# Analysis of Volatility Volume and Open Interest for Nifty Index Futures Using GARCH Analysis and VAR Model

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data Description

## 4. Model Specification

#### 4.1. GARCH (1, 1) Model:

#### 4.2. VAR Model

_{t}denotes volume, one of the liquidity proxies that is investigated, O

_{t}denotes volatility, p denotes the number of lags and ε

_{t}is an error term. The optimal lag length, p, is determined through an optimization process based on Akaike’s information criterion (AIC).

- “V
_{t}does not Granger-cause θ_{t}” for the first VAR model and - “θ
_{t}does not Granger-cause V_{t}” for the second equation.

#### 4.3. Variance Decomposition

#### 4.4. Impulse Response

_{t}be a K dimensional vector series given by

_{t}= ∑ ϕ

_{i.}

## 5. Empirical Findings

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Impulse response function of volatility, volume and open interest on innovations in the individual category.

Futures | Volume | ||
---|---|---|---|

Trader Category | All Trades | Percentage | |

1 | Individuals | 3,067,836,325 | 49.583 |

2 | Partnership firms, Hindu Undivided Family, HUF | 862,042,950 | 37.603 |

3 | Public/Private companies | 5,049,988,650 | 18.568 |

4 | Domestic Institutional Investors, DII | 82,143,925 | 4.472 |

5 | NRIs, Overseas Body Corporate, FDI | 66,961,850 | 3.655 |

6 | Foreign Institutional Investors FII | 2,671,117,850 | 0.416 |

Full sample | 11,800,091,550 | 23.730 |

Statistics | Volatility | Volume | Open Interest |
---|---|---|---|

Mean | −0.0005 | 3679578 | 17340433 |

Median | −0.0006 | 3816800 | 16865106 |

Maximum | 0.0289 | 8032767 | 28474865 |

Minimum | −0.0386 | 53200 | 5943600 |

Standard Deviation | 0.0091 | 2031685 | 4117847 |

Skewness | −0.15 | −0.28 | −0.04 |

Kurtosis | 4.50 | 2.30 | 2.71 |

Jarque-Bera test (p-value) | 46.11 (<0.0001) * | 15.64 (0.0004) * | 1.72 (0.4229) * |

ADF (p-value) | −22.74 (<0.0001) * | −1.75 (0.4046) * | −7.01 (0.4046) * |

No. of observations | 470 | 470 | 470 |

Parameters | Coefficient | p-Value | |
---|---|---|---|

Mean Equation | Constant (φ) | 0.00069 | 0.6800 |

Volume | 0.00000 | 0.6343 | |

Open interest | 0.00000 | 0.5156 | |

Variance Equation | constant (ω) | 0.00000 | 0.0319(S) |

ARCH effect (α) | 0.09445 | 0.0013(S) | |

GARCH effect (β) | 0.86022 | <0.0001(S) | |

α + β | 0.95466 | ||

ARCH-LM test for heteroscedasticity | |||

ARCH-LM test statistic (N*R2) | 1.5723 | ||

p-value | 0.2099 |

Parameters | Coefficient | p-Value | |
---|---|---|---|

Mean Equation | Constant (φ) | −0.00010 | 0.9516 |

Volume | 0.00000 | 0.7949 | |

Open interest | 0.00000 | 0.6823 | |

Variance Equation | Constant (ω) | −0.51452 | 0.0178 (S) |

ARCH effect (α) | 0.17961 | 0.0012 (S) | |

GARCH effect (β) | −0.07343 | 0.0333 (S) | |

Leverage effect (Υ) | 0.96001 | <0.0001 (S) | |

α + β | 0.10618 | ||

ARCH-LM test for heteroscedasticity | |||

ARCH-LM test statistic (N*R2) | 0.6708 | ||

p-value | 0.4128 |

Nifty Index Futures | ||||||
---|---|---|---|---|---|---|

Causal Relations | Volume—Volatility | Open Interest—Volatility | Open Interest—Volume | |||

Categories | Volume Volatility | Volatility Volume | Open Interest Volatility | Volatility Open Interest | Open Interest Volume | Volume Open Interest |

Individuals | 0.7532 | 0.8610 | 0.9574 | 0.6424 | 0.1699 | 0.4079 |

Partnership Firms | 0.3629 | 0.2895 | 0.7016 | 0.3631 | 0.2433 | 0.0411 |

Public and Private Firms | 0.1564 | 0.0155 | 0.6522 | 0.9984 | 0.2709 | 0.1002 |

DII | 0.5985 | 0.7706 | 0.9692 | 0.2938 | 0.4350 | 0.8465 |

Overseas Corporate | 0.5066 | 0.6589 | 0.8557 | 0.6486 | 0.6503 | 0.7458 |

FIIs | 0.2808 | 0.0801 | 0.7411 | 0.0572 | 0.3886 | 0.6363 |

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**MDPI and ACS Style**

Dungore, P.P.; Patel, S.H.
Analysis of Volatility Volume and Open Interest for Nifty Index Futures Using GARCH Analysis and VAR Model. *Int. J. Financial Stud.* **2021**, *9*, 7.
https://doi.org/10.3390/ijfs9010007

**AMA Style**

Dungore PP, Patel SH.
Analysis of Volatility Volume and Open Interest for Nifty Index Futures Using GARCH Analysis and VAR Model. *International Journal of Financial Studies*. 2021; 9(1):7.
https://doi.org/10.3390/ijfs9010007

**Chicago/Turabian Style**

Dungore, Parizad Phiroze, and Sarosh Hosi Patel.
2021. "Analysis of Volatility Volume and Open Interest for Nifty Index Futures Using GARCH Analysis and VAR Model" *International Journal of Financial Studies* 9, no. 1: 7.
https://doi.org/10.3390/ijfs9010007