We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional second moment of the score, (iii) the normalization of the score. Interestingly, the properties of the stochastic differential equation are strictly entangled with those of the discrete-time counterpart. Score-driven models with fat-tailed densities lead to continuous-time processes with finite volatility of volatility, as opposed to fat-tailed models with a GARCH update, for which the volatility of volatility is explosive. We examine in simulations the implications of such results on approximate estimation and filtering of diffusion processes. An extension to models with a time-varying conditional mean and to conditional covariance models is also developed.

The continuous-time limit of score-driven volatility models

Giuseppe Buccheri;Fulvio Corsi;Franco Flandoli;Giulia Livieri
2021

Abstract

We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional second moment of the score, (iii) the normalization of the score. Interestingly, the properties of the stochastic differential equation are strictly entangled with those of the discrete-time counterpart. Score-driven models with fat-tailed densities lead to continuous-time processes with finite volatility of volatility, as opposed to fat-tailed models with a GARCH update, for which the volatility of volatility is explosive. We examine in simulations the implications of such results on approximate estimation and filtering of diffusion processes. An extension to models with a time-varying conditional mean and to conditional covariance models is also developed.
2021
Settore SECS-P/01 - Economia Politica
Settore SECS-P/02 - Politica Economica
Settore SECS-P/03 - Scienza delle Finanze
Settore SECS-P/06 - Economia Applicata
Settore SECS-P/05 - Econometria
Settore SECS-P/07 - Economia Aziendale
Settore SECS-P/08 - Economia e Gestione delle Imprese
Settore SECS-P/10 - Organizzazione Aziendale
Settore SECS-P/11 - Economia degli Intermediari Finanziari
Settore SECS-P/09 - Finanza Aziendale
Settore SECS-P/13 - Scienze Merceologiche
Settore SECS-P/12 - Storia Economica
Settore SECS-P/04 - Storia del Pensiero Economico
Settore SECS-S/01 - Statistica
Settore SECS-S/02 - Statistica per La Ricerca Sperimentale e Tecnologica
Settore SECS-S/03 - Statistica Economica
Settore SECS-S/04 - Demografia
Settore SECS-S/05 - Statistica Sociale
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Weak diffusion limits Score-driven models Studen t- General error distribution
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/90862
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