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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

A European call option on a non-dividend-paying share has strike price Rs 500. At expiry the share price is Rs 460. Which statement about the holder's position at expiry is correct?

The call expires worthless because the share price of Rs 460 is below the strike of Rs 500, so the payoff is max(S-K,0)=0. The holder does not exercise and loses only the premium paid, since holders have a right, not an obligation.

  1. AThe option expires worthless and the holder's loss is limited to the premium paidCorrect
  2. BThe holder exercises and receives Rs 40
  3. CThe holder exercises and pays Rs 40 to the writer
  4. DThe writer must pay the holder the premium back
  5. The holder's loss is Rs 40 plus the premium

Explanation

A call payoff is max(S - K, 0) = max(460 - 500, 0) = 0. The holder will not exercise, so the only loss is the premium already paid. Options B, C and E treat the call as if it had a negative intrinsic value, but option holders have no obligation to exercise.

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