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CMA Final · Strategic Financial Management · Options

Shares of Sutlej Foods trade at Rs 100. In a one-period binomial model the price will become Rs 120 or Rs 80. A call has strike Rs 100 and the risk-free rate is 5% for the period. What is the call value using the risk-neutral approach (nearest rupee-paisa)?

The call is worth Rs 11.90. The risk-neutral up probability is 0.625, giving an expected payoff of Rs 12.50, which discounted at 5% gives about Rs 11.90. The hedge-ratio method of half a share minus borrowing confirms it.

  1. ARs 9.52Correct
  2. BRs 10.00
  3. CRs 12.50
  4. DRs 11.90

Explanation

u=1.2, d=0.8. Risk-neutral p = (1.05 - 0.8)/(1.2 - 0.8) = 0.625. Payoffs: up 20, down 0. Expected = 0.625 x 20 = 12.50. Discounted = 12.50/1.05 = Rs 11.90. Check with hedge ratio: delta = 20/40 = 0.5; portfolio: 0.5x80 = 40 payoff both states, PV = 38.10; call = 50 - 38.10 = 11.90. So correct is 11.90, option index 3.

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