Chapter 9: Stochastic calculus and Ito processes

Question 1

Alternative name for Geometric Brownian Motion

Answer 1

Continuous Time Lognormal Model

Question 2

Why might Geometric Brownian Motion (a.k.a Continuous Time Lognormal Model) not be appropriate for modelling share prices

Answer 2

• σ may not be constant over time (estimates of volatility from past data depend on the time period chosen)
• μ may not be constant over time (e.x. influenced by interest rates)
• Mean-reversion, as seen in some markets, are not consistent with the assumption of independent increments.
• Momentum effects “ “ “ “ “.
• Distribution of observed log returns has a smaller peak than implied by the normal distribution.
• The distribution of observed log returns has fatter tails than implied by the normal distribution.