Forecasting Realized Variance Using Jumps

1. Forecasting Realized Variance Using Jumps Andrey Fradkin Econ 201 4/18/2007

2. Outline • Theoretical Background • The HAR-RV-CJ Model • Is the HAR-RV-CJ model better than the HAR-RV model? • Does IV contain more information than RV, C, J? • How does market risk ask measured by the VIX affect the RV of individual stock? • Future Work AndreyFradkin: Forecasting Realized Variance

3. Formulas Part 1 Realized Variation: Realized Bi-Power Variation: Andrey Fradkin: Forecasting Realized Variance

4. Formulas Part 2 • Tri-Power Quarticity • Quad-Power Quarticity Andrey Fradkin: Forecasting Realized Variance

5. Formulas Part 3 • Z-statistics (max version) Andrey Fradkin: Forecasting Realized Variance

6. Original HAR-RV-J Model(Taken from Andersen, Bollerslev, Diebold 2006) Andrey Fradkin: Forecasting Realized Variance

7. The HAR-RV-CJ Model Andrey Fradkin: Forecasting Realized Variance

8. Summary Statistics Summary Statistics for Daily GS Realized Volatilities and Jumps RVt RVt 1/2 log(RVt ) Jt Jt ½ log(Jt+1) Mean .00025 .0145 -8.63 3.2e-06 .00018 .778 St.Dev. .00028 .0065 0.798 7e-05 .0017 1.53 Min. 9.6e-06 .0031 -11.54 .000 .000 -11.11 Max. .00394 .0628 -5.53 .0024 .049 1 Summary Statistics for Daily SPY Realized Volatilities and Jumps RVt RVt 1/2 log(RVt ) Jt Jt ½ log(Jt+1) Mean .0001 .009 -9.61 1.4e-06 .00016 .644 St.Dev. .0001 .0045 .885 2.3e-05 .0011 2.01 Min. 4.73e-06 .0021 -12.26 .000 .000 -12.62 Max. .0016 .0403 -6.422 .0008 .0281 1 Andrey Fradkin: Forecasting Realized Variance

9. Findings • Jump factors were usually insignificant and added very little to the R^2 • The highest R^2 was obtained by using either log values or square root values • To keep scaling the same I used square root values in the regressions in this presentation • Separating the continuous and jump parts of the realized variance did not improve the r^2 Andrey Fradkin: Forecasting Realized Variance

10. Does IV have more information than RV? • Steps to test this • First regress the average realized variance over a month (rv22) on the independent variables with the best adjusted R^2 • Then regress RV22 against the predicted values from the previous regression and the implied volatility • See which turns have the highest R^2 and significance Andrey Fradkin: Forecasting Realized Variance

11. For GS – 1st Regression Adj R-squared = 0.7410 Andrey Fradkin: Forecasting Realized Variance

12. For GS – 2nd Regression Adj R-squared = .7713 Adj R-squared = 0.7205 Adj R-squared = 0.7421 AndreyFradkin: Forecasting Realized Variance

13. For Spy – 1st Regression Adj R-squared = 0.6606 Andrey Fradkin: Forecasting Realized Variance

14. For SPY – 2nd Regression Adj R-Squared = 0.7075 Adj R-squared = 0.6724 Adj R-squared = 0.6621 Andrey Fradkin: Forecasting Realized Variance

15. How Does Market Volatility effect Individual Stock Volatility? (cont) Adj R-squared = 0.5691 Adj R-squared = 0.4731 Andrey Fradkin: Forecasting Realized Variance

16. How Does Market Volatility effect Individual Stock Volatility? • Tried a lot of regression of future realized variance on estimates, vix, rv of market • Found that the coefficients are not significant for the volatility of the market if the forecasts are included as independent variables • If future Realized Volatility is just regressed on VIX there is a significant coefficient • The Adj-R^2 increases by around .07 Andrey Fradkin: Forecasting Realized Variance

17. Future Work • Analyze more stock • Write up proposal • Try to use more advanced time-series techniques • More work with returns • What happens to implied volatility before and after jumps? Preliminary results (implied volatility changes much more than average on the day of jump) Andrey Fradkin: Forecasting Realized Variance