Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions

This paper considers multi-dimensionalaffine 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 exponentialmoments 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 exponentialmoments. These results provide a handle to study implied volatility asymptotics in models where log-returns of stock prices are described by affine processes whose exponentialmoments do not have an explicit formula