Double Calendar: Two Strikes, Two Expirations, Four Legs

Audit a double calendar with executable four-leg pricing, front-expiration surface values, position Greeks, assignment branches, and roll ledgers.

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

Direct answer

A double calendar is a market name, not a standardized contract definition. A common one-for-one construction combines a lower-strike put calendar and a higher-strike call calendar on the same underlying: sell the nearer-dated put and call, then buy later-dated options at the corresponding strikes. A different provider may use the name for another pair of calendars, so identify every signed leg, ratio, expiration, multiplier, deliverable, exercise style, and settlement method before using the label.

The nearer options disappear first while the later options retain time value. Consequently, the position has no ordinary single-expiration payoff diagram, fixed maximum gain, or pair of breakevens known at entry. Its value at the front expiration depends on executable back-option prices, the front obligations, two volatility surfaces, skew, rates, dividends, borrow, and operational choices.

Structure and exposure

Lock the underlying, lower strike K₁, upper strike K₂, front expiration T₁, back expiration T₂, with K₁<K₂ and T₁<T₂. Record each signed ratio, multiplier, live deliverable, style, settlement, currency, and cutoff.
Verify the common construction explicitly: sell P(K₁,T₁) and C(K₂,T₁), then buy P(K₁,T₂) and C(K₂,T₂). Do not infer those legs from the strategy name.
Use synchronized executable quotes. Define opening debit per underlying unit as D_exec=A_P2+A_C2−B_P1−B_C1, where A is the ask paid for a back option and B is the bid received for a front option. Add fees and impact; a midpoint or last price is not an executable opening cost.
Build separate pre-expiration and settlement ledgers. Before T₁, closing all four legs uses C_close=B_P2+B_C2−A_P1−A_C1. At T₁, define front liabilities H_P=max(K₁−S_set,0) and H_C=max(S_set−K₂,0); front intrinsic value cannot replace a close ask before settlement.
If surviving back options can be sold at bids B_P2,T1 and B_C2,T1, use the economic comparison V_T1=B_P2,T1+B_C2,T1−H_P−H_C. For quantity Q, compatible multiplier M, and total fees and financing F, calculate P/L_T1=Q×M×(V_T1−D_exec)−F.
Scan spot and both volatility surfaces. A conditional breakeven is a numerical root of V_t(S,surface)=D_exec+F/(Q×M) under a stated time, quote, and settlement scenario. There may be zero, two, or four roots. Normalize units and calculate signed sensitivity as X_net=X_P2+X_C2−X_P1−X_C1; no Greek sign is permanent.
Prewrite close-all, expire-or-close-fronts and retain the back strangle, roll-one-or-both-shorts, assignment, exercise, and cash-settlement branches. Reconcile fills, realized old-leg P/L, roll cash, new obligations, residual back value, stock, margin, funding, fees, and tax.

Four worked examples

Executable entry versus midpoint. A front 95 put is 1.55/1.65, its back put is 3.30/3.40, a front 105 call is 1.45/1.55, and its back call is 3.10/3.20. Thus D_exec=3.40+3.20−1.55−1.45=3.60 per share, or $360 with M=100. The midpoint debit is 3.35+3.15−1.60−1.50=3.40, or $340, which understates executable debit by $20. Four contract fees of $0.65 add $2.60, making initial cash outflow $362.60.
The same spot under different back surfaces. At T₁, let S_set=$100 and both front shorts expire worthless. If executable back bids are 1.80 and 1.90, then V_T1=3.70 and the fee-before result relative to D_exec=3.60 is +$10. If a volatility crush leaves bids of 1.55 and 1.60, then V_T1=3.15 and the result is −$45. Spot alone does not determine a fixed profit area.
Settlement style can break the debit-limit shortcut. Let S_set=$140, K₂=$105, the back put bid be 0.05, and a European back call bid be 34.00. A cash-settled front-call liability is $35 per unit, so V_T1=0.05+34.00−35.00=−0.95; relative to the 3.60 debit, P/L=(−0.95−3.60)×100=−$455, exceeding the $360 debit loss. With matched American physical calls instead, assignment of the short call creates −100 shares and +$10,500 cash. The holder may separately exercise the back 105 call, paying $10,500 for 100 shares, but that action is not automatic and can forfeit remaining time value.
Greeks, term skew, and a roll ledger. Per-unit (Delta,Gamma,Vega,Theta) values are front put (−0.30,0.025,0.08,−0.06), back put (−0.35,0.015,0.14,−0.03), front call (0.30,0.025,0.08,−0.06), and back call (0.35,0.015,0.14,−0.03). With short fronts, long backs, and M=100, net values are Delta=0 shares, Gamma=−2 shares/$1, Vega=+$12 per volatility point, and Theta=+$6/day. Frozen-Greek Gamma P/L for a $2 move is 0.5×(−2)×2²=−$4. If front IV rises 5 points while back IV falls 2 points, the Vega approximation is (−0.08−0.08)×100×5+(0.14+0.14)×100×(−2)=−$136, despite positive parallel Vega. Later, paying 0.60 to close both old shorts and receiving 1.40 for two new shorts produces a 0.80 roll credit. The old shorts realized 1.55+1.45−0.60=+2.40 per share, while the new 1.40 is cash against a new obligation, not profit.

Risk checklist

The strategy name may conceal different option types, directions, strikes, expirations, or ratios.
A wrong series, root, option type, strike, expiration, or position sign changes the claim.
Midpoints, last prices, and model marks are not executable package prices.
Four-leg partial fills or legging can leave unintended directional and volatility exposure.
Bid-ask spread, fees, market impact, and taxes can overwhelm a small modeled edge.
A fixed maximum gain or pair of breakevens is invalid without a stated time and surface.
Front and back implied volatilities can move independently.
Skew and term-structure changes can move both peaks and the center valley.
Net Delta, Gamma, Vega, and Theta can reverse; front Gamma can dominate near T₁.
Frozen-Greek approximations can fail under large moves, jumps, or surface changes.
American short options can be assigned before expiration.
Ex-dividend dates, borrow, and deep-in-the-money puts alter exercise incentives and funding.
Assignment of a short leg does not automatically exercise a protective back leg.
Pin risk, after-hours moves, and contrary instructions can change expiration inventory.
Official settlement values may differ from a close, last trade, or after-hours price.
AM/PM timing and physical/cash settlement mismatches can create unplanned exposure.
Adjusted deliverables, multipliers, and corporate actions can break an assumed match.
Temporary stock, margin, funding, and borrow needs can exceed the opening debit.
Roll credits and cumulative option cash are not automatically profit or a reset cost basis.
Liquidity, halts, model error, tax treatment, and broker records require final reconciliation.

Common misconceptions

“It is an iron condor with different dates.” A double calendar has surviving back options and no fixed one-date payoff.
“The area between the strikes guarantees profit with fixed maximum gain and breakevens.” Back-option surfaces and executable prices determine the result.
“The debit is the maximum loss under every style and settlement.” Settlement mismatch, assignment, costs, and funding can produce larger losses or cash needs.
“Theta and Vega stay positive.” Position Greeks can change sign across spot, time, skew, and term structure.
“The broker automatically protects the package.” Assignment, exercise, expiration, and rolling are separate events that require explicit management.