. The spread is long this leg.: US$4.61
Back leg value when the front expiresThe back leg repriced with 30 days left, at the same underlying and the same implied volatility.: US$3.18
Front leg value when it expiresAt its own expiry the short leg is worth only its intrinsic value.: US$0.00
Spread value at the front expiry, per share: US$3.18
Return on the debit paid: +217.65%
Shares controlled: 100

What this means

Selling the 30-day leg and buying the 60-day leg at the same strike is worth US$0.9762 per share at model value, against the US$1.00 entered. The back month sheds time value more slowly than the front, and subtracting one theta from the other leaves +US$2.21 a day across 100 shares. The same asymmetry runs the other way in vega, at +US$4.65 per percentage point of implied volatility. Holding the underlying where it is and the back month's implied volatility where it is, the back leg is worth US$3.18 per share when the front expires against US$0.00 of front-leg intrinsic value, which values the spread at US$3.18 per share. Both of those are assumptions held fixed for the arithmetic, not statements about where the underlying or the surface will be.

The value at the front expiry assumes the underlying has not moved. A calendar is at its most valuable with the underlying sitting at the strike, so holding it there is the most favourable case the arithmetic can be run under rather than a central estimate.
It also assumes the back month's implied volatility is unchanged. Where the front month was bid up for an event, the whole surface usually falls once the event passes, and the back leg is then repriced well below the figure shown here.
Both legs are valued as European options. A short American front leg can be assigned before expiry, which leaves the long back leg standing against an unwanted position in the underlying.
Excludes commission, assignment fees and the bid-ask spread on two legs opened and later closed. On a position whose whole edge is measured in cents per share, those costs are a material share of it.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Calendar Spread calculation

It works because time value does not drain away at a steady rate. An option's time value scales roughly with the square root of the time remaining, and the square root is steepest near zero, so a contract with three weeks left sheds a larger share of its value each day than one with seven weeks left. Selling the fast decay and buying the slow decay leaves a position that is paid for each day that passes, which is where the desk name theta spread comes from.

The same asymmetry runs in the other direction in vega. The back month has more time for volatility to act on and therefore carries more of it, so the spread comes out long volatility on balance. Earning from time and losing from a fall in implied volatility are two descriptions of one position, and a calendar opened into an event and held through it can be right about the pin and still lose.

A time spread calculator is only as good as the two implied volatilities it is handed, so both are fields here rather than assumptions. It prices each leg from the figure you supply, reports the model debit against the debit you actually paid, and gives the theta differential and net vega for the position rather than per share. It then reprices the back leg at the moment the front expires, with the underlying held where it stands and the back month's volatility held where you entered it, to produce the value the spread would carry at that point.

Calendar Spread formula

front leg = BlackScholes(S, K, Tf, σf, r, q)    — sold
back  leg = BlackScholes(S, K, Tb, σb, r, q)    — bought

shares          = contracts × shares per contract
model debit     = back leg − front leg                  (per share)
position theta  = (θ back − θ front) × shares           (per day)
position vega   = (vega back − vega front) × shares     (per 1% of σ)

at the front expiry, with S and σb held where they are:
  back value  = BlackScholes(S, K, Tb − Tf, σb, r, q)
  front value = max(S − K, 0) on a call, max(K − S, 0) on a put
  spread value = back value − front value

  profit = (spread value − debit paid) × shares
  return = (spread value − debit paid) ÷ debit paid × 100

Tf, Tb: Time to the front and back expiries in years, each as calendar days ÷ 365.
σf, σb: Annualised implied volatility of the front and back months, entered separately because the gap between them is the position.
θ (theta): Change in an option's value for one calendar day passing. Negative on both legs, since both are losing time value.
vega: Change in an option's value for one percentage point of implied volatility.
debit paid: What the spread actually cost per share, as quoted, rather than what the model says it is worth.
shares: Contracts × the shares one contract covers, read from your own contract specification.

The engine of the trade is the shape of the square root. For an at-the-money option, time value runs close to proportional to σ × √T, and the derivative of √T falls away as T grows — so each day removes more from a near-dated option than from a far-dated one. Both legs report a negative theta because both are options bleeding time value; subtracting the front from the back is what turns two negatives into the position's usually-positive daily income, since the leg being sold is the one decaying faster.

Vega follows the same √T and therefore lands on the opposite side of the ledger. The back month has more time over which a change in volatility compounds into the price, so its vega is larger, and the net figure comes out positive. That is not a defect to be hedged away; it is the other half of what the position is. A spread earning from decay is by construction a spread that loses when the surface falls, and the two cannot be separated.

At the front expiry the short leg no longer has any time value to have an opinion about, so it collapses to its intrinsic value — nothing at all if the underlying is at or beyond the strike in the wrong direction. The long leg is then repriced with only the gap between the two expiries left to run. Two assumptions hold that arithmetic together and both deserve stating plainly: the underlying is taken to be exactly where it is now, and the back month's implied volatility is taken to be exactly what you entered. Neither is a forecast, and the first of them is the most favourable place a calendar can be.

There is an identity worth carrying away from the output. When the front leg finishes at or out of the money, the spread's gain at that point is the front premium collected less whatever the back leg decayed over the same period. In the worked example below that is 6.75867 − 2.24753 = 4.51114 per share at model value, which is exactly the spread value of 6.52625 less the model debit of 2.01511. Written that way it is obvious where the money comes from and equally obvious what takes it away: the back leg decaying faster than expected, or being repriced at a lower volatility.

The model debit and the debit paid are reported separately because they answer different questions. The model debit is what the two volatilities you entered say the structure is worth; the paid debit is what the fill cost. The gap between them absorbs the bid-ask on two legs, any error in the volatilities read off the chain, and any premium the market is charging for a structure that is in demand. A large gap is not automatically a bad fill, but it is worth knowing about before the position is judged on its theta.

Everything scales by contracts times the shares per contract, and that multiplier is an input rather than an assumption. A theta differential of seven hundredths of a point per share sounds like nothing until it is multiplied by the shares two contracts control, which is precisely why the position figures are the ones given emphasis and the per-share figures are shown beneath them.

Calendar Spread: a worked example

A call calendar at the money on a 200 underlying: sell the 21-day 200 call at 34% implied volatility, buy the 49-day 200 call at 28%, two contracts of 100 shares, a 4.5% risk-free rate, no dividend, filled for a 2.35 debit per share.

Front leg valueBS(200, 200, 21 ÷ 365, 34%) = 6.75867
Back leg valueBS(200, 200, 49 ÷ 365, 28%) = 8.77378
Model net debit8.77378 − 6.75867 = 2.01511 per share
Paid versus model2.35 − 2.01511 = +0.33489 per share
Theta differential−0.09535 − (−0.16673) = +0.07138 per share per day
Position theta0.07138 × 200 shares = +14.28 a day
Net vega0.29057 − 0.19088 = +0.09969 per share, or +19.94 per point
Back leg at the front expiryBS(200, 200, 28 ÷ 365, 28%) = 6.52625
Front leg theremax(200 − 200, 0) = 0.00
Spread value then6.52625 − 0.00 = 6.52625 per share
Profit(6.52625 − 2.35) × 200 = 835.25
Return on the debit4.17625 ÷ 2.35 = 177.71%

835.25 on a 470.00 outlay, and the size of that number is the assumption rather than the edge. It requires the underlying to finish the front expiry at exactly 200, where the short call expires worthless and the whole 6.52625 of back-leg value is kept, and it requires the back month still to be quoted at 28%. Both are held fixed to make the arithmetic possible. A drift away from the strike in either direction erodes it, and a fall in the back month's implied volatility takes it apart from the other side, which is what the +19.94 of position vega is warning about.

How to use the Calendar Spread calculator

Choose call or put. Both legs share the type as well as the strike, so the choice applies to the whole structure.
Enter the underlying, then the strike both legs share. A calendar sits closest to its best case with the strike near the underlying.
Enter the calendar days to each expiry. The back month must be the later of the two, and the gap between them is what the back leg has left to run once the front has gone.
Read each month's implied volatility off the chain and enter them separately. Quoting both at one figure hides the term structure the trade is built on.
Enter the debit you actually paid per share, not per contract, then the number of contracts and the shares each one covers from your own contract specification.
Read the position theta and the position vega together. One is what the position earns for waiting and the other is what it stands to lose if the surface falls, and neither means much without the other.
Treat the value at the front expiry as the pin case. Re-running it with a lower back-month volatility shows how much of the figure depends on that assumption holding.

Limitations of the Calendar Spread calculator

Every calculation makes assumptions. These are the ones that matter here.

The value at the front expiry assumes the underlying has not moved. A calendar is at its most valuable with the underlying sitting on the strike, so this is the best case the arithmetic can be run under rather than a central estimate.
It also assumes the back month's implied volatility is unchanged. Where the front month was bid up for an event, the whole surface usually falls once the event has passed, and the back leg is then repriced well below the figure shown.
Only two points in time are valued: now, and the moment the front leg expires. The path between them is not modelled, and a spread closed early settles at whatever the two legs are quoted at on the day.
Both legs are valued as European options. A short American front leg can be assigned before its expiry, which leaves the long back leg standing against an unwanted position in the underlying.
Commission, exchange fees, assignment fees and the bid-ask spread on two legs opened and later closed are all excluded. On a structure whose edge is measured in cents per share, those costs take a material share of it.
Dividends are treated as a continuous yield. A discrete cash dividend falling between the two expiries affects the legs unequally, and that unevenness is not captured by a smooth yield.
Both legs must share a strike. A diagonal, where the strikes differ as well as the expiries, has a directional component this arithmetic does not describe.
No margin figure is produced. A long calendar's cash outlay is the debit, but the treatment of the short leg before the long one is established varies, and only the broker holding the position can state it.

Frequently asked questions about Calendar Spread

Why does a calendar spread make money if the underlying does not move?

Because both legs are losing time value and the one being sold is losing it faster. The near-dated option gives up a larger share of its remaining value each day than the far-dated one does, so the daily loss on the long leg is more than covered by the daily gain on the short leg. With the underlying pinned to the strike that difference is at its widest, which is why standing still is the position's best case.

Why is a calendar long volatility when it is short an option?

Vega grows with the time remaining, so the far-dated leg that was bought carries more of it than the near-dated leg that was sold. Netting the two leaves a positive figure. The position is short one option and long another, and it is the difference in their sensitivities rather than the count of contracts that decides which way the exposure points.

What happens if the short leg is assigned before its expiry?

You take on the underlying position the short contract obliges — short stock on an assigned call, long stock on an assigned put — while still holding the back-month option. The arithmetic here stops applying at that point, because the structure is no longer two options. Early assignment is most likely on an in-the-money short leg around an ex-dividend date.

Why is the model net debit different from what I paid?

The model debit is what the two volatilities you entered imply the structure is worth, and the fill is what the market charged for it. The difference absorbs the bid-ask on both legs, any inaccuracy in the volatilities read off the chain, and whatever the market is charging above mid for the structure. The paid-versus-model figure isolates that gap so it can be judged on its own.

Is the profit at the front expiry the maximum the spread can make?

It is the value at one specific moment under two fixed assumptions, and for an at-the-money calendar it is close to the peak of the payoff at that moment. It is not a ceiling on the whole position, because the back leg still has time to run afterwards and can be held or sold at whatever it is then worth. Nor is it a floor: a move away from the strike gives most of it back.

Can I use this as a diagonal spread calculator?

Not directly. A diagonal changes the strike as well as the expiry, which adds a directional component to the payoff that the arithmetic here does not carry, so a diagonal spread calculator has to price the two strikes separately at every point rather than netting them at one. Entering the shared strike as an average of the two would produce a number, but not one that describes the position you actually hold.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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