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FRM Exam Part I · Options Markets

Bull, Bear, Butterfly and Calendar Spread Strategies

Updated 11 October 2026 · Fact-checked

A spread combines options of the same type on the same underlying, differing in strike or expiry. Bull and bear spreads use two strikes to bet on direction with limited risk. A butterfly uses three strikes to profit from low volatility. A calendar spread uses two expiries. Find the payoff by adding each leg at key prices.

Understand Option Trading Strategies: Spreads

A spread takes a long position in one option and a short position in another option of the same type (both calls or both puts) on the same underlying. The short leg cuts the cost of the long leg. It also caps your profit. That is the trade-off in every spread.

A bull spread profits when the price rises. You buy a low-strike option and sell a high-strike option. With calls (bull call spread) you pay a net premium, because the lower-strike call costs more. With puts (bull put spread) you receive a net premium. Both have the same shape: payoff rises between the two strikes and is flat outside them. Profit and loss are both limited.

A bear spread is the mirror image and profits when the price falls. With puts, you buy the high-strike put and sell the low-strike put. With calls, you buy the high-strike call and sell the low-strike call. The call version brings in a net premium.

A butterfly spread uses three strikes, K1 < K2 < K3, usually evenly spaced. With calls you buy one K1 call, sell two K2 calls and buy one K3 call. It pays most if the price ends at K2 and gives a small loss, equal to the net premium paid, if the price ends far from K2. It suits a view that volatility will be low. Puts give the same payoff.

A calendar spread uses the same strike but two expiries. A typical one sells a near-dated option and buys a longer-dated one. You profit if the price stays near the strike when the near option expires, because the short option loses time value faster. Its payoff cannot be drawn at the first expiry without a pricing model, so exams test it conceptually.

Key formulas to remember

Bull call spread payoff
Payoff = max(S − K1, 0) − max(S − K2, 0), K1 < K2
Long K1 call, short K2 call. Maximum payoff is K2 − K1. Profit = payoff − net premium.
Bull call spread: max profit and max loss
Max profit = (K2 − K1) − net debit; Max loss = net debit
Breakeven = K1 + net debit.
Bull put spread
Max profit = net credit; Max loss = (K2 − K1) − net credit
Long K1 put, short K2 put. Breakeven = K2 − net credit.
Bear put spread payoff
Payoff = max(K2 − S, 0) − max(K1 − S, 0), K1 < K2
Long K2 put, short K1 put. Maximum payoff is K2 − K1. Breakeven = K2 − net debit.
Butterfly spread with calls
Payoff = max(S − K1, 0) − 2 max(S − K2, 0) + max(S − K3, 0)
Maximum payoff is K2 − K1 at S = K2. With evenly spaced strikes (K2 − K1 = K3 − K2), the minimum payoff is 0. With unequal spacing, the payoff for S ≥ K3 is 2K2 − K1 − K3, which is negative if K3 − K2 > K2 − K1.
Butterfly breakevens
Lower = K1 + net debit; Upper = K3 − net debit
Max profit = (K2 − K1) − net debit. Max loss = net debit.

How to solve Option Trading Strategies: Spreads questions

Use this method for any spread question. It works for payoffs, profits, breakevens and strategy identification.

  1. 1List every leg: long or short, call or put, strike, and premium paid or received.
  2. 2Compute the net premium. Premiums paid are negative; premiums received are positive. Note whether it is a debit or credit.
  3. 3Find the payoff of each leg in each price region: below the lowest strike, between strikes, above the highest strike.
  4. 4Add the leg payoffs in each region. Short legs enter with a negative sign.
  5. 5Subtract the net debit (or add the net credit) to get profit.
  6. 6Identify maximum profit, maximum loss and breakevens from the region results.
  7. 7Check the answer: bull spreads must gain as price rises, and a long butterfly's payoff must never be negative.

Quickest way: Corner-point check

When to use it: Use it when a question gives strikes and premiums and asks for maximum profit, loss or breakeven.

  1. For a vertical spread, the maximum payoff is the strike gap K2 − K1. The other extreme payoff is 0.
  2. Debit spread: max loss is the debit, max profit is the gap minus the debit.
  3. Credit spread: max profit is the credit, max loss is the gap minus the credit.
  4. Butterfly: the peak payoff is the gap between the first two strikes. Breakevens sit a debit inside the outer strikes.
  5. Check the sign: a debit spread has its maximum profit at the strike side it wants the price to reach.

Common mistakes in Option Trading Strategies: Spreads

  • Calling a bull put spread a bearish trade because you sell a put

    You focus on one leg instead of the whole position.

    Fix: Bull means long the lower strike and short the higher strike. The bull put spread has the same payoff shape as the bull call spread but is a credit trade.

  • Forgetting the net premium when finding profit

    Payoff diagrams are drawn without premiums, so the debit or credit gets dropped.

    Fix: Always compute net premium first. Profit = payoff + net credit, or payoff − net debit.

  • Using the wrong butterfly breakevens

    You use K2 as a breakeven because it is the peak.

    Fix: K2 is the point of maximum profit. Breakevens are K1 + debit and K3 − debit.

  • Buying the wrong strikes in a bear put spread

    You copy the bull spread pattern.

    Fix: In a bear put spread you buy the higher-strike put and sell the lower-strike one. The bought put costs more, so it is a debit.

  • Drawing the calendar spread payoff as a fixed shape

    You treat it like a vertical spread.

    Fix: A calendar spread's profit at the near expiry depends on the value of the longer option then. Remember the idea: it profits if the price stays near the strike.

  • Assuming the butterfly payoff is zero beyond the outer strikes when the gaps are unequal

    Textbook examples use symmetric strikes.

    Fix: The peak is still K2 − K1 at S = K2, whatever the spacing. But for S ≥ K3 the payoff is 2K2 − K1 − K3, which is not zero. It is negative if K3 − K2 > K2 − K1. The result that the payoff is never negative holds only for equal spacing, so with unequal gaps compute the payoff in each region directly.

Worked examples

Example 1

A stock trades at $50. You buy a 45-strike call for $7 and sell a 55-strike call for $2. Find the strategy, maximum profit, maximum loss and breakeven at expiry.

Show the solution
  1. Long lower-strike call, short higher-strike call: this is a bull call spread.
  2. Net debit = 7 − 2 = $5.
  3. Maximum payoff = 55 − 45 = $10, reached when S ≥ 55.
  4. Maximum profit = 10 − 5 = $5.
  5. Maximum loss = the debit = $5, reached when S ≤ 45.
  6. Breakeven = 45 + 5 = $50.

Answer: Bull call spread: maximum profit $5, maximum loss $5, breakeven $50.

Example 2

You buy one 40-strike call at $12, sell two 50-strike calls at $7 each and buy one 60-strike call at $3. Find the net cost, the profit if the stock ends at $50, and the breakevens.

Show the solution
  1. Net cost = 12 − 2 × 7 + 3 = 12 − 14 + 3 = $1 debit.
  2. At S = 50: long 40 call pays 10; the two short 50 calls pay 0; the 60 call pays 0. Payoff = $10.
  3. Profit = 10 − 1 = $9.
  4. Check: (K2 − K1) − debit = 10 − 1 = 9.
  5. Lower breakeven = 40 + 1 = $41.
  6. Upper breakeven = 60 − 1 = $59.

Answer: Net cost $1; profit at $50 is $9; breakevens are $41 and $59.

Exam tips

  • Identify the strategy from the leg signs first. Most questions are answered once you name it correctly.
  • Read whether the question asks for payoff or profit. The difference is the premium.
  • Expect conceptual questions on why a butterfly suits low expected volatility and why a bull put spread gives the same payoff shape as a bull call spread.
  • For calendar spreads, know the intuition: the short near-dated option decays faster than the long far-dated option.
  • Check the answer against the maximum possible value K2 − K1. A profit above it is wrong.

Practice questions from Options Markets

Option Trading Strategies: Spreads in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Option Trading Strategies: Spreads: frequently asked questions

What is the difference between a bull call spread and a bull put spread?

Both use a long lower strike and a short higher strike, and both gain when the price rises. The call version costs a net debit. The put version gives a net credit. Their payoff shapes are the same, but the premium flows differ.

How do I construct a long butterfly spread?

With calls, buy one call at the lowest strike, sell two calls at the middle strike and buy one call at the highest strike. Keep the strikes evenly spaced and the expiry the same. You pay a small net debit.

What view does a butterfly spread express?

It expresses a view that the price will finish close to the middle strike, so volatility is low. Your loss is limited to the net debit. Your profit is capped at the strike gap minus the debit.

How does a calendar spread work?

You sell an option with a near expiry and buy an option with the same strike but a later expiry. You gain if the price stays near the strike, because the near option loses time value faster. It is usually a net debit.