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Long Call Condor: Four Strikes, Unequal Wings, and Valid Breakevens

Analyze a long call condor from its signed four-leg inventory through unequal-wing expiration value, root domains, executable package cash, assignment, and cash-settlement risk.

Updated

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

Direct answer

This article defines a long call condor as four calls on the same claim and expiration with K₁<K₂<K₃<K₄: buy +C(K₁), sell −C(K₂), sell −C(K₃), and buy +C(K₄) in matched 1:1:1:1 quantities. It normally pays a signed net debit D>0, has bounded expiration results, and reaches its highest expiration value from K₂ through K₃.

The name is not enough to identify a position. A long put condor uses the same signed pattern in puts and has the same expiration value as the call condor only under aligned equal-wing claims. An iron condor mixes a put spread and a call spread; The Options Industry Council calls its common credit version Short Condor (Iron Condor). A provider’s short or reverse condor may mean something else. Save the signed legs, quantities, expirations, exercise styles, settlement methods, multipliers, and deliverables as the controlling inventory.

For the call condor, define w_L=K₂−K₁, w_R=K₄−K₃, strategy units u, common multiplier m, entry fees F, and signed package cost D=p₁−p₂−p₃+p₄, where D>0 is a debit and D<0 is a credit. At the contract’s official expiration settlement value S_T, gross value per quote unit is V_T=max(S_T−K₁,0)−max(S_T−K₂,0)−max(S_T−K₃,0)+max(S_T−K₄,0), and total profit or loss is Π_T=u m(V_T−D)−F.

How to build and validate the position

  1. Lock the product and name boundary: long call condor, long put condor, mixed put-call iron condor, or explicit reversal. Record the signed leg matrix rather than relying on a ticket label.
  2. Lock all four series: underlying or index, call or put, buy or sell side, K₁ through K₄, quantity, expiration, exercise style, physical or cash settlement, multiplier, deliverable, currency, adjustment, last trading time, and official settlement source.
  3. Build an executable entry ledger. Use an eligible complex-order fill or synchronized asks for bought legs and bids for sold legs, calculate D, u, m, and F, and distinguish a broker’s Debit/Credit label from this signed convention. Midpoints, stale legs, partial packages, and legging do not establish one executable net price.
  4. Derive the call-condor value without assuming equal wings: V_T=0 for S_T≤K₁; V_T=S_T−K₁ for K₁<S_T≤K₂; V_T=w_L for K₂<S_T≤K₃; V_T=w_L+K₃−S_T for K₃<S_T≤K₄; and V_T=w_L−w_R for S_T>K₄.
  5. Calculate amounts and roots in their valid regions. Maximum total profit is u m(w_L−D)−F; minimum total result is u m[min(0,w_L−w_R)−D]−F. Let fee-adjusted cost per quote unit be d=D+F/(u m). The lower root K₁+d is valid only if 0≤d≤w_L; the upper root K₃+w_L−d is valid only if w_L−w_R≤d≤w_L.
  6. Reprice before expiration under spot, each leg’s IV and skew, time, rates, dividends, borrow, liquidity, and event shocks. Separately run American physical exercise and assignment, Ex-by-Ex or contrary instructions, pin and after-hours paths, and European cash settlement using the official value rather than a screen close.
  7. Reconcile every fill, fee, remaining option, share, strike cash, cash-settlement debit or credit, dividend, borrow charge, margin, tax lot, correction, and final statement. Closing a package, exercising a long leg, or receiving assignment on a short leg are different transactions and do not automatically coordinate the other legs.

If w_L=w_R=W and, before fees, 0<D<W, both tails have value 0, the plateau profit per quote unit is W−D, and the familiar roots are K₁+D and K₄−D. Outside that domain, there may be zero, one, or two valid breakevens. A credit does not prove an arbitrage, a plateau does not prove profit after cost, and an unequal-wing call condor can retain a nonzero high-tail value or loss.

An equal-wing long put condor can reproduce the same expiration diagram. Under zero rates and aligned frictionless European claims, a long call condor costing D and a credit iron condor receiving C satisfy D+C=W; with nonzero deterministic rates, the controlled relation is D+C=PV(W). Execution, American rights, cash versus physical settlement, dividends, borrow, taxes, and mismatched claims prevent mechanical substitution.

Worked examples

  • Equal wings, fees, and the plateau. Buy the 95 call at 8.50, sell the 100 call at 5.50, sell the 105 call at 3.00, and buy the 110 call at 1.50. Then D=8.50−5.50−3.00+1.50=1.50, w_L=w_R=5, u=1, m=100, and four $0.65 entry fees give F=$2.60 and d=1.526. Fee-inclusive maximum loss is $152.60, maximum profit is $347.40, and breakevens are 96.526 and 108.474. At S_T=103, V_T=5, so net profit is (5−1.50)×100−2.60=$347.40.
  • Unequal wings invalidate the symmetric shortcut. Use K₁/K₂/K₃/K₄=90/100/105/120, so w_L=10, w_R=15, with D=2, u=1, m=100, and no fees. Low-tail, plateau, and high-tail profit per quote unit are −2, +8, and −7; maximum loss is $700 and maximum profit is $800. The valid roots are 92 and 113, because the upper root is 105+10−2=113; the equal-wing shortcut K₄−D=118 is wrong.
  • Call, put, and iron constructions can match only under controlled assumptions. With zero rates, no fees, and aligned 95/100/105/110 European claims, suppose the long call condor costs 1.50, the equal-wing long put condor also costs 1.50, and the credit iron condor receives 3.50. At S_T=97/103/109, each produces expiration profit 0.50/3.50/−0.50 per quote unit. Here 1.50+3.50=5.00; at nonzero deterministic rates the relation uses PV(5.00), and executable prices or mismatched contracts need not satisfy the teaching identity exactly.
  • Physical assignment and cash settlement are different branches. In a 95/100/105/110 American equity call condor, assignment on the short 100 call sells 100 shares at 100 and credits $10,000; the other three options remain open. If stock ask is $104.25 and the long 95 call bid is $9.30, selling that call for $930 and buying shares for $10,425 leaves event cash $10,000+$930−$10,425=$505. Exercising the call instead pays $9,500 for shares and leaves $500, sacrificing $5 of executable time value. By contrast, a European cash-settled index call condor with 4000/4050/4100/4150, D=18, m=100, and official S_T=4075 has V_T=50 and gross profit (50−18)×100=$3,200; at official S_T=4200, V_T=0 and loss is $1,800. It creates no shares or early assignment.

Contract, execution, and lifecycle risks

  • Define the signed legs; condor, short condor, and iron condor labels are ambiguous.
  • Verify option type, strike order, expiration, quantity ratio, and opening or closing effect.
  • Match multiplier, deliverable, currency, adjustment, and underlying or index identity.
  • Do not apply equal-wing formulas when w_L and w_R differ.
  • Keep the signed debit or credit convention consistent with the broker ticket.
  • Validate every algebraic breakeven inside the region that generated it.
  • Use executable complex-order or leg-side prices and available size, not optimistic midpoints.
  • Control partial package fills, legging, auction, cancellation, rejection, and correction risk.
  • Include four-leg entry and exit fees, exchange charges, slippage, and tax.
  • Separate expiration payoff from current mark, model value, or executable close value.
  • Stress each leg’s IV, skew, term structure, Gamma, Theta, and event response.
  • Treat the two short options as independently assignable American obligations.
  • Check dividends, borrow, rates, extrinsic value, and the cost of exercising long calls.
  • Plan for partial assignment, short stock, strike cash, margin, and forced liquidation.
  • Control exercise cutoffs, Ex-by-Ex, contrary instructions, pin, after-hours, and halts.
  • Distinguish American or European style from physical or cash settlement.
  • Use the contract’s official settlement value, not an ETF, future, last sale, or screen close.
  • Recalculate after corporate actions, adjusted deliverables, or series changes.
  • Confirm regulatory and house margin, buying power, concentration, and funding buffers.
  • Reconcile fills, options, shares, cash, fees, dividends, borrow, taxes, and final records.

Common misconceptions

  • Every condor is an iron condor with puts and calls.
  • Four ordered strikes automatically mean equal wings and symmetric tails.
  • The formulas W−D and K₄−D work for every debit, credit, or wing width.
  • A broad plateau guarantees profit or is always preferable to a narrower one.
  • Bounded expiration loss eliminates temporary execution, assignment, funding, and settlement risk.

Authoritative sources

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