Likelihood-based inference for asymmetric stochastic volatility models

A likelihood approach for 0tting asymmetric stochastic volatility models is proposed. It is 0rst shown that, using a quadrature method, the likelihood of these models may be approximated, with the required level of accuracy, by a function that may be easily evaluated using matrix calculus along with its 0rst and second derivatives. The approximated likelihood may be maximized using a standard Newton–Raphson algorithm, and con0dence intervals for the parameters may be computed. Moreover, the hypothesis of an asymmetric response of volatility to shocks in the series may be simply tested. Before applying the procedure to real data, a simulation study investigates the reliability of the parameter estimates. c © 2002 Elsevier Science B.V. All rights reserved.