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Financial Engineering

Financial Engineering. Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049. Random Behavior of Assets. Following Paul Wilmott, Introduces Quantitative Finance Chapter 6. Returns. Returns. See file 6.Random Behavior of Assets.XLS. Normal Distribution N( , ). . .

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Financial Engineering

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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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