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Efficient volatility estimation in a two-factor model

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Date
2018
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01966340
Dewey
Probabilités et mathématiques appliquées
Sujet
semipara-metric efficient bounds; Discrete observations; HJM models; time-to-maturity factor; Financial statistics; nonparametric estimation; Electricity market modelling
URI
https://basepub.dauphine.fr/handle/123456789/18661
Collections
  • CEREMADE : Publications
Metadata
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Author
Féron, Olivier
19229 Laboratoire des Composites Thermostructuraux [LCTS]
Gruet, Pierre
Hoffman, Marc
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
27
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.

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