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Forecasting Realized Variance Using Jumps

This paper by Andrey Fradkin explores the effectiveness of the HAR-RV-CJ model in forecasting realized variance compared to the traditional HAR-RV model. It investigates the significance of implied volatility (IV), realized volatility (RV), and jumps on market performance, examining important statistical metrics. The study highlights key findings regarding the insignificance of jump factors and the impact of market volatility on individual stock volatility. It also discusses directions for future research, including advanced time-series techniques and the relationship between implied volatility and market jumps.

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Forecasting Realized Variance Using Jumps

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  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

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