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Option strategies: what each one is actually a bet on

OPT · Chapter 314 min readAsked at Optiver, SIG, IMC, Akuna

Assumes Put–call parity.

After this lesson you should be able to

  • State the payoff, breakeven and maximum loss of each standard structure.
  • Read a structure’s Greek profile from its shape.
  • Choose the structure that expresses a given view most cleanly.

There are perhaps ten structures worth knowing, and they are combinations of two ideas: spreads cap a directional view, and straddle-like structures trade movement rather than direction. What an interviewer wants is not the list but the mapping — given a view, which structure, and why not the others.

StructureBuilt fromThe betMax loss
Call spreadLong low strike, short highUp, but not farNet premium
Put spreadLong high strike, short lowDown, but not farNet premium
StraddleCall and put, same strikeA big move, either wayBoth premiums
StrangleCall and put, different strikesA bigger move, more cheaplyBoth premiums
ButterflyLong wings, short two at the middleIt ends near the middleNet premium
CondorButterfly with a flat topIt ends in a rangeNet premium
CalendarShort near-dated, long far-datedQuiet now, moving laterNet premium
Risk reversalLong call, short putUp, financed by the downsideLarge — like stock
CollarLong stock, long put, short callProtect a holding cheaplyDown to the put strike
Table 3.1 · The structures. The risk-reversal row is the one to be careful with: it looks like a cheap way to be long, and its downside is essentially the same as owning the stock.

Two families, not nine structures. Everything in that table is one of two things. Either you have a directional view and are selling away the part of the distribution you do not believe in — that is every spread, and it converts an expensive option into a cheaper bounded one. Or you have a view on how much the underlying will move and none on direction — that is the straddle family, and the strikes you choose decide which part of the distribution you are trading. Butterflies and condors are the short-movement side of the same family. Recognising which family a question is in narrows nine choices to about three.

StructureDeltaGammaVegaTheta
Long call spreadPositive, cappedSmallSmallSmall either way
Long straddleNear zero at the moneyLongLongShort
Short strangleNear zeroShortShortLong
Long butterflyNear zeroShort at the middleShortLong
Calendar spreadNear zeroShort near, long farLongPositive early
Table 3.2 · Greek profile by structure. Two patterns run through it. Long gamma and short theta always travel together, and so do short gamma and long theta — you are either paying rent for convexity or collecting it for supplying convexity.

Example 3.3

A stock is at $100\$100. The $100\$100 call costs $6\$6 and the $110\$110 call costs $2\$2. Describe the 100/110100/110 call spread.

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Worked solution

  1. Formula
    cost=6−2,max payoff=110−100\text{cost} = 6 - 2, \quad \text{max payoff} = 110 - 100
  2. Substitute
    net debit=$4\text{net debit} = \$4
  3. Solve
    max profit=10−4=$6\text{max profit} = 10 - 4 = \$6
  4. breakeven=100+4=$104\text{breakeven} = 100 + 4 = \$104
  5. max loss=$4\text{max loss} = \$4
  6. Answer
    risk $4 to make $6, breakeven at $104\text{risk } \$4 \text{ to make } \$6, \text{ breakeven at } \$104

Sanity check. The outright call costs $6\$6 and breaks even at $106\$106; the spread costs $4\$4 and breaks even at $104\$104, at the price of capping the upside at $110\$110. That trade-off — a lower breakeven for a capped payoff — is what every spread is doing.

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