lecture9 (1)

lecture9 (1) - Lecture 9: Random Walk Models Steven Skiena...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 9: Random Walk Models Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794–4400 http://www.cs.sunysb.edu/ skiena
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Financial Time Series as Random Walks J. P. Morgan’s famous stock market prediction was that “Prices will fluctuate.” Bachelier’s Theory of Speculation in 1900 postulated that prices fluctuate randomly. Indeed, simple random processes can generate time series which closely resemble real financial time series.
Background image of page 2
Why Random Price Changes? Random price movements makes sense in a world where Most price changes result from temporary imbalances between buyers and sellers, Stronger price shocks are inherently unpredictable, and The efficient market hypothesis, where the current price of a stock reflects all information about it. If the next price movement was predictable, the market would have previously predicted it, leaving only random fluctuations.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Monte Carlo Methods Monte Carlo methods use statistics gathered from random sampling to model and simulate a complicated distribution. Generating random walks with the properties of financial time series and analyzing the resulting price distributions is a powerful technique in options pricing.
Background image of page 4
Models and Randomness Models are useful when they have predictive power. Simple models which capture large-scale phenomena are useful. The model that “the earth is flat” is a very useful model. If “the future” is the random selection of one sequence of events from a probability space, our focus should revolve around modeling the distribution more so than identifying the ultimate future path. Random walk models give us a simple but powerful tool to model financial price distributions.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Binomial Random Walks In a simple discrete random walk model, each step we move a distance of 1 either up or down, with the probability
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.

Page1 / 20

lecture9 (1) - Lecture 9: Random Walk Models Steven Skiena...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online