We show how the value of a finite-lived option can be interpreted as the limit of a sequence of perpetual option values subject to default risk. This interpretation yields new closed form approximations for European and American option values in the Black Scholes model. Numerical results...

While American calls on non-dividend paying stocks may be valued as European, there is no completely explicit exact solution for the values of American puts. We introduce a novel technique called randomization to value American puts and calls on dividend-paying stocks. This technique yields a...