Efficient volatility estimation in a two-factor model

Marc Hoffmann; Olivier F\'eron; Pierre Gruet

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Efficient volatility estimation in a two-factor model

Olivier Féron, Pierre Gruet, Marc Hoffmann

Statistics Theory · Submitted 26 Nov 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.68 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.08 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We statistically analyse a multivariate HJM diffusion model with stochastic volatility.	contribution 0.66	0.94	0.04	asserted 0.99
s1	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.	method 0.91	0.37	0.05	asserted 1.00
s2	This exponential term includes some real parameter measuring the rate of increase of the second factor as time goes to maturity.	method 0.88	0.31	0.04	asserted 1.00
s3	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.	contribution 0.66	0.97	0.33	asserted 1.00
s4	We also identify nonparametrically the paths of the volatility processes and achieve minimax bounds.	contribution 0.59	0.96	0.17	asserted 1.00
s5	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.	contribution 0.88	0.91	0.10	asserted 1.00
s6	We consistently analyse the numerical behaviour of our estimators on simulated and real datasets of prices of forward contracts on electricity markets.	method 0.44	0.95	0.11	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.59 · evidence from proof or derivation 0.60.

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Original abstract

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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