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lecture10 (1) - Lecture 10 Price Distributions and Binomial...

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Lecture 10: Price Distributions and Binomial Trees Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794–4400 http://www.cs.sunysb.edu/ skiena
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Quasi-random Number Generation Quasi-random sequences fill space more uniformly than uncorrelated random points. Intuition : on a line, consider repeatedly picking the next point in the middle of the largest remaining interval. Note these are (1) not “randomly” ordered, and (2) will not be uniform if you don’t know the ultimate number in advance.
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Random Walks with Memory Successive movements in the random walks models to discussed to date are independent , which contradicts our perception about how markets move. Hurst random walks are discrete random walks which reverse direction with probability h . A value of h = 0 . 5 generates a coin flipping random walk, while a value of h = 1 . 0 generates a walk which moves in only one direction. Intermediate values of h should generate walks more “driven” than simple coin-flipping, although the eye often mistakenly identifies trends in such walks. Hurst walks arise in the analysis of fractal phenomenon.
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Several design decisions remain to build a reasonable stock price distribution model: The number of steps per simulated time period. The up-tick and down-tick probabilities. The drift rate, perhaps the historical stock market average returns. The step size, which is a function of each given stock’s volatility. The number of walks simulated per distribution.
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This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.

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lecture10 (1) - Lecture 10 Price Distributions and Binomial...

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