  Discretely sampled variance and volatility swaps trade actively in OTC
markets. To price these swaps, the continuously sampled approximation is often
used to simplify the computations. The purpose of this paper is to study the
conditions under which this approximation is valid. Our first set of theorems
characterize the conditions under which the discretely sampled swap values are
finite, given the values of the continuous approximations exist. Surprisingly,
for some otherwise reasonable price processes, the discretely sampled swap
prices do not exist, thereby invalidating the approximation. Examples are
provided. Assuming further that both swap values exist, we study sufficient
conditions under which the discretely sampled values converge to their
continuous counterparts. Because of its popularity in the literature, we apply
our theorems to the 3/2 stochastic volatility model. Although we can show
finiteness of all swap values, we can prove convergence of the approximation
only for some parameter values.
