Mathematical Modeling in Finance with Stochastic Processes

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1.6. RANDOMNESS 53


1.6 Persi Diaconis’ mechanical coin flipper


Randomness and the Markets


A branch of financial analysis, generally calledtechnical analysis, claims to
be able to predict security prices by relying on the assumption that market
data, such as price, volume, and patterns of past behavior can help predict
future (usually short-term) market trends. Technical analysis also usually
assumes that market psychology influences trading in a way that enables
predicting when a stock will rise or fall.
In contrast israndom walk theory. This theory claims that market
prices follow a random path without influence by past price movements. The
randomness makes it impossible to predict which direction the market will
move at any point, especially in the short term. More refined versions of the
random walk theory postulate a probability distribution for the market price
movements. In this way, the random walk theory mimics the mathematical
model of a coin flip, substituting a probability distribution of outcomes for
the ability to predict what will really happen.
If the coin flip, although deterministic and ultimately simple in execution
cannot be practically predicted with well-understood physical principles, then
it should be hard to believe that market dynamics can be predicted. Mar-
ket dynamics are based on the interactions of thousands of variables and

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