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IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices

A non-dividend-paying share trades at Rs 100. Under Black-Scholes, for a European call with strike Rs 100, maturity 1 year, risk-free force of interest 5% and volatility 20%, d1 = 0.35 and d2 = 0.15. Given N(0.35)=0.6368 and N(0.15)=0.5596 and e^(-0.05)=0.9512, what is the call price?

The call price is about Rs 10.45. It equals 100 times N(d1) of 0.6368, which is 63.68, minus the discounted strike 95.12 multiplied by N(d2) of 0.5596, which is 53.23, giving 10.45.

  1. ARs 10.45Correct
  2. BRs 6.37
  3. CRs 5.40
  4. DRs 12.10
  5. Rs 8.20

Explanation

C = S N(d1) - K e^(-rT) N(d2) = 100(0.6368) - 100(0.9512)(0.5596) = 63.68 - 53.23 = 10.45. Omitting the discount factor gives 63.68-55.96=7.72, which is not an option; using N(d1) alone gives 6.37 only after misscaling.

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