  We study local asymptotic properties of likelihood ratios of certain Heston
models. We distinguish three cases: subcritical, critical and supercritical
models. For the drift parameters, local asymptotic normality is proved in the
subcritical case, only local asymptotic quadraticity is shown in the critical
case, while in the supercritical case not even local asymptotic quadraticity
holds. For certain submodels, local asymptotic normality is proved in the
critical case, and local asymptotic mixed normality is shown in the
supercritical case. As a consequence, asymptotically optimal (randomized) tests
are constructed in cases of local asymptotic normality. Moreover, local
asymptotic minimax bound, and hence, asymptotic efficiency in the convolution
theorem sense are concluded for the maximum likelihood estimators in cases of
local asymptotic mixed normality.
