Negative volatility for a 2-dimensional square root SDE
  In affine term structure models the short rate is modelled as an affine transformation of a multi-dimensional square root process. Sufficient conditions to avoid negative volatility factors are the multivariate Feller conditions. We will prove their necessity for a 2-dimensional square root SDE with one volatility factor by presenting a methodology based on measure transformations and solving linear systems of ordinary differential equations. 
Peter Spreij (University of Amsterdam), Enno Veerman (University of   Amsterdam)