Lesson 4 of 7 · 13 min

Options and call payoffs

An option gives its buyer the right, but not the obligation, to buy (call) or sell (put) at a fixed price, so the buyer's payoff can never be negative and the buyer pays a premium for that.

In short

  • Options are contingent claims: the buyer decides whether the trade happens. The seller must perform if the buyer exercises.
  • The buyer pays the seller a premium up front. The agreed price is the exercise (strike) price, X. European options exercise only at maturity; American at any time.
  • A call is in the money when St>XS_t > X; its intrinsic value is St−XS_t - X. At or out of the money, the price is pure time value, which decays to zero at maturity.
  • Long call: payoff cT=max⁡(0,ST−X)c_T = \max(0, S_T - X), profit max⁡(0,ST−X)−c0\max(0, S_T - X) - c_0, breakeven X+c0X + c_0. Loss capped at the premium; upside unlimited.
  • Short call: profit at most the premium, losses unlimited. Once the premium is paid, only the buyer faces counterparty credit risk.

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Options and call payoffs · Forward Commitment and Contingent Claim Features and Instruments