Presentation 3 Kunal Jain March 24 2010 Economics

HAR-RV Model n Heterogeneous Autoregressive model of the Realized Volatility (HAR -RV), Corsi 2003,

HAR-RV Model n n Model implemented in Mat. Lab Regression Results (AMZN) RVt+1 n

HAR-RV Model- Kernel Density n Residuals- Kernel Density Plot (Observed-Expected) ¨ Non-parametric way of

HAR-RV: Squared Overnight n Including squared overnight returns to look at volatility RVt+1 Coefficient

HAR-RV Model- Kernel Density *Including overnight returns

HAR-RV Model n Normalizing overnight returns ¨ [Sqrt(RV) & Abs(Overnight)] vs. [RV & Overnight

HAR-RV Model: Med. V n n n Use Med. V as a dummy variable

HAR-RV Model n Regression results with: ¨ Squared Overnight returns n ¨ RV &

Further Research n n n Significant Levels STATA integration More stocks New Regressors ¨

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Presentation 3 Kunal Jain March 24, 2010 Economics 201 FS

HAR-RV Model n Heterogeneous Autoregressive model of the Realized Volatility (HAR -RV), Corsi 2003, uses average realized variance over daily, weekly, and monthly time intervals to build a conditional volatility model. n h=1 corresponds to daily periods, h=5 corresponds to weekly periods, h=22 corresponds to monthly periods. This model uses volatilities realized over a 1 -day, 5 -day, and 1 -month time interval to build the conditional volatilities. n

HAR-RV Model n n Model implemented in Mat. Lab Regression Results (AMZN) RVt+1 n n n Coefficient Standard Error T-Statistic RVt . 3921 0. 0220 17. 82* RVt-5, t . 3638 0. 0339 10. 73* RVt-22, t . 1766 0. 0282 6. 26 constant . 0001 0. 0000 0. 000 Coefficient sum approximates one. Constant? Reject the null hypothesis?

HAR-RV Model- Kernel Density n Residuals- Kernel Density Plot (Observed-Expected) ¨ Non-parametric way of estimating the probability density function of a random variable- want to resemble a normal distribution.

HAR-RV: Squared Overnight n Including squared overnight returns to look at volatility RVt+1 Coefficient Standard Error T-Statistic RVt . 3742 . 0217 17. 24 RVt-5, t . 3542 . 0334 10. 60 RVt-22, t . 1786 . 0277 6. 45 BON . 0656 . 0067 9. 79 Constant . 0001 0. 0000 0. 000

HAR-RV Model- Kernel Density *Including overnight returns

HAR-RV Model n Normalizing overnight returns ¨ [Sqrt(RV) & Abs(Overnight)] vs. [RV & Overnight 2] [Sqrt(RV) & Abs(Overnight)] [RV & Overnight 2] RVt+1 n n Coefficient Standard Error T-Statistic RVt+1 Coefficient Standard Error T-Statistic RVt . 3742 . 0217 17. 24 RVt . 3856 . 0216 17. 85 RVt-5, t . 3542 . 0334 10. 60 RVt-5, t . 3472 . 0326 10. 65 RVt-22, t . 1786 . 0277 6. 45 RVt-22, t . 1886 . 0250 7. 54 BON . 0656 . 0067 9. 79 BON . 1012 . 0082 12. 34 Constant . 0001 0. 0000 0. 000 Constant . 0011 0. 0004 2. 75 Normalize outliars -> T-statistic for Overnight Which one is better?

HAR-RV Model: Med. V n n n Use Med. V as a dummy variable in regression Results with Med. V Z-values at 5% significance level (10 minute interval) T-Distribution with 5 DOF RVt+1 Coefficient Standard Error T-Statistic RVt . 2731 . 0185 14. 76 RVt-5, t . 1683 . 0286 5. 88 RVt-22, t . 1524 . 0233 6. 54 BMed. V . 0030 . 0001 30 Constant . 0003 0. 0000 -

HAR-RV Model n Regression results with: ¨ Squared Overnight returns n ¨ RV & Overnight 2 Med. V 5% significant Z-statistic dummy variable (10 minute interval) RVt+1 Coefficient Standard Error T-Statistic RVt . 2508 . 0182 13. 78 RVt-5, t . 1533 . 0280 5. 475 RVt-22, t . 1469 . 0228 6. 44 BON . 0108 . 0009 12 BMed. V . 0030 . 0001 30 Constant . 0002 0 -

Further Research n n n Significant Levels STATA integration More stocks New Regressors ¨ Integrate Earnings Surprises ¨