  We study the mesoscopic fluctuations of thermodynamic observables in a
nanosized metallic grain in which the single-particle dynamics are chaotic and
the dimensionless Thouless conductance is large. Such a grain is modeled by the
universal Hamiltonian describing the competition between exchange and pairing
correlations. The exchange term is taken into account exactly by a
spin-projection method, and the pairing term is treated in the static-path
approximation together with small-amplitude quantal fluctuations around each
static fluctuation of the pairing field. Odd-even particle-number effects
induced by pairing correlations are included using a number-parity projection.
We find that the exchange interaction shifts the number-parity effects in the
heat capacity and spin susceptibility to lower temperatures. In the regime
where the pairing gap is similar to or smaller than the single-particle mean
level spacing, these number-parity effects are suppressed by exchange
correlations, and the fluctuations of the spin susceptibility may be
particularly large. However, for larger values of the pairing gap, the
number-parity effects may be enhanced by exchange correlations.
