# Role of the Global Volatility Indices in Predicting the Volatility Index of the Indian Economy

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Research Design and Methodology

#### 3.1. Data Collection and Pre-Processing

#### 3.2. Feature Variables

#### 3.3. Target Variable

#### 3.4. Definition of Model

#### 3.5. Description of the Models Used

#### 3.5.1. Logistic Regression

_{1}and L

_{2}, the regularisation term becomes:

_{1}term sets the insignificant feature variables’ coefficient to zero, while in L

_{2}regularisation, insignificant feature variables’ coefficient converses towards zero. Regularisations play a significant role in protecting overfitting models and, thereby, the ranking of feature variables. The mix of L

_{1}and L

_{2}is called elastic net. As there were enough feature variables available, higher mixing parameters signified more L

_{1}regularisation along with the penalty, which set some unimportant features to zero. This was decided during the hyper-tuning process.

#### 3.5.2. Random Forest Classifier

#### 3.5.3. Extreme Gradient Boosting Classifier

#### 3.6. Performance Evaluation

#### 3.7. Validation Procedure

## 4. Findings

**Logistic Regression:**The logistic regression model achieved an accuracy score of 56.47% and an ROC AUC score of 56.71%. Its l1_ratio (L

_{1}and L

_{2}mixing parameter), as seen in Table 3, was 0.95. Due to a higher l1_ratio, which was indicative of more L

_{1}regularisation, most of the coefficient of redundant feature variables were set to zero and only seven were set to non-zero, which are stated in Table 8. Since these were coefficients, their absolute values were compared. According to Table 8, the coefficient of Delta_VVIX-1 was the most significant. Hence, it can be said that change in volatility of the CBOE VIX Index on the previous day is one of the most influential factors in predicting the present day’s binary movements of the India VIX Index. The top seven influencing factors, from highest to lowest in order, were Delta_VVIX-1, Delta_OVX-1, Delta_VVIX-5, Delta_RVX-1, Delta_VVIX-4, Delta_VIX-1 and Delta_VVIX-3. This clearly indicated that most of the US implied volatility indices had the predictive power in forecasting the India VIX Index. Most importantly, 1-day, 3-day, 4-day and 5-day prior changes in the volatility of the CBOE VIX Index (VVIX) were accountable, but the India VIX’s previous values did not count as an influencing factor.

**Random Forest:**The Random Forest model achieved an accuracy score of 51.76% and an ROC AUC score of 55.49%. Table 7 and Figure 2 display the ranked feature variables from most to least important. There were only 20 feature variables set to non-zero; the rest were set to 0. From the top five ranked features, Delta_VIX-1, Delta_VXN-1, Delta_VXD-1, Delta_VVIX-1 and Delta_RVX-1 were the most significant, because their scores were significantly higher. These were the 1-day prior to changes in the US implied volatility indices, which affected the binary movement in the India VIX the most. As Delta_VSTOXX-1 was ranked 6th, the 1-day prior to changes in the Eurozone implied volatility index was also important. However, changes in the India VIX, as feature variables, were ranked 8th, 10th, 12th and 15th, among the top 20. Hence, changes in India VIX were not so important, but changes in the US implied volatility indices were most important in predicting the India VIX Index.

**XG Boost:**The XG Boost model achieved an accuracy score of 60% and an ROC AUC score of 60.98%. It is evident from Table 9 that the top five features, Delta_VXN-1, Delta_VVIX-1, Delta_VXD-1, Delta_VIX-1 and Delta_RVX-1, were most significant because their scores were significantly higher. Additionally, they were all US implied volatility indices. Hence, a change in US implied volatility indices had a greater impact than other implied volatility indices on the binary movements of the India VIX Index. Unfortunately, among the top 20 features ranked in Table 9, changes in India VIX ranked 10th, 11th, 13th and 14th in predicting its own movements. The 1-day and 5-day prior changes in the Eurozone implied volatility index placed 6th and 7th. From Table 10, the 1-day prior changes in the Australian implied volatility index (AXVI), the 4-day prior Hang Seng implied volatility Index (VHSI), and the 5-day prior Japan implied volatility index (JNIV) ranked 23rd 27th and 32nd, respectively.

## 5. Conclusions

**Implication**: It is important for traders and investors of emerging economies, like India’s economy, to know the influencing power of various global implied volatility indices in predicting the movement of the volatility index of the emerging economy, which, in turn, estimates the risk in that economy’s stock market. The outcome of this research is crucial for traders and investors of Indian economies in estimating risk in the stock market by creating a watch list of the most crucial global implied volatility indices. Hedgers, risk-averse investors, portfolio managers, and options and volatility traders are more interested in minimising risk over maximising return and the predicted value of the VIX Index could be very useful to them.

**Contribution:**Generally, to analyse the significance of independent variables (features), a regression technique is used, while considering features and target variables in the same timeline, and, subsequently, hypothesis testing is performed. However, this study considered a different approach to investigate the significance of feature variables for forecasting volatility, while considering features and target variables in a different timeline. Hence, this study provides another technique for significance testing.

**Limitation and future scope:**This study is restricted to the India VIX Index, but similar implied volatility indices of other emerging economies could be investigated in the future. In addition to the Random Forest and XG Boost, other ensemble learning algorithms, required to rank the set of feature variables, could be used in future studies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Change in Volatility Index | 24 November 2021 | 25 November 2021 | 26 November 2021 | 29 November 2021 | 30 November 2021 |
---|---|---|---|---|---|

Delta_INDIAVIX | −0.920 | −0.433 | 4.140 | 0.028 | 0.338 |

Delta_VIX | −0.800 | −0.800 | 10.040 | −5.660 | 4.230 |

Delta_OVX | −0.310 | −0.310 | 30.930 | −2.380 | 11.890 |

Delta_VXN | −0.610 | −0.610 | 4.630 | −3.820 | 2.760 |

Delta_EVZ | −0.260 | −0.260 | 0.590 | −0.420 | 0.430 |

Delta_VVIX | −4.550 | −4.550 | 39.260 | −18.500 | 11.310 |

Delta_GVZ | −0.060 | −0.060 | 1.240 | −0.440 | 0.440 |

Delta_RVX | −0.480 | −0.480 | 13.170 | −6.020 | 3.560 |

Delta_VXD | −0.360 | −0.360 | 6.990 | −1.710 | 3.440 |

Delta_VHSI | −0.430 | −0.660 | 4.520 | 1.040 | −0.670 |

Delta_JNIV | 0.860 | −0.530 | 3.320 | 5.000 | 1.800 |

Delta_AXVI | −0.324 | −0.758 | 1.695 | 2.264 | −1.051 |

Delta_VSTOXX | 0.030 | −0.790 | 12.430 | −3.510 | 1.270 |

Ticker | Implied Volatility Index | Exchange | Underlying Asset | Source of Data |
---|---|---|---|---|

VIX | CBOE Volatility Index | CBOE | S&P 500 | Cboe.com |

OVX | CBOE Crude Oil ETF Volatility Index | CBOE | U.S. Oil Fund | Cboe.com |

VXN | CBOE Nasdaq 100 Volatility Index | CBOE | Nasdaq 100 | Cboe.com |

EVZ | CBOE Eurocurrency Volatility Index | CBOE | Currency Shares Euro Trust | Cboe.com |

VVIX | VIX of VIX Index | CBOE | VIX Index | Cboe.com |

GVZ | CBOE Gold ETF Volatility Index | CBOE | SPDR Gold Shares ETF | Cboe.com |

RVX | CBOE Russell 2000 Volatility Index | CBOE | CBOE Russell 2000 | Cboe.com |

VXD | CBOE DJIA Volatility Index | CBOE | Dow Jones Industrials Average | Cboe.com |

INDIAVIX | India VIX Index | NSE of India | NOFTY 50 | NSE of India |

VHSI | HSI Volatility Index | Hong Kong Exchanges | Hang Seng Index | in.investing.com |

JNIV | Nikkei Volatility Index | Nikkei Stock Average, Japan | Nikkei 225 | in.investing.com |

AXVI | S&P/ASX 200 VIX Index | Australia | S&P/ASX 200 | in.investing.com |

VSTOXX | STOXX 50 Volatility Index | Eurozone | Euro Stoxx 50 | Wall Street Journal |

Estimators | Hyperparameters |
---|---|

Random Forest | n_estimators = 320, criterion = ‘entropy’, max_depth = 3, min_samples_split = 16, min_samples_leaf = 6, min_weight_fraction_leaf = 0.01, max_features = 29, min_impurity_decrease = 0.01, max_leaf_nodes = 8, max_samples = 0.85, bootstrap = True, oob_score = True, ccp_alpha = 0.0 |

Logistic Regression | solver = ‘saga’, l1_ratio = 0.95, C = 0.0054, max_iter = 5, tol = 1 × 10^{−8}, penalty = ‘elasticnet’ |

XGBoost | max_depth = 5, booster = ‘gbtree’, n_estimators = 120, learning_rate = 0.0001, objective = ‘binary:logistic’, importance_type = ‘gain’, eval_metric = ‘logloss’, reg_lambda = 1e-14, reg_alpha = 1.0, min_child_weight = 7.5, subsample = 0.55, colsample_bytree = 0.9, gamma = 6.4, tree_method = ‘approx’ |

Logistic Regression | Random Forest | XGBoost | |
---|---|---|---|

split0 validation score | 58.87% | 58.64% | 58.39% |

split1 validation score | 55.75% | 56.10% | 56.75% |

mean validation score | 57.31% | 57.37% | 57.57% |

Logistic Regression | Random Forest | XG Boost | |
---|---|---|---|

ROC AUC Score | 56.71% | 55.49% | 60.98% |

Accuracy Score | 56.47% | 51.76% | 60.00% |

Logistic Regression | Random Forest | XG Boost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Precision | Recall | F1-Score | Precision | Recall | F1-Score | Precision | Recall | F1-Score | Support | |

0 | 0.57 | 0.68 | 0.62 | 0.52 | 0.82 | 0.64 | 0.60 | 0.68 | 0.64 | 44 |

1 | 0.56 | 0.44 | 0.49 | 0.50 | 0.20 | 0.28 | 0.60 | 0.51 | 0.55 | 41 |

macro avg | 0.56 | 0.56 | 0.56 | 0.51 | 0.51 | 0.46 | 0.60 | 0.60 | 0.60 | 85 |

weighted avg | 0.56 | 0.56 | 0.56 | 0.51 | 0.52 | 0.47 | 0.60 | 0.60 | 0.60 | 85 |

Rank | Feature Name | Feature Score |
---|---|---|

1 | Delta_VIX-1 | 0.197344 |

2 | Delta_VXN-1 | 0.180418 |

3 | Delta_VXD-1 | 0.178520 |

4 | Delta_VVIX-1 | 0.177455 |

5 | Delta_RVX-1 | 0.152439 |

6 | Delta_VSTOXX-1 | 0.066945 |

7 | Delta_GVZ-1 | 0.012593 |

8 | Delta_INDIAVIX-3 | 0.006570 |

9 | Delta_OVX-5 | 0.006398 |

10 | Delta_INDIAVIX-1 | 0.006362 |

11 | Delta_OVX-1 | 0.001998 |

12 | Delta_INDIAVIX-2 | 0.001883 |

13 | Delta_VIX-5 | 0.001777 |

14 | Delta_AXVI-2 | 0.001730 |

15 | Delta_INDIAVIX-4 | 0.001514 |

16 | Delta_VXN-5 | 0.001467 |

17 | Delta_GVZ-5 | 0.001236 |

18 | Delta_AXVI-1 | 0.001188 |

19 | Delta_VXN-4 | 0.001087 |

20 | Delta_VVIX-5 | 0.001076 |

Feature Name | Feature Coefficient |
---|---|

Delta_VVIX-1 | 0.036774 |

Delta_OVX-1 | 0.005020 |

Delta_VVIX-5 | 0.003561 |

Delta_RVX-1 | 0.002598 |

Delta_VIX-1 | 0.000163 |

Delta_VVIX-3 | 0.000003 |

Delta_VVIX-4 | −0.002448 |

Feature Name | Feature Score | |
---|---|---|

1 | Delta_VXN-1 | 0.030782 |

2 | Delta_VVIX-1 | 0.030110 |

3 | Delta_VXD-1 | 0.027539 |

4 | Delta_VIX-1 | 0.025819 |

5 | Delta_RVX-1 | 0.025151 |

6 | Delta_VSTOXX-1 | 0.018124 |

7 | Delta_VSTOXX-5 | 0.017636 |

8 | Delta_OVX-5 | 0.017171 |

9 | Delta_VXD-5 | 0.016782 |

10 | Delta_INDIAVIX-1 | 0.016677 |

11 | Delta_INDIAVIX-3 | 0.015998 |

12 | Delta_VVIX-4 | 0.015941 |

13 | Delta_INDIAVIX-4 | 0.015898 |

14 | Delta_INDIAVIX-5 | 0.015777 |

15 | Delta_VIX-4 | 0.015571 |

16 | Delta_GVZ-5 | 0.015470 |

17 | Delta_RVX-4 | 0.015441 |

18 | Delta_VXN-3 | 0.015430 |

19 | Delta_VIX-5 | 0.015310 |

20 | Delta_VXN-5 | 0.015194 |

Order | Feature Name | Feature Importance | Order | Feature Name | Feature Importance |
---|---|---|---|---|---|

1 | Delta_VXN-1 | 0.030782 | 34 | Delta_JNIV-1 | 0.014305 |

2 | Delta_VVIX-1 | 0.030110 | 35 | Delta_AXVI-2 | 0.014198 |

3 | Delta_VXD-1 | 0.027539 | 36 | Delta_OVX-1 | 0.014102 |

4 | Delta_VIX-1 | 0.025819 | 37 | Delta_VVIX-2 | 0.014090 |

5 | Delta_RVX-1 | 0.025151 | 38 | Delta_VHSI-5 | 0.014053 |

6 | Delta_VSTOXX-1 | 0.018124 | 39 | Delta_OVX-3 | 0.014035 |

7 | Delta_VSTOXX-5 | 0.017636 | 40 | Delta_EVZ-1 | 0.013992 |

8 | Delta_OVX-5 | 0.017171 | 41 | Delta_VSTOXX-3 | 0.013906 |

9 | Delta_VXD-5 | 0.016782 | 42 | Delta_GVZ-4 | 0.013902 |

10 | Delta_INDIAVIX-1 | 0.016677 | 43 | Delta_RVX-3 | 0.013892 |

11 | Delta_INDIAVIX-3 | 0.015998 | 44 | Delta_JNIV-2 | 0.013807 |

12 | Delta_VVIX-4 | 0.015941 | 45 | Delta_VHSI-1 | 0.013641 |

13 | Delta_INDIAVIX-4 | 0.015898 | 46 | Delta_JNIV-4 | 0.013628 |

14 | Delta_INDIAVIX-5 | 0.015777 | 47 | Delta_AXVI-5 | 0.013435 |

15 | Delta_VIX-4 | 0.015571 | 48 | Delta_GVZ-2 | 0.013418 |

16 | Delta_GVZ-5 | 0.015470 | 49 | Delta_VXN-4 | 0.013415 |

17 | Delta_RVX-4 | 0.015441 | 50 | Delta_VIX-3 | 0.013291 |

18 | Delta_VXN-3 | 0.015430 | 51 | Delta_VIX-2 | 0.013208 |

19 | Delta_VIX-5 | 0.015310 | 52 | Delta_OVX-4 | 0.013162 |

20 | Delta_VXN-5 | 0.015194 | 53 | Delta_VXD-3 | 0.013105 |

21 | Delta_VXD-4 | 0.015151 | 54 | Delta_JNIV-3 | 0.013072 |

22 | Delta_VVIX-3 | 0.015041 | 55 | Delta_AXVI-4 | 0.013030 |

23 | Delta_AXVI-1 | 0.015007 | 56 | Delta_VXD-2 | 0.013030 |

24 | Delta_VXN-2 | 0.014954 | 57 | Delta_VHSI-3 | 0.013005 |

25 | Delta_INDIAVIX-2 | 0.014787 | 58 | Delta_EVZ-2 | 0.012905 |

26 | Delta_GVZ-3 | 0.014706 | 59 | Delta_EVZ-4 | 0.012893 |

27 | Delta_VHSI-4 | 0.014654 | 60 | Delta_VVIX-5 | 0.012805 |

28 | Delta_VSTOXX-4 | 0.014613 | 61 | Delta_RVX-5 | 0.012723 |

29 | Delta_VSTOXX-2 | 0.014590 | 62 | Delta_VHSI-2 | 0.012514 |

30 | Delta_GVZ-1 | 0.014589 | 63 | Delta_EVZ-5 | 0.012230 |

31 | Delta_OVX-2 | 0.014553 | 64 | Delta_EVZ-3 | 0.012139 |

32 | Delta_JNIV-5 | 0.014507 | 65 | Delta_RVX-2 | 0.011732 |

33 | Delta_AXVI-3 | 0.014361 |

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**MDPI and ACS Style**

Prasad, A.; Bakhshi, P.
Role of the Global Volatility Indices in Predicting the Volatility Index of the Indian Economy. *Risks* **2022**, *10*, 223.
https://doi.org/10.3390/risks10120223

**AMA Style**

Prasad A, Bakhshi P.
Role of the Global Volatility Indices in Predicting the Volatility Index of the Indian Economy. *Risks*. 2022; 10(12):223.
https://doi.org/10.3390/risks10120223

**Chicago/Turabian Style**

Prasad, Akhilesh, and Priti Bakhshi.
2022. "Role of the Global Volatility Indices in Predicting the Volatility Index of the Indian Economy" *Risks* 10, no. 12: 223.
https://doi.org/10.3390/risks10120223