# Markov-Regime Switches in Oil Markets: The Fear Factor Dynamics

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Markov-Regime Switching Modeling of Return Dynamics in Oil Futures Markets

## 4. Empirical Evidence

#### 4.1. Data Description and Distributional Properties

#### 4.2. Model Estimation Results

#### 4.3. Robustness Checks

## 5. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | It is noted that the study by Fleming et al. (1995) was performed with a volatility index based on the S&P 100 stock market index, formerly known as VIX index. |

2 | The focus is also placed, as in Mencia and Sentana (2013), on the valuation of VIX derivatives, where the volatility index serves as the underlying asset for derivatives contracts. |

3 | See for instance, S. Kim et al. (2019), Wang and Xie (2012), Choi and Hammoudeh (2010), Mensi et al. (2013), Raza et al. (2016) and Creti et al. (2013), inter alia. |

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**Figure 1.**The behavior of price levels and returns in WTI futures, OVX, dollar index, and equity markets.

Distributional Moments | Mean | Std. Dev. | Skewness | Kurtosis | Jarque Bera | ADF Test |
---|---|---|---|---|---|---|

WTI returns | −0.0007 | 0.062728 | −33.5240 | 1569.688 | 3.61 × 10^{8} | −43.544 ***b |

OVX daily changes | 0.00174 | 0.063033 | 4.9582 | 87.09921 | 1,052,944.0 | −61.760 ***a |

Dollar index daily changes | 0.00009 | 0.004761 | −0.0492 | 5.870737 | 1211.493 | −58.464 ***b |

S&P 500 returns | 0.00045 | 0.012766 | −0.2904 | 17.14844 | 29,442.39 | −68.718 ***a |

Model Parameters | Full Period (July 2008–December 2021) | |
---|---|---|

Markov-Regime 1 | Markov-Regime 2 | |

$\omega $ | −0.0001 (0.6697) | 0.0174 (0.2269) |

$\alpha $ | −0.0196 (0.1708) | 0.1592 *** (0.0045) |

$\beta $ | −0.1452 *** (0.0000) | −0.9643 *** (0.0000) |

$\gamma $ | −0.8659 *** (0.0000) | −1.4004 (0.4340) |

$\delta $ | 0.3820 *** (0.0000) | −0.6599 (0.2359) |

$Log\left(\sigma \right)$ | −4.1048 *** (0.0000) | −1.6497 *** (0.0000) |

Log likelihood | 9124.611 | |

AIC | −4.9880 | |

Hypothesis Tests | ||

${\omega}_{1}={\omega}_{2}$ | 1.4408 (0.2300) | |

${\alpha}_{1}={\alpha}_{2}$ | 9.5865 *** (0.0020) | |

${\beta}_{1}={\beta}_{2}$ | 76.7273 *** (0.0000) | |

${\gamma}_{1}={\gamma}_{2}$ | 0.0259 (0.8723) | |

${\delta}_{1}={\delta}_{2}$ | 3.2807 * (0.0701) |

^{2}distribution. Figures in round brackets represent probability values.

Model Parameters | Subperiod A (January 2018–December 2019) | Subperiod B (January 2020–December 2021) | ||
---|---|---|---|---|

Regime 1 | Regime 2 | Regime 1 | Regime 2 | |

$\omega $ | −0.0009 (0.2648) | 0.0056 * (0.0811) | 0.0014 * (0.0835) | 0.0135 (0.7792) |

$\alpha $ | 0.0145 (0.7738) | −2.4246 ** (0.0153) | 0.0014 (0.9667) | 0.1383 (0.1553) |

$\beta $ | −0.2205 *** (0.0000) | 0.2100 *** (0.0000) | −0.1802 *** (0.0000) | −1.2691 *** (0.0000) |

$\gamma $ | −0.4526 * (0.0671) | −0.1772 (0.8440) | −0.5188 ** (0.0379) | −2.3555 (0.7371) |

$\delta $ | 0.0913 (0.3084) | 0.8216 ** (0.0488) | 0.2888 *** (0.0003) | −1.9662 (0.1892) |

$Log\left(\sigma \right)$ | −4.3179 *** (0.0000) | −3.7329 *** (0.0000) | −4.1164 ** (0.0000) | −1.1437 *** (0.0000) |

Log Likelihood | 1403.674 | 1219.407 | ||

AIC | −5.324421 | −4.609587 | ||

Hypothesis tests | ||||

${\omega}_{1}={\omega}_{2}$ | 3.4875 * (0.0618) | 0.0636 (0.8009) | ||

${\alpha}_{1}={\alpha}_{2}$ | 4.3483 ** (0.0370) | 1.7564 (0.1851) | ||

${\beta}_{1}={\beta}_{2}$ | 84.6471 *** (0.0000) | 38.8884 *** (0.0000) | ||

${\gamma}_{1}={\gamma}_{2}$ | 0.0783 (0.7796) | 0.0684 (0.7936) | ||

${\delta}_{1}={\delta}_{2}$ | 2.6231 (0.1053) | 2.2305 (0.1353) |

Model Parameters | Subperiod C (July 2008–June 2010) | |
---|---|---|

Markov-Regime 1 | Markov-Regime 2 | |

$\omega $ | 0.0006 (0.4797) | −0.0008 (0.8519) |

$\alpha $ | 0.0621 (0.1126) | −0.0018 (0.8062) |

$\beta $ | −0.1402 *** (0.0000) | −0.0958 (0.1062) |

$\gamma $ | −1.7029 *** (0.0000) | −1.1439 ** (0.0169) |

$\delta $ | 0.3553 *** (0.0000) | 0.4894 *** (0.0006) |

$Log\left(\sigma \right)$ | −4.1663 *** (0.0000) | −2.9762 *** (0.0000) |

Log likelihood | 1220.131 | |

AIC | −4.6212 | |

Hypothesis Tests | ||

${\omega}_{1}={\omega}_{2}$ | 0.1054 (0.7454) | |

${\alpha}_{1}={\alpha}_{2}$ | 0.8807 (0.3480) | |

${\beta}_{1}={\beta}_{2}$ | 0.3969 (0.5287) | |

${\gamma}_{1}={\gamma}_{2}$ | 1.0965 (0.2950) | |

${\delta}_{1}={\delta}_{2}$ | 0.5650 (0.4523) |

Model Parameters [ARDL (5,3,2,0)] | Subperiod A (January 2018–December 2019) | |
---|---|---|

Coefficient | t-Statistic | |

$\omega $ | 0.0007 | 0.8380 |

${\alpha}_{t-1}$ | −0.1567 *** | −3.5950 |

${\alpha}_{t-2}$ | −0.0658 | −1.4974 |

${\alpha}_{t-3}$ | −0.0814 * | −1.8818 |

${\alpha}_{t-4}$ | 0.0582 | 1.4148 |

${\alpha}_{t-5}$ | 0.0733 * | 1.7949 |

${\beta}_{t}$ | −0.1010 *** | −6.2670 |

${\beta}_{t-1}$ | −0.0648 *** | −4.0226 |

${\beta}_{t-2}$ | −0.0360 ** | −2.2070 |

${\beta}_{t-3}$ | −0.0317 * | −1.9481 |

${\gamma}_{t}$ | −0.2385 | −0.9302 |

${\gamma}_{t-1}$ | −0.5504 ** | −2.1447 |

${\gamma}_{t-2}$ | −0.4391 * | −1.7066 |

${\delta}_{t}$ | 0.2806 *** | 2.9526 |

Log Likelihood | 1340.482 | |

AIC | −5.0823 | |

F-Bounds Test (At the 1% significance level) | ||

F-Statistic | I(0) | I(1) |

29.9258 | 3.65 | 4.66 |

Model Parameters [ARDL (4,0,4,1)] | Subperiod B (January 2020–December 2021) | |
---|---|---|

Coefficient | t-Statistic | |

$\omega $ | 0.0037 | 0.7861 |

${\alpha}_{t-1}$ | 0.2494 *** | 7.2207 |

${\alpha}_{t-2}$ | −0.1279 *** | −3.6187 |

${\alpha}_{t-3}$ | 0.0400 | 1.1396 |

${\alpha}_{t-4}$ | 0.0577 * | 1.7318 |

${\beta}_{t}$ | −0.8823 *** | −18.6752 |

${\gamma}_{t}$ | −1.2195 | −0.9081 |

${\gamma}_{t-1}$ | 0.5592 | 0.4318 |

${\gamma}_{t-2}$ | −1.5832 | −1.2145 |

${\gamma}_{t-3}$ | −3.7311 *** | −2.8466 |

${\gamma}_{t-4}$ | 3.2288 ** | 2.4446 |

${\delta}_{t}$ | −1.4937 *** | −4.2291 |

${\delta}_{t-1}$ | −1.5759 *** | −4.5938 |

Log Likelihood | 426.7656 | |

AIC | −1.5823 | |

F-Bounds Test (At the 1% significance level) | ||

F-Statistic | I(0) | I(1) |

109.6350 | 3.65 | 4.66 |

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**MDPI and ACS Style**

Okawa, H.
Markov-Regime Switches in Oil Markets: The Fear Factor Dynamics. *J. Risk Financial Manag.* **2023**, *16*, 67.
https://doi.org/10.3390/jrfm16020067

**AMA Style**

Okawa H.
Markov-Regime Switches in Oil Markets: The Fear Factor Dynamics. *Journal of Risk and Financial Management*. 2023; 16(2):67.
https://doi.org/10.3390/jrfm16020067

**Chicago/Turabian Style**

Okawa, Hiroyuki.
2023. "Markov-Regime Switches in Oil Markets: The Fear Factor Dynamics" *Journal of Risk and Financial Management* 16, no. 2: 67.
https://doi.org/10.3390/jrfm16020067