Paper Title:

Maximum likelihood estimation in continuous affine Volterra processes in the ergodic regime

Published on:

8 April 2024

Primary Category:

Statistics Theory

Paper Authors:

Mohamed Ben Alaya,

Martin Friesen,

Jonas Kremer

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Studies MLE for drift parameters of two Volterra processes modeling rough volatility

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Proves estimators strongly consistent and asymptotically normal

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Uses asymptotic independence to establish laws of large numbers

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Shows stationary processes are ergodic

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Applies to both continuous and discrete observations

Parameter estimation for rough volatility models

This paper studies maximum likelihood estimation of drift parameters for Volterra Ornstein-Uhlenbeck and Volterra Cox-Ingersoll-Ross processes, which can model rough volatility. The estimators are shown to be strongly consistent and asymptotically normal under ergodic regime assumptions. For both continuous and discrete observations, convergence proofs rely crucially on establishing laws of large numbers through introducing a notion of asymptotic independence. As a side result, the stationary processes are proven ergodic. Overall, this contributes towards statistical inference for stochastic Volterra equations modeling rough behavior.

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