The valuation of many types of financial contracts and contingent claim agreements is complicated by the possibility that one party will default on their contractual obligations. This dissertation develops a general model that prices Black-Scholes options subject to intertemporal default risk using stochastic barrier option pricing theory. The explicit closed-form solution is obtained by generalizing the reflection principle to k-space to determine the appropriate transition density function. The European analytical valuation formula has a straightforward economic interpretation and preserves much of the intuitive appeal of the traditional Black-Scholes model. The hedging properties of this model are compared and contrasted with the default-free model. The model is extended to include partial recoveries. In one situation, the option holder is assumed to recover α (a constant) percent of the value of the writer’s assets at the time of default. This version of the partial recovery option leads to an analytical valuation formula for a first passage option - an option with a random payoff at a random time.