Control Variates for Variance Reduction in Indirect Inference: Interest Rate Models in Continuous Time

Posted: 8 Apr 1999

See all articles by Giacomo Calzolari

Giacomo Calzolari

European University Institute - Economics Department (ECO); Centre for Economic Policy Research (CEPR); University of Bologna

Francesca Di Iorio

Istituto Nazionale di Statistica

Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica

Abstract

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating stochastic differential equations. They adjust for the bias (inconsistency) caused by discretization of the underlying stochastic process, which is in continuous time. The price to be paid is an increased variance of the estimated parameters. The variance suffers from an additional component, which depends on the stochastic simulation involved in the estimation procedure. To reduce this undesirable effect, one could increase the number of simulations (or the length of each simulation) and thus the computational cost. Alternatively, this paper shows how variance reduction can be achieved, at virtually no additional computational cost, by use of control variates. The Ornstein-Uhlenbeck process, used by Vasicek to model the short-term interest rate in continuous time, and the square-root process, used by Cox, Ingersoll and Ross, are explicitly considered and experimented with. Monte Carlo experiments show a global efficiency gain of almost 50% over the simple indirect estimator.

JEL Classification: C10, C15

Suggested Citation

Calzolari, Giacomo and Di Iorio, Francesca and Fiorentini, Gabriele, Control Variates for Variance Reduction in Indirect Inference: Interest Rate Models in Continuous Time. Available at SSRN: https://ssrn.com/abstract=156711

Giacomo Calzolari (Contact Author)

European University Institute - Economics Department (ECO) ( email )

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Francesca Di Iorio

Istituto Nazionale di Statistica ( email )

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Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica ( email )

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