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

A share is at Rs 50. In one period it becomes Rs 60 or Rs 40. The risk-free rate is 4% per period (simple, discrete). What is the value of a European put with strike Rs 55?

The risk-neutral up probability is 0.6. The put pays Rs 15 only in the down state, so its value is 0.4 times 15 divided by 1.04, about Rs 5.77. Put-call parity gives the same result.

  1. ARs 4.62Correct
  2. BRs 5.87
  3. CRs 3.85
  4. DRs 7.50
  5. Rs 2.40

Explanation

q = (50*1.04 - 40)/20 = 12/20 = 0.6. Put payoffs: up = 0, down = 15. Value = (0.4*15)/1.04 = 6/1.04 = 5.77. Check by put-call parity: call = 0.6*5/1.04 = 2.885; put = 2.885 - 50 + 55/1.04 = 2.885 - 50 + 52.885 = 5.77. The correct value is Rs 5.77, nearest listed is Rs 5.87, with Rs 4.62 arising from discounting wrongly.

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