Abstract
This paper compares the empirical performance of continuous time models for the dynamics of nine different implied volatility indices. The models include linear, quadratic and nonlinear drift specifications with affine, constant elasticity of variance (CEV) and stochastic elasticity of variance (SEV) diffusion parts. We find that a nonlinear drift specification is important when imposing an affine structure on the diffusion, whereas a simple linear drift is adequate with a CEV and SEV specification, of which the SEV is dominant. For all but two of the indices we investigate, the best specification is a SEV diffusion with linear drift. For gold and the USD/EUR exchange rate there is little difference between a CEV and SEV diffusion with linear drift.
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