Reconsidering the continuous time limit of the GARCH ( 1 , 1 ) process
نویسنده
چکیده
In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let > k and p2 k denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (> k , p2 k ). We show that, by choosing di!erent parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate di!usion limit. We then show that GARCH(1, 1) processes can be obtained as Euler approximations of degenerate di!usions, while any Euler approximation of a non-degenerate di!usion is a stochastic volatility process. ( 2000 Elsevier Science S.A. All rights reserved.
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