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Random Asset Behavior in Quantitative Finance

Explore the random behavior of assets in quantitative finance, covering topics such as normal distribution, covariance, correlation, volatility, simulation, and the Central Limit Theorem. Dive into practical examples and calculations to grasp key concepts effectively.

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Random Asset Behavior in Quantitative Finance

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  1. Financial Engineering Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Random Behavior of Assets Following Paul Wilmott, Introduces Quantitative Finance Chapter 6 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  3. Returns FE-Wilmott-IntroQF Ch6

  4. Returns See file 6.Random Behavior of Assets.XLS FE-Wilmott-IntroQF Ch6

  5. Normal Distribution N(, ) FE-Wilmott-IntroQF Ch6

  6.  Normal Distribution N(, ) FE-Wilmott-IntroQF Ch6

  7. Normal Distribution 1%  quantile FE-Wilmott-IntroQF Ch6

  8. Lognormal Distribution FE-Wilmott-IntroQF Ch6

  9. Covariance • Shows how two random variables are connected • For example: • independent • move together • move in opposite directions • covariance(X,Y) = FE-Wilmott-IntroQF Ch6

  10. Correlation • -1    1 •  = 0 independent •  = 1 perfectly positively correlated •  = -1 perfectly negatively correlated FE-Wilmott-IntroQF Ch6

  11. Properties FE-Wilmott-IntroQF Ch6

  12. Time Aggregation Assuming normality FE-Wilmott-IntroQF Ch6

  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: FE-Wilmott-IntroQF Ch6

  14. Volatility FE-Wilmott-IntroQF Ch6

  15. Simulation of a Random Walk See spreadsheet A general formula FE-Wilmott-IntroQF Ch6

  16. Geometrical Brownian Motion Arithmetical Brownian Motion FE-Wilmott-IntroQF Ch6

  17. Central Limit Theorem • The mean of n independent and identically distributed variables converges to a normal distribution as n increases. FE-Wilmott-IntroQF Ch6

  18. Home Assignment • Read chapter 6 in Wilmott. • Follow Excel files coming with the book. FE-Wilmott-IntroQF Ch6

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