1. Econ 201 by David Kim 3.2.11

2. Measuring & Forecasting Measuring and forecasting latent volatility is important in regards to: – Asset allocation – Option pricing – Risk management

3. Brownlees and Gallo (2009) Looks at different volatility measures improve out-of-sample forecasting ability of standard methods Looks into issue of forcasting Value-at-Risk (VaR) by looking at various volatility measures – Realized volatility – Bipower volatility – Two-scales realized volatility – Realized kernel – Daily range

4. VaR Modeling Assumes – h t – conditional variance of daily return – n t – i.i.d. unit variance from an appropriate cumulative distribution F – One-day-ahead VaR is defined as maximum one- day-ahead loss

5. Volatility Measures Realized volatility Bipower realized volatility

6. Volatility Measures (cont’d) Two-scales realized volatility – Let – Define: – This estimator combines information from both slow and fast time scales

7. Volatility Measures (cont’d) Realized kernel – Y h (p t ) = – k( ) = appropriate weight function as the sample frequency increases, realized kernel can get the fastest convergence rate ·

8. Volatility Measures (cont’d) Daily Range – p high,t – largest log-price – p low,t – lowest log-price – Affected by a much lower measurement error It is as precise as realized volatility if using a sample of low frequency data and certain conditions

9. Companies HJ Heinz Company (HNZ) and Kraft Foods Inc. (KFT) – Consumer goods sector within the food industry – Both diversified companies

10. HNZ: Price

11. HNZ: Returns

12. HNZ: Relative Contribution of Jumps

13. HNZ: RV Volatility Signature

14. HNZ: BV Volatility Signature

15. KFT: Price

16. KFT: Returns

17. KFT: Relative Contribution of Jumps

18. KFT: RV Volatility Signature

19. KFT: BV Volatility Signature

20. HNZ: RV

21. HNZ: BV

22. KFT: RV

23. KFT: BV

24. Look further into all volatility measures If an appropriate area for research, include more stocks Other potential areas of interest: – How presence of jumps has information relevant to forecasting volatility HAR modelling frame