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Efficient volatility estimation in a two‐factor model
Author(s) -
Féron Olivier,
Gruet Pierre,
Hoffmann Marc
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12431
Subject(s) - mathematics , volatility (finance) , estimator , stochastic volatility , econometrics , exponential function , minimax , lévy process , mathematical optimization , statistics , mathematical analysis
Abstract We statistically analyze a multivariate Heath‐Jarrow‐Morton 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 nonparametrically identify 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 analyze the numerical behavior of our estimators on simulated and real datasets of prices of forward contracts on electricity markets.