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Call and put payoffs versus profit

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Start with the idea

A call benefits from finishing above strike; a put benefits from finishing below strike. The buyer paid for that right.

Symbols, units & horizon
  • S_T: settlement underlying price at expiry T, currency per unit
  • K: strike in same units
  • H_C,H_P: call/put terminal payoffs per underlying unit
  • c₀: call premium per unit at entry
  • m: underlying units per contract
  • Π_C: cash profit for one call ignoring financing and fees

When and why to use this

Build the first row of an option trade cash-flow and scenario worksheet.

A call benefits from finishing above strike; a put benefits from finishing below strike. The buyer paid for that right.

Begin with a cash-settled European contract and one underlying unit. Exercise style, settlement reference and multiplier are contract terms, not details to infer from the symbol. A physical-delivery contract requires a separate cash-and-position ledger.

For the simple undiscounted illustration, subtract the premium from terminal payoff. Financing the premium changes the break-even threshold; commissions and exercise fees must also be included before calling the result net profit.

HC=max⁡(ST−K,0),HP=max⁡(K−ST,0),ΠC=m(HC−c0)
Contract payoff definition and simplified profit accounting

Call and put payoffs versus profit

  1. Compare settlement price with strike and keep only the positive exercise difference.
  2. Calculate call and put separately because their positive regions differ.
  3. For call profit subtract premium per unit, then multiply by the contract multiplier.
Work it by hand

S_T=108, K=100, c₀=5 and m=100 give call payoff 8 per unit, put payoff 0 and call profit $300.

Apply it in a strategy

  • Freeze inputs at the stated decision time and record their units.
  • Build the first row of an option trade cash-flow and scenario worksheet.
  • Recompute the example, then change the material assumption and explain the difference.

Research deliverable

Call and put payoffs versus profit: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: Using an incorrect settlement reference, exercise style or multiplier invalidates the cash result.

These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.

Research sources, review dates and limitations

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
def terminal_options(settlement,strike,call_premium,multiplier):
    if min(settlement,strike,call_premium)<0 or multiplier<=0: raise ValueError('Invalid contract inputs')
    call=max(settlement-strike,0); put=max(strike-settlement,0)
    return call,put,multiplier*(call-call_premium)

assert terminal_options(108,100,5,100)==(8,0,300)
print(terminal_options(108,100,5,100))

Continue learning

Options: Payoffs, Replication & Hedge Accounting — all lessons
  1. Call and put payoffs versus profit
  2. A bull call spread caps gains and initial cost
  3. Put–call parity as identical terminal cash flows
  4. Replicate a one-step option with stock and cash
  5. Black–Scholes as a conditional benchmark
  6. Delta and gamma are local sensitivities
  7. Cash accounting for a discretely hedged option
  8. Early exercise compares immediate and continuation value

Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations