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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

A share of an Indian company trades at Rs 400 and follows GBM with mu = 12% p.a. and sigma = 20% p.a. What is the expected share price after 2 years, E[S_2], to the nearest rupee?

The expected price under geometric Brownian motion is S_0 times e to the power mu t, so 400 times e to the power 0.24, which is about Rs 509. No volatility correction applies to the mean of the price itself.

  1. ARs 480
  2. BRs 509Correct
  3. CRs 497
  4. DRs 524
  5. Rs 452

Explanation

For GBM, E[S_t] = S_0 e^{mu t}. So E[S_2] = 400 e^{0.24} = 400 x 1.27125 = 508.5, about Rs 509. Rs 497 uses the drift mu - sigma^2/2 (a wrong adjustment, which gives the median: 400 e^{0.2} = 489 is not it either, but 497 is nearby from a partial correction). Rs 480 is simple interest.

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