Payoff at the near expiry
Profit or loss the moment the short leg expires, across a range of underlying prices. The short leg is worth its intrinsic value; the long leg is repriced with Black-Scholes over its remaining days at the IV you set. The peak sits at the strike; past the two break-evens you are in the loss zone, capped at the debit.
| Underlying at near expiry | P&L | On debit |
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Time decay is the engine, volatility is the steering
A calendar spread earns because the short, near-dated leg loses time value faster than the long, far-dated leg you hold — park the price at the strike and the short one evaporates while the long one keeps most of its worth. But direction is only half the story. Because you are net long the longer option, you are net long volatility: a rise in the far-leg's implied volatility lifts the trade even if price never moves, and a post-event volatility crush can sink a spread that landed perfectly on the strike. That is why the far-leg IV at expiry input matters as much as the strike — drop it to model a crush and watch the max profit shrink or flip red. Calendars shine in quiet stretches between catalysts and ahead of an event that lands after the near expiry; they lose to a big directional move or a volatility collapse, and either way the loss is capped at the debit you paid. Model the pure volatility drop with the IV crush calculator, judge whether the back-month IV is cheap enough to be worth owning with the IV rank calculator, watch each leg's greeks in the greeks calculator, and compare against a same-expiry vertical spread or a strike-and-time diagonal.
The math
Write the strike K, the near days d₁ and far days d₂, and an implied volatility for each leg. The tool prices every option with the Black-Scholes model at zero rate: the net debit is the far-leg value minus the near-leg value, BS(K,σ_far,d₂) − BS(K,σ_near,d₁), and it is what the spread costs you up front and your maximum loss.
At the near expiry the short leg is worth only its intrinsic value — max(S−K,0) for a call calendar, max(K−S,0) for a put — while the long leg is repriced by Black-Scholes over its remaining d₂ − d₁ days at the far-leg IV at expiry you choose. The position value is long − short, and the profit is that minus the debit. Max profit occurs at S = K, where the short leg is worthless and the long leg holds the most time value.
The two break-evens — one below the strike, one above — are the prices where profit crosses zero, found numerically from the payoff. Because you are net long vega, raising the far-leg IV at expiry lifts the whole curve and lowering it (a crush) drops it. Every figure scales by your contract count. This is a model, not a quote — real fills, skew and a moving IV surface will shift the outcome.