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

A share is priced at ₹100. Over one year it will either rise to ₹120 or fall to ₹90. The continuously compounded risk-free rate is such that e^r = 1.05. What is the value of a one-year European call option with strike ₹100?

The risk-neutral probability of an up-move is 0.5, the up payoff is ₹20 and the down payoff is zero. The call is worth 0.5 × 20 divided by 1.05, which is ₹9.52.

  1. A₹5.56
  2. B₹6.35Correct
  3. C₹7.94
  4. D₹9.52
  5. ₹10.00

Explanation

q = (1.05 − 0.9)/(1.2 − 0.9) = 0.5. The payoffs are 20 in the up state and 0 in the down state. The value is 0.5 × 20 / 1.05 = 9.52. Checking via hedge: Δ = 20/30 = 0.667; the portfolio of Δ shares less one call is worth 60 in both states, so PV = 57.14. The call = 66.67 − 57.14 = 9.52. So the keyed option must be ₹9.52.

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