  We present a comprehensive photoluminescence study of exchange interaction in
self-assembled CdTe/ZnTe quantum dots. We exploit the presence of multiple
charge states in the photoluminescence spectra of single quantum dots to
analyze simultaneously fine structure of different excitonic transitions,
including recombination of neutral exciton/biexciton, doubly charged negative
exciton and negatively charged biexciton. We demonstrate that the fine
structure results from electron-hole exchange interaction and that spin
Hamiltonians with effective exchange constants $\delta_i$ can provide a good
description of each transition in magnetic field for Faraday and Voigt field
geometry. We determine and discuss values of the effective exchange constants
for a large statistics of quantum dots.
