### Abstract

The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes' volatility. Examples and applications are considered.

Original language | English (US) |
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Pages (from-to) | 2565-2574 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 387 |

Issue number | 11 |

DOIs | |

State | Published - Apr 15 2008 |

### Fingerprint

### Keywords

- Range process
- Risk
- Volatility

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes.** / Vallois, Pierre; Tapiero, Charles.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 387, no. 11, pp. 2565-2574. https://doi.org/10.1016/j.physa.2007.12.018

}

TY - JOUR

T1 - Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes

AU - Vallois, Pierre

AU - Tapiero, Charles

PY - 2008/4/15

Y1 - 2008/4/15

N2 - The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes' volatility. Examples and applications are considered.

AB - The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes' volatility. Examples and applications are considered.

KW - Range process

KW - Risk

KW - Volatility

UR - http://www.scopus.com/inward/record.url?scp=39549106896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39549106896&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2007.12.018

DO - 10.1016/j.physa.2007.12.018

M3 - Article

VL - 387

SP - 2565

EP - 2574

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 11

ER -