# A Low Price Correction for Improved Volatility Estimation and Forecasting

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## Abstract

**:**

## 1. Introduction

## 2. Low Price Effect and Low Price Correction

**Definition**

**1.**

**Remark**

**1.**

**Remark**

**2.**

**Definition**

**2.**

**Remark**

**3.**

**Definition**

**3.**

**Definition**

**4.**

**Remark**

**4.**

#### 2.1. Backtesting and Method’s Advantages

**Remark**

**5.**

**Definition**

**5.**

- The method is simple and straightforward.
- It is general since it is applied after the forecast and it can be applied for every risk measure and estimation method.
- It either leaves estimations intact when $mp{r}_{t}<\mathsf{\Theta}$ or it improves the associated VR.
- After the correction, we no longer observe irrational values.
- It does not produce new extreme overestimations.
- It is useful especially in extreme scenarios when stocks collapse.
- The bigger the collapse, the better the improvement. Thus, when models tend to fail, the proposed method provides its best results.
- For backtesting, VR is always improved while VaR volatility2 does not seem to be affected.

## 3. Application

- ARCH(1), ARCH(4) and ARCH(5) with normal innovations
- GARCH(1,1) with normal and t-Student innovations
- GARCH(1,1), (4,1), (5,1), (2,2) and (3,2) with skew t-Student innovations
- APARCH(1,1) with Normal, t-Student and skew t-Student innovations and with Normal innovations and $\delta =2$,
- APARCH(2,2) with Normal, t-Student and skew t-Student innovations
- IGARCH(1,1) with and without a constant and with a constant with Student’s t innovations
- FIGARCH(0,d,0), (1,d,0),(0,d,1),(1,d,1) and (1,d,1) with Student’s t Errors

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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1. | The loss on a trading portfolio such that there is a probability p of losses equaling or exceeding VaR in a given trading period and a $1-p$ probability of losses being lower than the VaR. |

2. | VaR volatility is the standard deviation of the VaR forecasts. |

**Figure 7.**QQ plot for Normal and Student-t distributions. (

**a**) QQ plot Normal; (

**b**) QQ plot 3-Student; (

**c**) QQ plot 5-Student.

VR without lpe | VR with lpe | VaR vol without lpe | VaR vol with lpe | |
---|---|---|---|---|

EWMA | 0.6285714 | 0.6285714 | 0.06026717 | 0.0603289 |

MA | 0.8571429 | 0.7428571 | 0.001316615 | 0.002102242 |

HS | 0.9142857 | 0.8 | 0.001710221 | 0.002358666 |

GARCH(1,1) | 0.9142857 | 0.8 | 0.05176546 | 0.05173457 |

GARCH(2,2) | 3.771429 | 3.257143 | 0.02092407 | 0.02087996 |

APARCH(1,1) | 3.657143 | 3.085714 | 0.02497998 | 0.02502232 |

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**MDPI and ACS Style**

Siouris, G.-J.; Karagrigoriou, A.
A Low Price Correction for Improved Volatility Estimation and Forecasting. *Risks* **2017**, *5*, 45.
https://doi.org/10.3390/risks5030045

**AMA Style**

Siouris G-J, Karagrigoriou A.
A Low Price Correction for Improved Volatility Estimation and Forecasting. *Risks*. 2017; 5(3):45.
https://doi.org/10.3390/risks5030045

**Chicago/Turabian Style**

Siouris, George-Jason, and Alex Karagrigoriou.
2017. "A Low Price Correction for Improved Volatility Estimation and Forecasting" *Risks* 5, no. 3: 45.
https://doi.org/10.3390/risks5030045