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

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Presentation on theme: "Forecasting Realized Variance Using Jumps Andrey Fradkin Econ 201 4/4/2007."— Presentation transcript:

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

2 Introduction Theoretical Background Summary Graphs and Statistics for data The HAR-RV-CJ Model and regressions using it. Addition of IV to the regression Analysis of possible benefits to using IV Forecasting IV-RV using jumps, do jumps effect risk premiums? Future Work 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 2

3 Formulas Part 1 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 3 Realized Variation: Realized Bi-Power Variation:

4 Formulas Part 2 Tri-Power Quarticity Quad-Power Quarticity 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 4

5 Formulas Part 3 Z-statistics (max version) 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 5

6 Realized Variance and Jumps 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 6

7 Original HAR-RV-J Model (Taken from Andersen, Bollerslev, Diebold 2006) 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 7

8 The HAR-RV-CJ Model 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 8

9 My Regressions – 1 day forward 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 9 Newey-WestR^2=.4922 rvCoef.Std. Err.tP>t[95% Conf.Interval] c1.3216361.07788814.130.000.168826.4744461 c5.3233613.10084743.210.001.1255069.5212156 c22.2478666.06257693.960.000.1250959.3706373 _cons.0000285.00001032.760.0068.21e-06.0000488

10 Jumps Don’t Matter 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 10 Newey-West R^2=.4985 rvCoef.Std. Err.tP>t[95% Conf. Interval] c1.3262136.07558434.320.000.177923.4745042 c5.3091024.09751483.170.002.1177858.5004191 c22.2419664.06017374.020.000.1239103.3600226 j11.584021.97181731.630.103-.3226096 3.490652 j5-.84711691.134404-0.750.455-3.07273 1.378496 j223.5872643.7860840.950.344-3.840741 11.01527 _cons.0000261.00001012.590.0106.35e-06.0000459

11 1 day forward using logs 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 11 Newey-West R^2=0.7737 logrvCoef.Std. Err.tP>t[95% Conf.Interval] logc1.2407742.0415315.800.000.1592938.3222545 logc5.4396577.05928657.420.000.3233424.5559731 logc22.2749495.04182616.570.000.19289.357009 _cons-.4548797.1309848-3.470.001-.7118613 -.1978982 Jump terms are insignificant if added to this regression

12 Regression 5 days forward 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 12 Newey-West F5.rv5Coef.Std. Err. tP>t[95% Conf.Interval] c1.1902404.0405141 4.700.000.1107546.2697263 c5.3198168.1070031 2.990.003.1098841.5297494 c22.2966428.0782428 3.790.000.1431358.4501498 j1-.0887148.4668765 -0.190.849-1.004694.8272648 j53.1297521.447759 2.160.031.2893476 5.970156 j222.9969985.738814 0.520.602-8.26216 14.25616 _cons.0000419.0000154 2.710.007.0000116.0000721 Practically no change in R^2 w/o jumps

13 My Regressions – 22 day 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 13 Newey-West R^2=.5172 F22.rv22Coef.Std. Err.tP>t[95% Conf.Interval] c1.1216783.02301435.290.000.0765252.1668314 c5.2577073.10830632.380.017.0452148.4701998 c22.2752547.09092783.030.003.096858.4536513 j1.2384794.29049840.820.412-.3314668.8084255 j51.5703852.2676990.690.489-2.878747 6.019518 j225.201899.9373980.520.601-14.29488 24.69866 _cons.0000799.0000263.080.002.000029.0001308 Practically no change in R^2 w/o jumps

14 Work on Options Data Code for filtering through the many options Takes the implied volatility of the option that is closest to the average of the starting and closing price, provided volume is high enough. Calculate variables: IV t,t+h =h -1 (IV t+1 + IV t+2 … + IV t+h ) Diff t = IV t -RV t 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 14

15 Means Observations: 1219 Mean RV=.0002635 Mean IV=.0003173 Mean Diff=.0000523 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 15 Diff

16 Autocorrelation of Diff 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 16

17 IV is a better predictor than RV of future RV 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 17 R-squared= 0.5023 Root MSE=.00026 Robust rvCoef.Std. Err.tP>t[95% Conf.Interval] iv11.050039.096255210.910.000.8611945 1.238884 j1.6298041.90921650.690.489-1.154003 2.413611 _cons-.0000698.0000254-2.740.006-.0001197 -.0000199 R-squared= 0.4271 Root MSE=.00028 Robust rvCoef.Std. Err.tP>t[95% Conf.Interval] c1.6478913.10018236.470.000.4513421.8444406 j11.897893.84029382.260.024.24930623.546479 _cons.0000913.00002234.100.000.0000476.0001351

18 Is Diff Significant in forecasting RV? 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 18 R-squared= 0.5465 Root MSE=.00025 Robust rvCoef.Std. Err.tP>t[95% Conf.Interval] rv11.039644.094139211.040.000.85495051.224337 L1.Diff.7441405.10723396.940.000.5337562.9545247 _cons-.0000496.0000239-2.070.038-.0000966 -2.64e-06

19 Using Diff in HAR-RV-CJ Model 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 19 Newey-West R-squared =.5611 rvCoef. Std. Err. t P>t [95% Conf.Interval] c1.8782383.1949678 4.50 0.000.4957259 1.260751 c5.1978388.0789141 2.51 0.012.0430151.3526624 c22 -.0109185.1064608 -0.10 0.918 -.2197868.1979499 j1 2.379697.984771 2.42 0.016.4476485 4.311745 j5 -4.892927 1.876258 -2.61 0.009 -8.574008 -1.211847 j22 3.648466 3.529547 1.03 0.301 -3.276246 10.57318 L1.diff.6761671.2257157 3.00 0.003.2333295 1.119005 _cons -.000053.0000262 -2.02 0.044 -.0001044 -1.55e-06 Newey-West R-squared = 0.6447 F5.rv5Coef. Std. Err. t P>t [95% Conf.Interval] c1.6181182.1238336 4.99 0.000.3751648.8610715 c5.2326215.107413 2.17 0.031.0218843.4433588 c22.1019241.0628666 1.62 0.105 -.021416.2252642 j1.5261682.5163181 1.02 0.308 -.4868141 1.53915 j5 -.0505589 1.846144 -0.03 0.978 -3.672573 3.571455 j22 3.228812 5.368064 0.60 0.548 -7.302979 13.7606 L1.Diff.5242109.143786 3.65 0.000.2421122.8063096 _cons -.0000199.0000132 -1.51 0.131 -.0000457 5.96e-06

20 Using Diff in HAR-RV-CJ Model cont. 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 20 Newey-West R-Squared: 0.5676 F22.rv22Coef.Std. Err.tP>t[95% Conf.Interval] c1.4739452.08033045.900.000.31634.6315504 c5.1862154.10687581.740.082-.0234709.3959018 c22.115742.07424761.560.119-.0299291.2614131 j1.7448536.33281712.240.025.09187881.397828 j5-1.0320862.406812-0.430.668-5.7541623.689989 j225.35544610.284480.520.603-14.8223325.53322 L1.diff.4314511.09389834.590.000.247226.6156761 _cons.0000285.0000211.360.175-.0000127.0000696

21 Predicting Diff Using Jumps 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 21 Newey-West R-squared = 0.1235 diff Coef. Std. Err. tP>t [95% Conf.Interval] c1 -.1973631.0706515 -2.790.005 -.3359759-.0587504 c5 -.1441686.063503 -2.270.023 -.2687566-.0195806 c22.1650903.0995486 1.660.097 -.0302165.3603971 j1 -1.591713.8951938 -1.780.076 -3.348014.1645889 j5 7.162149 1.46073 4.900.000 4.29630910.02799 j22 -3.263902 2.958828 -1.100.270 -9.0688952.541092 _cons.0000949.0000215 4.420.000.0000528.0001371 Newey-West R-squared = 0.0548 F5.diff Coef. Std. Err. tP>t [95% Conf.Interval] c1.025571.0435225 0.590.557 -.0598172.1109593 c5 -.3173051.1317263 -2.410.016 -.5757431-.0588671 c22.2137709.1007057 2.120.034.0161933.4113484 j1 -.6373502.8629953 -0.740.460 -2.3304881.055787 j5 -1.319912 1.440435 -0.920.360 -4.1459461.506122 j22 -2.634389 3.527186 -0.750.455 -9.5544854.285707 _cons.0000781.0000198 3.940.000.0000392.0001169

22 Predicting Diff Using Jumps 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 22 Newey-West R-squared = 0.0072 F22.diff Coef. Std. Err. tP>t [95% Conf.Interval] c1.0278554.029698 0.940.348 -.0304108.0861216 c5 -.0189465.0709693 -0.270.790 -.1581855.1202924 c22.0304386.0706686 0.430.667 -.1082103.1690875 j1.7447953.23193 3.210.001.2897581.199833 j5 -2.931345 2.05406 -1.430.154 -6.9613271.098638 j22.6472574 5.335948 0.120.903 -9.82165511.11617 _cons.0000405.0000126 3.210.001.0000158.0000653 Adding or removing jumps does not effect R-Squared

23 Jumps matter if regressing Diff on IV and Jumps 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 23 Newey-West R-Squared:.1018 diffCoef.Std. Err.tP>t[95% Conf.Interval] iv1-.5454239.2838641-1.920.055-1.102344.0114957 iv5-.0509571.1503595-0.340.735-.3459508.2440366 iv22.5652849.17733013.190.001.217377.9131929 j1-1.557493.9155883-1.700.089-3.353807.2388207 j510.236822.0565674.980.0006.20199314.27165 j22-9.4624023.553551-2.660.008-16.4342-2.490609 _cons.0000605.00002192.760.006.0000175.0001036 Newey-West R-Squared:.16 diffCoef.Std. Err.tP>t[95% Conf.Interval] L1.diff.2575236.09868532.610.009.0639104.4511368 iv1-.5944392.2546254-2.330.020-1.093995-.094883 iv5.1370913.2000450.690.493-.2553824.529565 iv22.4336471.15368462.820.005.1321293.7351649 j1-1.37075.946662-1.450.148-3.228031.4865313 j58.8623411.9824124.470.0004.97299312.75169 j22-9.1336312.995484-3.050.002-15.01055-3.256713 _cons.0000459.0000153.060.002.0000165.0000752

24 Future Work Do same regressions on data for other stocks. Add volatility of SPY to regression terms. See if there are possible applications of GARCH models for these regressions. Experiment with other alphas. 4/4/2007 Andrey Fradkin: Forecasting Realized Variance 24

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