## Abstract

One established fact in financial economics and mathematics is the convergence of realised to integrated volatility according to the quadratic variation principle. When computed in general semimartingale asset price models, the cumulative squared high frequency returns represent consistent estimators of the integrated volatility. Both time and frequency domain estimators are available for solving what, in an unifying approach, could be considered an inverse problem, the recovery of latent volatility from the realizations of observable return processes. Since the relation between realised and integrated volatility implies that one is transformed into the other with noise, we work in a simulated environment of Brownian motion paths for exemplifying the semimartingale context and produce randomized estimators for the volatility. With the support of experimental evidence, we can show the consistency of time- and frequency-based volatility estimators and their speed of convergence to the quadratic variation limit.

Original language | English (US) |
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Pages (from-to) | 165-180 |

Number of pages | 16 |

Journal | Electronic Journal of Theoretical Physics |

Volume | 4 |

Issue number | 15 |

State | Published - Jul 20 2007 |

Externally published | Yes |

## Keywords

- Periodogram analysis
- Semimartingles
- Signal processing
- Volatility recovery

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)