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FE-W http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049 Financial Engineering
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FE-W http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Following Paul Wilmott, Introduces Quantitative Finance Chapter 6 Random Behavior of Assets
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 3 Returns
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 4 Returns See file 6.Random Behavior of Assets.XLS
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 5 Normal Distribution N( , )
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 6 Normal Distribution N( , )
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 7 Normal Distribution quantile 1%
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 8 Lognormal Distribution
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 9 Covariance Shows how two random variables are connected For example: independent move together move in opposite directions covariance(X,Y) =
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 10 Correlation -1 1 = 0 independent = 1 perfectly positively correlated = -1 perfectly negatively correlated
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 11 Properties
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 12 Time Aggregation Assuming normality
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 13 Time Aggregation Assume that yearly parameters of CPI are: mean = 5%, standard deviation (SD) = 2%. Then daily mean and SD of CPI changes are:
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 14 Volatility
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 15 Simulation of a Random Walk See spreadsheet A general formula
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 16 Geometrical Brownian Motion Arithmetical Brownian Motion
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 17 Central Limit Theorem The mean of n independent and identically distributed variables converges to a normal distribution as n increases.
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Zvi WienerFE-Wilmott-IntroQF Ch6 slide 18 Home Assignment Read chapter 6 in Wilmott. Follow Excel files coming with the book.
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