
Efficient volatility estimation in a two-factor model
Féron, Olivier; Gruet, Pierre; Hoffmann, Marc (2020), Efficient volatility estimation in a two-factor model, Scandinavian Journal of Statistics, 47, 3, p. 862-898. 10.1111/sjos.12431
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Type
Article accepté pour publication ou publiéDate
2020Nom de la revue
Scandinavian Journal of StatisticsVolume
47Numéro
3Éditeur
Wiley
Ville d’édition
Paris
Pages
862-898
Identifiant publication
Métadonnées
Afficher la notice complèteAuteur(s)
Féron, OlivierLaboratoire des Composites Thermostructuraux [LCTS]
Gruet, Pierre
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (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. Mathematics Subject Classification (2010): 62M86, 60J75, 60G35, 60F05.Mots-clés
semipara-metric efficient bounds; Discrete observations; HJM models; time-to-maturity factor; Financial statistics; nonparametric estimation; Electricity market modellingPublications associées
Affichage des éléments liés par titre et auteur.
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Deschatre, Thomas; Féron, Olivier; Hoffmann, Marc (2020) Article accepté pour publication ou publié
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Hoffmann, Marc; Ray, Kolyan (2022) Document de travail / Working paper
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Bourgia, Mathilde; Féron, Olivier; Marin, Jean-Michel; Robert, Christian P. (2010) Communication / Conférence
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Hoffmann, Marc; Olivier, Adélaïde (2016) Article accepté pour publication ou publié
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Hoffmann, Marc; Olivier, Adélaïde; Valère Bitseki Penda, Siméon (2017) Article accepté pour publication ou publié