The Continuous-Time Limit of Score-Driven Volatility Models

44 Pages Posted: 13 Jun 2019

See all articles by Giuseppe Buccheri

Giuseppe Buccheri

Scuola Normale Superiore

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Franco Flandoli

Scuola Normale Superiore

Giulia Livieri

Scuola Normale Superiore

Date Written: May 30, 2019

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 limiting diffusion depends only on the link function and on the conditional second moment 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-tail densities lead to continuous-time processes with finite volatility of volatility, as opposed to fat-tail models with a GARCH update, for which the volatility of volatility is explosive. An extension of our results to models with a time-varying conditional mean and to conditional covariance models is also developed.

Keywords: Weak diffusion limits, Score-driven models, Student-t, General error distribution

JEL Classification: C10, C58

Suggested Citation

Buccheri, Giuseppe and Corsi, Fulvio and Flandoli, Franco and Livieri, Giulia, The Continuous-Time Limit of Score-Driven Volatility Models (May 30, 2019). Available at SSRN: https://ssrn.com/abstract=3382479 or http://dx.doi.org/10.2139/ssrn.3382479

Giuseppe Buccheri (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy
+39 3341046378 (Phone)

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Franco Flandoli

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Giulia Livieri

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

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