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Forecasting Realized Variance Using Jumps

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

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Forecasting Realized Variance Using Jumps

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  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 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. Realized Variance and Jumps Andrey Fradkin: Forecasting Realized Variance

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

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

  9. My Regressions – 1 day forward Newey-West R^2=.4922 rv Coef. Std. Err. t P>t [95% Conf. Interval] c1 .3216361 .0778881 4.13 0.000 .168826 .4744461 c5 .3233613 .1008474 3.21 0.001 .1255069 .5212156 c22 .2478666 .0625769 3.96 0.000 .1250959 .3706373 _cons .0000285 .0000103 2.76 0.006 8.21e-06 .0000488 Andrey Fradkin: Forecasting Realized Variance

  10. Jumps Don’t Matter Newey-West R^2=.4985 rv Coef. Std. Err. t P>t [95% Conf. Interval] c1 .3262136 .0755843 4.32 0.000 .177923 .4745042 c5 .3091024 .0975148 3.17 0.002 .1177858 .5004191 c22 .2419664 .0601737 4.02 0.000 .1239103 .3600226 j1 1.584021 .9718173 1.63 0.103 -.3226096 3.490652 j5 -.8471169 1.134404 -0.75 0.455 -3.07273 1.378496 j22 3.587264 3.786084 0.95 0.344 -3.840741 11.01527 _cons .0000261 .0000101 2.59 0.010 6.35e-06 .0000459 Andrey Fradkin: Forecasting Realized Variance

  11. 1 day forward using logs Newey-West R^2=0.7737 logrv Coef. Std. Err. t P>t [95% Conf.Interval] logc1 .2407742 .041531 5.80 0.000 .1592938 .3222545 logc5 .4396577 .0592865 7.42 0.000 .3233424 .5559731 logc22 .2749495 .0418261 6.57 0.000 .19289 .357009 _cons -.4548797.1309848 -3.47 0.001 -.7118613 -.1978982 Jump terms are insignificant if added to this regression Andrey Fradkin: Forecasting Realized Variance

  12. Regression 5 days forward Newey-West F5.rv5 Coef. Std. Err. t P>t [95% Conf.Interval] c1 .1902404 .0405141 4.70 0.000 .1107546 .2697263 c5 .3198168 .1070031 2.99 0.003 .1098841 .5297494 c22 .2966428 .0782428 3.79 0.000 .1431358 .4501498 j1 -.0887148 .4668765 -0.19 0.849 -1.004694 .8272648 j5 3.129752 1.447759 2.16 0.031 .2893476 5.970156 j22 2.996998 5.738814 0.52 0.602 -8.26216 14.25616 _cons .0000419 .0000154 2.71 0.007 .0000116.0000721 Practically no change in R^2 w/o jumps Andrey Fradkin: Forecasting Realized Variance

  13. My Regressions – 22 day Newey-West R^2=.5172 F22.rv22 Coef. Std. Err. t P>t [95% Conf.Interval] c1 .1216783 .0230143 5.29 0.000 .0765252 .1668314 c5 .2577073 .1083063 2.38 0.017 .0452148 .4701998 c22 .2752547 .0909278 3.03 0.003 .096858 .4536513 j1 .2384794 .2904984 0.82 0.412 -.3314668 .8084255 j5 1.570385 2.267699 0.69 0.489 -2.878747 6.019518 j22 5.20189 9.937398 0.52 0.601 -14.29488 24.69866 _cons .0000799 .000026 3.08 0.002 .000029 .0001308 Practically no change in R^2 w/o jumps Andrey Fradkin: Forecasting Realized Variance

  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: IVt,t+h=h-1 (IVt+1 + IVt+2 … + IVt+h) • Difft= IVt-RVt Andrey Fradkin: Forecasting Realized Variance

  15. Means • Observations: 1219 Mean RV=.0002635 • Mean IV=.0003173 Mean Diff=.0000523 Diff AndreyFradkin: Forecasting Realized Variance

  16. Autocorrelation of Diff Andrey Fradkin: Forecasting Realized Variance

  17. IV is a better predictor than RV of future RV R-squared = 0.5023 Root MSE = .00026 Robust rv Coef. Std. Err. t P>t [95% Conf.Interval] iv1 1.050039 .0962552 10.91 0.000 .8611945 1.238884 j1 .6298041 .9092165 0.69 0.489 -1.154003 2.413611 _cons -.0000698.0000254 -2.74 0.006 -.0001197 -.0000199 R-squared = 0.4271 Root MSE = .00028 Robust rv Coef. Std. Err. t P>t [95% Conf. Interval] c1 .6478913 .1001823 6.47 0.000 .4513421 .8444406 j1 1.897893 .8402938 2.26 0.024 .2493062 3.546479 _cons .0000913 .0000223 4.10 0.000 .0000476 .0001351 AndreyFradkin: Forecasting Realized Variance

  18. Is Diff Significant in forecasting RV? R-squared = 0.5465 Root MSE = .00025 Robust rv Coef. Std. Err. t P>t [95% Conf.Interval] rv1 1.039644 .0941392 11.04 0.000 .8549505 1.224337 L1.Diff .7441405 .1072339 6.94 0.000 .5337562 .9545247 _cons -.0000496.0000239 -2.07 0.038 -.0000966 -2.64e-06 Andrey Fradkin: Forecasting Realized Variance

  19. Using Diff in HAR-RV-CJ Model Newey-West R-squared = .5611 rv Coef. 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.rv5 Coef. 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 Andrey Fradkin: Forecasting Realized Variance

  20. Using Diff in HAR-RV-CJ Model cont. Newey-West R-Squared: 0.5676 F22.rv22 Coef. Std. Err. t P>t [95% Conf. Interval] c1 .4739452 .0803304 5.90 0.000 .31634 .6315504 c5 .1862154 .1068758 1.74 0.082 -.0234709 .3959018 c22 .115742 .0742476 1.56 0.119 -.0299291 .2614131 j1 .7448536 .3328171 2.24 0.025 .0918788 1.397828 j5 -1.032086 2.406812 -0.43 0.668 -5.754162 3.689989 j22 5.355446 10.28448 0.52 0.603 -14.82233 25.53322 L1.diff .4314511 .0938983 4.59 0.000 .247226 .6156761 _cons .0000285 .000021 1.36 0.175 -.0000127 .0000696 Andrey Fradkin: Forecasting Realized Variance

  21. Predicting Diff Using Jumps Newey-West R-squared = 0.1235 diff Coef. Std. Err. t P>t [95% Conf. Interval] c1 -.1973631 .0706515 -2.79 0.005 -.3359759 -.0587504 c5 -.1441686 .063503 -2.27 0.023 -.2687566 -.0195806 c22 .1650903 .0995486 1.66 0.097 -.0302165 .3603971 j1 -1.591713 .8951938 -1.78 0.076 -3.348014 .1645889 j5 7.162149 1.46073 4.90 0.000 4.296309 10.02799 j22 -3.263902 2.958828 -1.10 0.270 -9.068895 2.541092 _cons .0000949 .0000215 4.42 0.000 .0000528 .0001371 Newey-West R-squared = 0.0548 F5.diff Coef. Std. Err. t P>t [95% Conf. Interval] c1 .025571 .0435225 0.59 0.557 -.0598172 .1109593 c5 -.3173051 .1317263 -2.41 0.016 -.5757431 -.0588671 c22 .2137709 .1007057 2.12 0.034 .0161933 .4113484 j1 -.6373502 .8629953 -0.74 0.460 -2.330488 1.055787 j5 -1.319912 1.440435 -0.92 0.360 -4.145946 1.506122 j22 -2.634389 3.527186 -0.75 0.455 -9.554485 4.285707 _cons .0000781 .0000198 3.940.000 .0000392 .0001169 Andrey Fradkin: Forecasting Realized Variance

  22. Predicting Diff Using Jumps Newey-West R-squared = 0.0072 F22.diff Coef. Std. Err. t P>t [95% Conf. Interval] c1 .0278554 .029698 0.94 0.348 -.0304108 .0861216 c5 -.0189465 .0709693 -0.27 0.790 -.1581855 .1202924 c22 .0304386 .0706686 0.43 0.667 -.1082103 .1690875 j1 .7447953 .23193 3.21 0.001 .289758 1.199833 j5 -2.931345 2.05406 -1.43 0.154 -6.961327 1.098638 j22 .6472574 5.335948 0.12 0.903 -9.821655 11.11617 _cons .0000405 .0000126 3.21 0.001 .0000158 .0000653 Adding or removing jumps does not effect R-Squared Andrey Fradkin: Forecasting Realized Variance

  23. Jumps matter if regressing Diff on IV and Jumps Newey-West R-Squared: .1018 diff Coef. Std. Err. t P>t [95% Conf. Interval] iv1 -.5454239 .2838641 -1.92 0.055 -1.102344 .0114957 iv5 -.0509571 .1503595 -0.34 0.735 -.3459508 .2440366 iv22 .5652849 .1773301 3.19 0.001 .217377 .9131929 j1 -1.557493 .9155883 -1.70 0.089 -3.353807 .2388207 j5 10.23682 2.056567 4.98 0.000 6.201993 14.27165 j22 -9.462402 3.553551 -2.66 0.008 -16.4342 -2.490609 _cons .0000605 .0000219 2.76 0.006 .0000175 .0001036 Newey-West R-Squared: .16 diff Coef. Std. Err. t P>t [95% Conf. Interval] L1.diff .2575236 .0986853 2.61 0.009 .0639104 .4511368 iv1 -.5944392 .2546254 -2.33 0.020 -1.093995 -.094883 iv5 .1370913 .200045 0.69 0.493 -.2553824 .529565 iv22 .4336471 .1536846 2.82 0.005 .1321293 .7351649 j1 -1.37075 .946662 -1.45 0.148 -3.228031 .4865313 j5 8.862341 1.982412 4.47 0.000 4.972993 12.75169 j22 -9.133631 2.995484 -3.05 0.002 -15.01055 -3.256713 _cons .0000459 .000015 3.06 0.002 .0000165 .0000752 Andrey Fradkin: Forecasting Realized Variance

  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. Andrey Fradkin: Forecasting Realized Variance

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