  We present three models of stock price with time-dependent interest rate,
dividend yield, and volatility, respectively, that allow for explicit forms of
the optimal exercise boundary of the finite maturity American put option. The
optimal exercise boundary satisfies the nonlinear integral equation of Volterra
type. We choose time-dependent parameters of the model so that the integral
equation for the exercise boundary can be solved in the closed form. We also
define the contracts of put type with time-dependent strike price that support
the explicit optimal exercise boundary.
