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IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices

A share pays no dividends and trades at Rs 200. The continuously compounded risk-free rate is 6% per year. A European call and put on it both have strike Rs 190 and expire in one year. The call is priced at Rs 25. Given e^-0.06 = 0.9418, which is the price of the put, to the nearest rupee?

The put costs about Rs 4. By put-call parity, put equals call minus share price plus discounted strike: 25 - 200 + 190 x 0.9418 = 3.94. The strike must be discounted at the continuously compounded risk-free rate.

  1. ARs 4Correct
  2. BRs 6
  3. CRs 14
  4. DRs 25
  5. Rs 3

Explanation

Put-call parity: P = C - S + K e^-rT = 25 - 200 + 190*0.9418 = 25 - 200 + 178.94 = 3.94, about Rs 4. Using K without discounting gives 15, and the sign mistake of S - C gives other wrong values.

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