Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning
Abstract
:1. Introduction
2. Literature Review
 How can we forecast the binary daytoday movements of the India VIX using machine learning classifiers?
 How can we measure the performance of the classifiers?
 How can we say whether classifiers have similar performances?
 How do we know whether the models’ performances are acceptable?
 To forecast the binary daytoday movements of the India VIX, a standard classifier called logistic regression and 11 ensemble machine learning classifiers are trained.
 To measure the predictability of the classifiers, several metrics are applied.
 To distinguish the classifiers’ predictability, a statistical test is performed.
 To judge the predictability of the models in the context of the stock market, the performance of the developed models is compared with the past studies, and additionally, a basic classifier called logistic regression is trained for comparison.
3. Research Methodology
3.1. Description of the Models Used
3.2. Feature Computation Techniques
3.3. Data Transformation
3.4. Performance Evaluation
4. Modelling Procedure
4.1. Data Collection
4.2. Data PreProcessing
4.3. Preparation of Feature Variables
4.4. Feature Scaling
4.5. Target Variable
4.6. Execution of the Model
4.7. Optimal Models
5. Findings
6. Conclusions
7. Practical Implications
 Traders: When volatility is expected to increase sharply, intraday trades run the risk of stoplosses, quickly becoming triggered. To mitigate such risk, traders can either reduce their leverage or widen their stoplosses accordingly.
 Hedgers: For derivative contracts, such as a future contract where marttomarket (MTM) is executed daily, institutional investors and proprietary desks face the risk of MTM being executed and, thereby, generating losses. To manage such risks, they can increase their hedge when volatility is expected to be higher and viceversa.
 Volatility traders: They can take advantage of high validity by taking the long position on straddles and low validity by taking the short position on straddles. Implied volatility also anticipates options prices. When the volatility is expected to rise, the options price becomes more valuable, and when the volatility is expected to subside, the options price becomes less valuable. More precisely, the expected move in the implied volatility is used in conjunction with the outlook on the trend of the underlying index for volatility trading and hedging, as depicted in Table 9.
 Derivative trading: when the implied volatility index (the India VIX) is about to increase, buying calls on the India VIX is a better hedge than buying puts on the underlying stock index (the NIFTY 50 Index) because the implied volatility index is more sensitive. Hence, if the India VIX level is anticipated to be higher, buying calls on the India VIX and selling calls on the NIFTY 50 Index are recommended.
 Portfolio managers: The VIX also helps in selecting stocks to rebalance a portfolio. Portfolio managers can increase exposure to highbeta stocks when volatility is about to bounce from its peak level. Similarly, portfolio managers can increase exposure to lowbeta stocks when volatility is about to bounce from its bottom level.
8. Academic Contributions
9. Limitations and Future Scope
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Logistic regression: penalty=‘elasticnet’, l1_ratio=0.3, solver=‘saga’, C=0.1, max_iter=20, tol=1e08 
Random Forest: n_estimators=180, criterion=‘entropy’, max_depth=5, min_samples_split=2, min_samples_leaf=5, min_weight_fraction_leaf=0.01, max_features=29, min_impurity_decrease=0.01, max_leaf_nodes=7, max_samples=0.85, bootstrap=True, oob_score=True 
Extra Trees: n_estimators=100, criterion=‘entropy’, max_depth=7, min_samples_split=17, min_samples_leaf=5, min_weight_fraction_leaf=0.001, max_leaf_nodes=19, max_features=29, min_impurity_decrease=0.001, bootstrap=True, oob_score=True 
Bagging: n_estimators=310, max_samples=0.85, max_features=32, bootstrap=True, bootstrap_features=False

AdaBoost: n_estimators=221, algorithm=‘SAMME’, learning_rate=0.01

Stacking: passthrough=True, estimators=[e1, e2], final_estimator=e3

Voting: voting=‘soft’, estimators=[e1, e2]

Stochastic GBoosting: n_estimators=111, loss=‘deviance, learning_rate=0.5, subsample=0.45, criterion=‘friedman_mse, max_depth=2, min_samples_split=2, min_samples_leaf=2, min_weight_fraction_leaf=0.4, min_impurity_decrease=0.4, max_features=32, max_leaf_nodes=2, 
Hist GBoosting: max_iter=300, loss=‘binary_crossentropy’, max_depth=2, min_samples_leaf=46, max_leaf_nodes=2, learning_rate=0.012, l2_regularization=1e15, max_bins=200, tol=1e8 
XGBoost: n_estimators=90, max_depth=4, learning_rate=0.01, objective=‘binary:logistic’, eval_metric=‘error’, booster=‘gbtree’, tree_method=‘approx’, gamma=13.6, reg_alpha=1.0, reg_lambda=1e14, min_child_weight=7.7, subsample=0.55, colsample_bytree=0.9, importance_type=‘gain’, 
LightGBM: n_estimators=625, objective=‘binary’, max_depth=2, num_leaves=3, learning_rate=0.001, subsample=0.05, colsample_bytree=0.95, boosting_type=‘gbdt’, reg_alpha=1.0, reg_lambda=10.0, min_child_weight=1e08, min_child_samples=80, 
CatBoost: n_estimators=3000, max_depth=4, learning_rate=0.001, min_child_samples=4, reg_lambda=30, bootstrap_type=‘Bayesian’, bagging_temperature=0, rsm=0.8, leaf_estimation_method=‘Gradient’, boosting_type=‘Plain’, langevin=True, score_function=‘L2’ 
Logistic Regression  Random Forest  Extra Trees  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.67  0.68  0.68  0.70  0.70  0.70  0.68  0.67  0.67  168 
1  0.59  0.58  0.59  0.62  0.62  0.62  0.59  0.61  0.60  132 
macro avg  0.63  0.63  0.63  0.66  0.66  0.66  0.64  0.64  0.64  300 
weighted avg  0.64  0.64  0.64  0.67  0.67  0.67  0.64  0.64  0.64  300 
Bagging  AdaBoost  Stacking  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.70  0.70  0.70  0.69  0.67  0.68  0.70  0.74  0.72  168 
1  0.62  0.61  0.62  0.60  0.61  0.60  0.64  0.60  0.62  132 
macro avg  0.66  0.66  0.66  0.64  0.64  0.64  0.67  0.67  0.67  300 
weighted avg  0.66  0.66  0.66  0.65  0.65  0.65  0.67  0.68  0.68  300 
Voting  Stochastic GBoosting  Hist GBoosting  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.69  0.70  0.70  0.67  0.68  0.68  0.68  0.73  0.70  168 
1  0.62  0.61  0.61  0.59  0.57  0.58  0.62  0.57  0.59  132 
macro avg  0.65  0.65  0.65  0.63  0.63  0.63  0.65  0.65  0.65  300 
weighted avg  0.66  0.66  0.66  0.63  0.63  0.63  0.65  0.66  0.65  300 
XGBoost  LightGBM  CatBoost  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.70  0.70  0.70  0.70  0.70  0.70  0.70  0.71  0.71  168 
1  0.62  0.61  0.62  0.62  0.61  0.62  0.62  0.61  0.62  132 
macro avg  0.66  0.66  0.66  0.66  0.66  0.66  0.66  0.66  0.66  300 
weighted avg  0.66  0.66  0.66  0.66  0.66  0.66  0.67  0.67  0.67  300 
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#  Ensemble Classifier  Reference 

1  Random Forest  Breiman (2001) 
2  Extremely randomised trees (Extra Trees)  Geurts et al. (2006) 
3  Bagging  Breiman (1996); Ho (1998); Louppe and Geurts (2012) 
4  AdaBoost  Freund and Schapire (1996, 1997); Hastie et al. (2009) 
5  Stacking  Florian (2002) 
6  Voting  Ruta and Gabrys (2005) 
7  Stochastic gradient boosting (Stochastic GBoosting)  Friedman (2002) 
8  Histogrambased gradient boosting (Hist GBoosting)  Guryanov (2019) 
9  Extreme Gradient Boosting (XGBoost)  Chen and Guestrin (2016) 
10  Light Gradient Boosted Machine (LightGBM)  Ke et al. (2017) 
11  CatBoost  Dorogush et al. (2018) 
#  Classifier  Location of the Python library 

1  Logistic regression  sklearn.linear_model.LogisticRegression 
2  Random Forest  sklearn.ensemble.RandomForestClassifier 
3  Extra Trees  sklearn.ensemble.ExtraTreesClassifier 
4  Voting  sklearn.ensemble.VotingClassifier 
5  Stacking  sklearn.ensemble.StackingClassifier 
6  Bagging  sklearn.ensemble.BaggingClassifier 
7  AdaBoost  sklearn.ensemble.AdaBoostClassifier 
8  Gradient boosting  sklearn.ensemble.GradientBoostingClassifier 
9  Hist GBoosting  sklearn.ensemble. HistGradientBoostingClassifier 
10  XGBoost  xgboost.XGBClassifier 
11  LightGBM  lightgbm.LGBMClassifier 
12  CatBoost  catboost.CatBoostClassifier 
Predicted Class  

0  1  
Actual class  0  TN (True Negative)  FP (False Positive) 
1  FN (False Negative)  TP (True Positive) 
Index  Features  Descriptions  References 

1  Value of the India VIX (open, high, low and close)  Open, high, low and close values of the India VIX  Ballestra et al. (2019) Dixit et al. (2013) Prasad et al. (2022) 
2  Days of week  0 to 6 for Sunday to Saturday  Dixit et al. (2013) 
3  EWMA  The EWMA of the India VIX with 5, 10, 15 and 20day moving windows  Dixit et al. (2013) 
4  EWMV  EWMV of returns on the NIFTY 50 Index with a 10day moving window  Chaudhuri and Ghosh (2016) 
5  Return on the NIFTY 50 Index  Log returns on NIFTY 50 Index  Bantwa (2017) Carr (2017) Fernandes et al. (2014) Mall et al. (2011) Shaikh and Padhi (2016) 
6  Return on volume of the NIFTY 50 Index  Log return on volume of underlying NIFTY 50 Index  Fernandes et al. (2014) 
7  ATR  ATR (volatility indicator) of the NIFTY 50 Index with a 10day moving window  Included to capture the volatility of the underlying index 
8  DIV  DIV of the NIFTY 50 Index with a 10day moving window  Yang and Zhang (2000) 
9  Return on the S&P 500  Log return on close value of the S&P 500 Index  Onan et al. (2014) 
10  Return on DJIA  Log return on close value of the DJIA Index  Onan et al. (2014) 
11  Changes in VIX  First difference of the closing value of the CBOE VIX Index  Onan et al. (2014) 
Classifier  Class Weights to 0s Label  Class Weights to 1s Label 

Random Forest  0.95  1.18 
Extra Trees  0.95  1.39 
Bagging  0.95  1.16 
AdaBoost  0.95  1.16 
Stacking  0.95  1.15 
Voting  0.95  1.16 
Gradient boosting  0.95  1.19 
Hist GBoosting  0.94  1.14 
XGBoost  0.96  1.10 
LightGBM  0.95  1.09 
Logistic regression  0.95  1.40 
Classifier  Split0 Score  Split1 Score  Mean Score  Std Score 

Logistic regression  0.500206  0.504043  0.502124  0.001919 
Random Forest  0.590954  0.614735  0.602845  0.011891 
Extra Trees  0.466468  0.423695  0.445082  0.021387 
Bagging  0.580314  0.591281  0.585797  0.005484 
AdaBoost  0.611933  0.616224  0.614078  0.002145 
Stacking  0.579413  0.596283  0.587848  0.008435 
Voting  0.578771  0.592769  0.585770  0.006999 
Stochastic GBoosting  0.589778  0.585407  0.587592  0.002185 
Hist GBoosting  0.583003  0.610750  0.596876  0.013873 
XGBoost  0.580665  0.616893  0.598779  0.018114 
LightGBM  0.609343  0.609410  0.609377  0.000033 
CatBoost  0.549842  0.491619  0.520730  0.029111 
Classifier  TN  FP  FN  TP  Accuracy Score  AUC  PrecisionRecall AUC  GMean f1Score 

Logistic regression  114  54  55  77  63.67%  69.04%  66.38%  62.94% 
Random Forest  118  50  50  82  66.67%  67.77%  63.44%  66.06% 
Extra Trees  112  56  52  80  64.00%  68.57%  64.90%  63.47% 
Bagging  118  50  51  81  66.33%  68.11%  64.65%  65.68% 
AdaBoost  113  55  51  81  64.67%  67.98%  62.87%  64.15% 
Stacking  124  44  53  79  67.67%  69.48%  65.48%  66.74% 
Voting  118  50  52  80  66.00%  68.32%  64.54%  65.30% 
Stochastic GBoosting  115  53  57  75  63.33%  68.72%  65.32%  62.47% 
Hist GBoosting  122  46  57  75  65.67%  66.93%  63.73%  64.57% 
XGBoost  118  50  51  81  66.33%  67.42%  63.89%  65.68% 
LightGBM  118  50  51  81  66.33%  67.30%  63.25%  65.68% 
CatBoost  120  48  52  80  66.67%  68.38%  64.07%  65.91% 
Rank  Classifier  Class Score  Overall Score  Accuracy Score 

1  CatBoost  0.4458  0.3972  66.67% 
1  LightGBM  0.4458  0.3972  66.33% 
1  XGBoost  0.4458  0.3972  66.33% 
1  Voting  0.4458  0.3972  66.00% 
1  Stacking  0.4458  0.3972  67.67% 
1  Bagging  0.4458  0.3972  66.33% 
1  Random Forest  0.4458  0.3972  66.67% 
8  Hist GBoosting  0.4125  0.3639  65.67% 
9  AdaBoost  0.3917  0.3639  64.67% 
9  Extra Trees  0.3917  0.3639  64.00% 
11  Stochastic Gboosting  0.3500  0.3639  63.33% 
11  Logistic regression  0.3500  0.3639  63.67% 
Outlook on the Trend of Underlying Index (Nifty 50)  

Bearish  Neutral  Bullish  
Expected move in implied volatility (India VIX)  Decrease  Write calls  Write straddles  Write puts 
Remain unchanged  Write calls and buy puts  Calendar spread  Buy calls and write puts  
Increase  Buy puts  Buy straddle  Buy calls 
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Prasad, A.; Bakhshi, P. Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning. J. Risk Financial Manag. 2022, 15, 552. https://doi.org/10.3390/jrfm15120552
Prasad A, Bakhshi P. Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning. Journal of Risk and Financial Management. 2022; 15(12):552. https://doi.org/10.3390/jrfm15120552
Chicago/Turabian StylePrasad, Akhilesh, and Priti Bakhshi. 2022. "Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning" Journal of Risk and Financial Management 15, no. 12: 552. https://doi.org/10.3390/jrfm15120552