Abstract #301856

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JSM 2003 Abstract #301856
Activity Number: 68
Type: Invited
Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
Sponsor: International Chinese Statistical Association
Abstract - #301856
Title: Equivalence of GARCH, SV, and the Diffusion Models
Author(s): Linda H. Zhao*+
Companies: University of Pennsylvania
Address: 3000 Steinberg Hall, Philadelphia, PA, 19104,
Keywords: financial modeling ; frequency ; stochastic differential equation ; stochastic volatility
Abstract:

It is known that stochastic volatility (SV) models and multiplicative GARCH models share the same diffusion limits in a weak-convergence sense. Here we investigate a much stronger convergence notion. We show that SV models are asymptotically equivalent to their diffusion limits at the basic frequency of their construction, while multiplicative GARCH models match to the diffusion limits only for observations singled out at frequencies lower than the square root of the basic frequency of construction. These results also reveal that the structure of the multiplicative GARCH models at frequencies lower than the square root of the basic frequency no longer obey the GARCH framework at the observed frequencies. Instead they behave there like the SV models.

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