FRM: Option payoffs

Explanations, applications and practice for option payoffs.

• Build a bear put spread and net premium

  Reconcile a long higher-strike put with a short lower-strike put.

  Worked examples

• Build a bull call spread by price region

  Subtract the higher-strike writer amount before deducting the net premium.

  Worked examples

• An in-the-money call with a negative simple profit

  Reconcile a positive payoff that does not recover the premium.

  Worked examples

• Calculate a collar’s terminal band and net credit

  Combine stock, a lower-strike put and a higher-strike written call.

  Worked examples

• Calculate a covered call’s terminal value and simple profit

  Add one stock unit and a same-unit short call under an explicit record.

  Worked examples
• 

  Option-scenario date and value record

  Distinguish current prices, terminal scenarios and dated cash amounts.

  Templates

• One expiry scenario versus an exercise policy

  Separate terminal algebra from decisions or rules at earlier dates.

  Concepts

• Forward and straddle terminal exposures

  Compare a signed linear outcome with a two-sided option payout.

  Comparisons

• Allowing negative holder payoff in a vanilla option

  Apply the contract floor before adding the premium or writer sign.

  Common mistakes

• Option-expiry tool input and chart scope

  Check units, date roles and plot range before interpreting the outputs.

  Tool guides

• Explain an option-payoff record in an interview

  Practice a clear model explanation with units, dates and limits.

  Careers

• Expiry payoff and pre-expiry option value

  Use the appropriate date before interpreting a max expression.

  Concepts
• 

  Option-position leg and premium sheet

  Keep side, unit quantity and premium direction for each original leg.

  Templates

• Add option legs on a common expiry basis

  Reconcile quantities, signs and premiums before combining positions.

  Lessons

• European put–call parity with a discount factor

  Match terminal portfolios before writing their current-value equality.

  Formulas

• Option payoff and simple profit

  Distinguish the contract’s terminal amount from the position’s cost-adjusted result.

  Concepts

• Derive option payoffs by terminal-price region

  Write the contract expression on each side of its strike.

  Lessons

• Reading a finite payoff chart as a risk cap

  Separate the displayed scenario range from the payoff function’s domain.

  Common mistakes

• Option combinations and replication boundaries

  Check leg algebra, cost bases and terminal-versus-current values.

  Practice

• Option signs, premiums and contract units

  Check original vanilla expiry records with explained alternatives.

  Practice

• Dropping premium from an option profit

  Inspect whether the calculation reported contract payoff as position profit.

  Common mistakes

• Solve a put price from a compatible parity record

  Keep strike cash and its present value distinct in the current-cost equation.

  Worked examples

• Calculate a protective put’s terminal floor and cost

  Keep the payoff floor separate from the position’s premium-adjusted loss.

  Worked examples

• Using call subtraction for a put payoff

  Recover the strike-minus-price difference in the below-strike region.

  Common mistakes

• Separate expiry replication from current-price equality

  Prove the terminal identity before applying a pricing assumption.

  Lessons

• Option-payoff and replication checklist

  Review contract regions, premium signs, units and dates before accepting a diagram.

  Revision

• Option-payoff learning sequence

  Build from one contract to a compatible multi-leg and price-identity explanation.

  Study plans

• Scale a short-call record into contract amounts

  Apply the writer sign and multiplier once to every cash movement.

  Worked examples

• Reconcile a short put’s premium and settlement

  Use the writer’s side in an original below-strike outcome.

  Worked examples

• Holder and writer signs in option records

  Keep the premium and settlement directions on one consistent side.

  Concepts

• Signed vanilla option payoff and simple profit

  Apply the position sign and unit quantity to a nonnegative holder payoff.

  Formulas

• Vertical call-spread payoff by region

  Derive the capped terminal amount of two same-expiry call legs.

  Formulas

• Covered-call and protective-put payoff choices

  Compare the terminal cap and floor created by different stock-option legs.

  Comparisons

• Calculate a long straddle’s two profit boundaries

  Add the same-strike call and put payoffs before deducting both premiums.

  Worked examples

• Reconcile long call minus short put at expiry

  Prove a signed linear payoff from two contingent claims.

  Worked examples

• Match a protective put with call plus terminal cash

  Verify the terminal identity with original scenario values.

  Worked examples

• Build an option-position cash-flow timeline

  Separate initiation premium from expiry settlement before calculating a result.

  Lessons
• 

  Option expiry payoff and simple-profit calculator

  Inspect calls, puts and position sides with explicit premium and contract units.

  Tools

• A put premium above strike and an unattainable boundary

  Use the nonnegative-price domain before reporting a breakeven.

  Worked examples

• Option contracts and underlying-unit amounts

  Scale a per-unit quote into one position total without applying the multiplier twice.

  Concepts