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

A share priced at Rs 400 will pay a certain dividend of Rs 10 in 3 months. European call and put options expire in 6 months with strike Rs 420. The continuously compounded risk-free rate is 5% per year. Present value of dividend = 10 e^{-0.0125} = 9.876 and K e^{-0.025} = 409.60. If the call costs Rs 20, what is the put price?

With a known dividend, parity is C - P = S0 - PV(dividend) - K e^{-rT}. This gives -19.476, so the put is 20 + 19.476 = Rs 39.48. Ignoring the dividend gives a wrong figure.

  1. ARs 39.72Correct
  2. BRs 29.72
  3. CRs 19.48
  4. DRs 39.48
  5. Rs 49.60

Explanation

With dividends, C - P = S0 - PV(D) - K e^{-rT} = 400 - 9.876 - 409.60 = -19.476. So P = C + 19.476 = 39.476, about 39.48. Checking options: Rs 39.48 is option 4, not option 1.

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