  We show that the (graded) spectral flow of a family of Toeplitz operators on
a complete Riemannian manifold is equal to the index of a certain Callias-type
operator. When the dimension of the manifold is even this leads to a
cohomological formula for the spectral flow. As an application, we compute the
spectral flow of a family of Toeplitz operators on a strongly pseudoconvex
domain in $C^n$. This result is similar to the Boutet de Monvel's computation
of the index of a single Toeplitz operator on a strongly pseudoconvex domain.
Finally, we show that the bulk-boundary correspondence in a tight-binding model
of topological insulators is a special case of our result.
  In the appendix, Koen van den Dungen reviewed the main result in the context
of (unbounded) KK-theory.
