# Control variates for variance reduction in indirect inference: interest rate models in continuous time

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## 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. There is, in fact, an additional component of the variance, which depends on the stochastic simulation involved in the estimation procedure. To reduce this udesirable effect one should enlarge the number of simulations (or the length of each simulation) and thus the computation cost. Alternatively, this paper shows how variance reduction can be achieved, at virtually no additional computation cost, by use of control variates. The Ornstein-Uhlenbeck equation, used by Vasicek to model the short term interest rate in continuous time, and the so called square root equation, used by Cox, Ingersoll and Ross, are explicitly considered and experimented with. Monte Carlo experiments show that, for some parameters of interest, a global efficiency gain about 35%-45% over the simplest indirect estimator is obtained at about the same computation cost.

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