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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 publié
Date
2020
Journal name
Scandinavian Journal of Statistics
Volume
47
Number
3
Publisher
Wiley
Published in
Paris
Pages
862-898
Publication identifier
10.1111/sjos.12431
Metadata
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Author(s)
Féron, Olivier
Laboratoire des Composites Thermostructuraux [LCTS]
Gruet, Pierre
Hoffmann, 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. Mathematics Subject Classification (2010): 62M86, 60J75, 60G35, 60F05.
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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