Skip to content

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

A share follows GBM with S(0) = ₹200, μ = 8% and σ = 25%. Over one year, what is the probability that S(1) exceeds ₹200? Φ(0.0488) = 0.5195 and Φ(0.2) = 0.5793; use the closest value.

The log return is normal with mean 4.875% and standard deviation 25%. The probability that the price rises is Φ(0.195), about 0.52, closest to 0.5195. The drag of σ²/2 pushes the probability only slightly above one half.

  1. A0.4805
  2. B0.5793
  3. C0.5195Correct
  4. D0.4207
  5. 0.5000

Explanation

ln(S(1)/S(0)) ~ N(μ − σ²/2, σ²) = N(0.08 − 0.03125, 0.0625) = N(0.04875, 0.0625). P(>0) = Φ(0.04875/0.25) = Φ(0.195) ≈ 0.5193, closest to 0.5195. Using μ without the adjustment gives Φ(0.32)≈0.6255, which is not offered; 0.5793 comes from a wrongly scaled value.

Did you get it right without looking?

One question tells you little. A timed set on Stochastic models for security prices shows your real accuracy, how long you take and where you lose marks.

Practise Stochastic models for security pricesFree diagnostic mock

More Stochastic models for security prices questions