  This paper considers multi-dimensional affine processes with continuous
sample paths. By analyzing the Riccati system, which is associated with affine
processes via the transform formula, we fully characterize the regions of
exponents in which exponential moments of a given process do not explode at any
time or explode at a given time. In these two cases, we also compute the
long-term growth rate and the explosion rate for exponential moments. These
results provide a handle to study implied volatility asymptotics in models
where returns of stock prices are described by affine processes whose
exponential moments do not have an explicit formula.
