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

A non-dividend-paying share trades at Rs 100. A one-year European call with strike Rs 100 is worth Rs 10.45 under Black-Scholes with a continuously compounded risk-free rate of 5% a year. What is the value of the European put with the same strike and expiry? (e^-0.05 = 0.951229)

The put is worth about Rs 5.57. Put-call parity gives P = C - S + K e^{-rT}, so 10.45 - 100 + 95.12 = 5.57. The strike must be discounted continuously at 5% for one year, not compounded or discounted discretely.

  1. ARs 10.45
  2. BRs 15.33
  3. CRs 5.57Correct
  4. DRs 15.58
  5. Rs 5.69

Explanation

Put-call parity: P = C - S + K e^{-rT} = 10.45 - 100 + 95.1229 = 5.57. Rs 5.69 comes from discounting with 1/1.05 instead of continuous discounting. Rs 15.58 compounds the strike forward instead of discounting it, and Rs 15.33 reverses the signs of C and S.

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