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Efficient volatility estimation in a two-factor model

Féron, Olivier; Gruet, Pierre; Hoffman, Marc (2018), Efficient volatility estimation in a two-factor model. https://basepub.dauphine.fr/handle/123456789/18661

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01966340
Date
2018
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
27
Metadata
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Author(s)
Féron, Olivier
Laboratoire des Composites Thermostructuraux [LCTS]
Gruet, Pierre

Hoffman, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We statistically analyse a multivariate HJM diffusion model with stochastic volatility. The volatility process of the first factor is left totally unspecified while the volatility of the second factor is the product of an unknown process and an exponential function of time to maturity. This exponential term includes some real parameter measuring the rate of increase of the second factor as time goes to maturity. From historical data, we efficiently estimate the time to maturity parameter in the sense of constructing an estimator that achieves an optimal information bound in a semiparametric setting. We also identify nonparametrically the paths of the volatility processes and achieve minimax bounds. We address the problem of degeneracy that occurs when the dimension of the process is greater than two, and give in particular optimal limit theorems under suitable regularity assumptions on the drift process. We consistently analyse the numerical behaviour of our estimators on simulated and real datasets of prices of forward contracts on electricity markets.
Subjects / Keywords
semipara-metric efficient bounds; Discrete observations; HJM models; time-to-maturity factor; Financial statistics; nonparametric estimation; Electricity market modelling

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