Chapter 9 - Discrete/Continuous Lognormal Model

Question 1

What are the 7 main defects of the Lognormal Model (Geometric Random Walk)?

Answer 1

1. Continuity
   Stock markets are not continuous - the price of a share when the market closes maybe be different to when the market opens I.e in reality there are step jumps in share prices.
2. Normality of share prices
   In reality the distribution of share prices tend to have fatter tails (more extreme movements) and taller peaks (more days of little or no movement).
3. Independent Increments
   The assumptions state the the increments of share prices are independent. This is not a true reflection of reality - imperial evidence suggests that a rise in share prices is much more likely to be followed by another rise (and same for fall in share price)
4. Constant Volatility
   We assume volatility is constant. Volatility cannot be calculated and has to be estimated. Estimates of volatility from past data are critically dependant on the time period chosen.

5.Independent Increments
There is evidence in real markets of mean-reverting behaviour which is inconsistent with independent increments .

6. Constant drift parameter
   In real markets, the long term drift parameter may not be constant e.g. interests rates will impact the drift.