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

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

3. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 3 Returns

4. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 4 Returns See file 6.Random Behavior of Assets.XLS

5. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 5 Normal Distribution N( ,  )

6. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 6 Normal Distribution N( ,  )  

7. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 7 Normal Distribution  quantile 1%

8. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 8 Lognormal Distribution

9. 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) =

10. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 10 Correlation -1    1  = 0 independent  = 1 perfectly positively correlated  = -1 perfectly negatively correlated

11. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 11 Properties

12. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 12 Time Aggregation Assuming normality

13. 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:

14. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 14 Volatility

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

16. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 16 Geometrical Brownian Motion Arithmetical Brownian Motion

17. 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.

18. Zvi WienerFE-Wilmott-IntroQF Ch6 slide 18 Home Assignment Read chapter 6 in Wilmott. Follow Excel files coming with the book.