Computational Finance

1
Computational Finance

• Lecture 4
• A Small Digression
• Efficient Market and Random Walk

2
Option Pricing and Stock Dynamics

• A good model for the underlying stock prices
  plays an important role in option pricing.
• We take a small digression here to discuss the
  dynamics for stock prices.

3
Is the Stock Market Predictable?

• Suppose that Prof. Chen had discovered that stock
  prices are predictable.
• Investors could reap unending profits simply by
  purchasing stocks that were about to increase and
  by selling stocks about to fall.
• A moment reflection should convince yourself that
  this is too good to happen in reality.

4
Is the Stock Market Predictable?

• For example, suppose my model predicts that stock
  XYZ will rise dramatically in three days to 110
  from 100. The prediction must induce a great
  wave of immediate buy orders.
• Huge demands on stock XYZ will push its price to
  jump to 110 immediately, which invalidates my
  prediction immediately.

5
Is the Stock Market Predictable?

• Any forecast of a future price increase will lead
  to an immediate price increase.
• In other words, any information that could be
  used to predict stock performance must already be
  reflected in stock prices.
• The genuine driving force behind is new
  information or unpredictable information.

6
Efficient Market Hypothesis and Random Walk

• Efficient market hypothesis (EMH) Maurice
  Kendall (1953), Harry Roberts (1959), Eugene Fama
  (1965)
• Weak form
• Stock prices already reflect all information
  that can be derived by examining market trading
  data.
• Strong form
• Stock prices reflect all information relevant
  to the firm, even including information available
  only to the company insiders.

7
Efficient Market Hypothesis and Random Walk

• Under EMH, stock prices should follow a random
  walk, that is, price changes should be random and
  unpredictable.

8
Implication of EMH

• Technical analysis The search for recurrent and
  predictable patterns in stock prices. EMH implies
  that technical analysis is without merit.

9
Implication of EMH

• Fundamental analysis
• Attempts to determine proper stock prices
  using basic information such as earnings and
  dividend prospects of a firm, expectations of
  future interest rates, and risk evaluation, etc.
• EMH implies that most of such analysis is doomed
  to failure.

10
Evidence for EMH

• Since 1988, the Wall Street Journal has run a
  competition between investment analysts and
  darts.
• Analysts choose stocks by their analysis and the
  other group chooses blindly----- throwing
• darts. In 79 contests, stock
• analysts have won
• 45 times and darts 34 times.
  

11
Evidence Against EMH

• Like all other economics theory, the market
  efficient hypothesis is also challenged by
  several evidences.
• According to the hypothesis, no predictable
  pattern should exist in the market. However, that
  is not true.

12
Evidence Against EMH

• January Effect
• Over long periods of time, stock prices have
  tended to experience an abnormal price rise
  during the period starting on the last day of
  December and ending on the fifth trading day of
  January.