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Calendar Spread: Two Expirations, Conditional Value, and Greeks

Understand a long calendar spread through executable package prices, near-expiry conditional value, signed Greeks, volatility-term shocks, assignment, and settlement.

Updated

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

A conventional long calendar spread, or time spread, sells a nearer-dated call or put and buys a later-dated option of the same type and strike in matched quantity. It usually opens for a net debit. A different strike creates a diagonal spread; a reversed near-long and far-short position is a short calendar. Matching labels are not enough if multiplier, deliverable, exercise style, settlement or adjustment differs.

The position has no fixed terminal payoff at the near expiration because the far option remains alive. With executable leg sides, gross opening debit per underlying unit is D₀ = Ask_far,0 − Bid_near,0. Before near expiry, conservative close credit is X_t = Bid_far,t − Ask_near,t; after a European near leg settles, it is the far executable bid less the near official cash debit. Package P&L is M × Q × (X_t − D₀) before fees and other cash flows. The often-shown peak near the common strike is a scenario-model result, not contractual maximum profit.

Seven-step calendar analysis

  1. Lock the strategy and claims. Record underlying and root, call or put, common strike, near and far expirations, ratio, American or European exercise, cash or physical settlement, multiplier, deliverable, currency, adjustment, last trading times and official settlement sources. Different strikes are diagonal, and unmatched claims do not form the conventional calendar described here.
  2. Price the executable entry. Buy the far option at ask and sell the near option at bid, or use the actual complex-package fill. Multiply by actual quantity and multiplier and add all opening costs. Midpoint, last and model value are not cash debit; a complex book may improve the leg-implied price but does not guarantee it.
  3. Separate the two lifecycle stages. Before the near expiration, both legs remain open. At the near expiration, close or settle that leg and value the surviving far option at its executable bid. If the far leg is retained, the calendar has ended and the account now owns a standalone long option with a current opportunity cost.
  4. Build a conditional value grid. Vary spot, time, near IV, far IV, skew and executable spread separately. At the near date, combine the contract’s official payoff or close cost with the far bid. Do not label one modeled value at the strike as maximum gain or assume the initial debit is the only possible account-level funding need.
  5. Add signed sensitivities. For each Greek G, use G_net = G_far − G_near. Net Delta can change sign, near-expiry Gamma can be negative, and positive Theta or Vega is only a local model derivative. Shock near and far IV independently in vol points and include Gamma, cross terms, discrete events and nonlinear repricing before relying on a linear estimate.
  6. Run contract and assignment branches. Treat European call-put parity only under matched deterministic-carry assumptions; dividends, borrow and American exercise alter the relationship. Test early assignment, exercise-by-exception, contrary instructions, pin, after-hours and halts; call assignment can create short stock, put assignment can create long stock, and the far option does not automatically cover either.
  7. Plan execution and reconciliation. Define the spot region, event exposure, review date, loss limit, profit review, package-liquidity minimum, roll and residual-leg rules. Reconcile option fills, exercise or assignment, shares, official cash settlement, strike cash, dividends, borrow, fees, margin and tax lots from final broker records.

Worked examples

  • Executable package value. A 1:1 call calendar opens with far ask $5.20 and near bid $3.00, so D₀ = $2.20, multiplier is 100, and gross debit is $220. A $1.30 entry fee makes all-in cost $221.30. Later, far bid is $4.10 and near ask is $2.30, so X_t = $1.80; gross close credit is $180 and $178.70 after a $1.30 exit fee. Whole-trade P&L is $178.70 − $221.30 = −$42.60, or −$42.60 ÷ $221.30 = −19.2499%. Close credit is not profit, and favorable leg midpoints do not change these executable cash flows.
  • Near-expiry value is conditional. A European cash-settled K = 100 call calendar cost $2.00 × 100 = $200; the far call has 30 days left when the near call settles, and fees are ignored. At official S_settle = $90, near payoff is $0 and far bid $0.80 gives $80 exit value and −$120 P&L. At S_settle = $100, near payoff is $0 and far bid $3.50 gives $350 and +$150. At S_settle = $110, the near cash debit is $10 × 100 = $1,000, while far bid $11.20 × 100 = $1,120 leaves $120 and −$80 P&L. The apparent peak at $100 depends on the assumed far bid and IV rather than a contractually fixed maximum.
  • Signed Greeks and nonparallel IV. Per underlying unit, suppose the near long-option Greeks are Delta 0.50, Gamma 0.060 per $1², Theta −$0.080 per day, and Vega $0.10 per vol point; far values are 0.52, 0.035, −$0.045, and $0.18. The long calendar has net Delta 0.02, Gamma −0.025, Theta +$0.035, and Vega +$0.08; multiplier 100 makes local Theta +$3.50 per day. Over one day, let ΔS = +$2, near IV fall 2 vol points, and far IV fall 5 vol points. Far change is 0.52×2 + 0.5×0.035×2² − 0.045 + 0.18×(−5) = +$0.165; near option change is 0.50×2 + 0.5×0.060×2² − 0.080 + 0.10×(−2) = +$0.840. Calendar change is $0.165 − $0.840 = −$0.675 per share, or about −$67.50 per contract despite positive Theta.
  • American assignment and the far option. Before an ex-dividend date, a near K = $100 short call is assigned. Without stock, the account receives $10,000 strike proceeds and holds −100 shares; the far call remains open. Stock ask is $107.55, while the far call bid is $8.40, containing $7.55 intrinsic and $0.85 executable extrinsic value. Buying stock and selling the far call gives event cash $10,000 − $10,755 + $840 = +$85 before the original calendar debit, fees and tax. Exercising the far call at $100 can cover the shares but gives up that $85; leaving short stock adds gap, borrow, dividend and margin exposure.

Risks and validation controls

  • Stress spot above, below and near the common strike at each decision time.
  • Shock near and far implied volatility independently rather than in parallel.
  • Include term-structure reshaping and the location of earnings or macro events.
  • Stress strike skew and its different effect on each expiration.
  • Treat Theta as a local sensitivity rather than guaranteed daily income.
  • Stress near-expiry short Gamma, nonlinear Delta changes and spot gaps.
  • Recalculate net Delta as spot, time and the volatility surface change.
  • Use executable complex-package bid and ask, displayed size and limit orders.
  • Predefine legging order, timeout and emergency hedge for partial execution.
  • Include spread, slippage, commissions, exchange charges, borrow and tax.
  • Review short-call dividend incentives and early-assignment exposure.
  • Review deep-ITM short-put extrinsic, rates and early-assignment exposure.
  • Do not assume the far option automatically sells, exercises or covers assignment.
  • Reserve physical stock notional, strike cash, funding and margin capacity.
  • Check short-stock locate, borrow, recall, buy-in and dividend obligations.
  • Reserve liquidity for European cash settlement and use official S_settle.
  • Lock AM or PM convention, last trading time, expiry and broker cutoffs.
  • Plan exercise-by-exception, contrary instruction, pin, after-hours and halt outcomes.
  • Verify adjusted deliverable, multiplier, strike and corporate-action treatment.
  • Size for debit plus temporary stock, cash, margin, gap and residual-far-option risk.

Common misconceptions

  • “A calendar simply collects Theta.” Spot, Gamma, skew and nonparallel near/far volatility changes can dominate time decay.
  • “The initial debit is always the complete account risk.” Legging, assignment, stock, borrow, funding and poor expiration handling can add exposure.
  • “Maximum profit is known at entry.” Near-expiry value depends on the surviving far option’s future IV, time and executable bid.
  • “Spot at the strike guarantees a gain.” The far bid can be too low to recover debit and costs.
  • “Call calendars are naturally bullish, put calendars bearish, and both cost the same.” Direction and value depend on strike placement, stage, carry, dividends, exercise and the quoted surface.

Authoritative sources

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