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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

A stock is priced at ₹100. In each of two periods it can rise by 20% or fall by 20%. The risk-free rate is 10% per period. Using the two-period binomial model, what is the present value of a European call with a strike price of ₹100 expiring at the end of period two?

The call is worth about ₹20.45. Only the up-up outcome of ₹144 gives a payoff of ₹44, and its risk-neutral probability is 0.75 × 0.75 = 0.5625. The expected payoff of ₹24.75 is discounted for two periods at 10%, which is divided by 1.21.

  1. A₹9.09
  2. B₹20.45Correct
  3. C₹22.50
  4. D₹24.75

Explanation

Risk-neutral p = (1.10 − 0.8)/0.4 = 0.75. The terminal prices are 144, 96 and 64, so only the up-up node pays ₹44. The expected payoff is 0.75² × 44 = ₹24.75. Discounting over two periods gives 24.75/1.21 = ₹20.45. ₹22.50 discounts for only one period, and ₹9.09 uses p = 0.5.

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