Option contracts allow investors to hedge risk and speculate on the volatility of an asset's future price. In 1973, Black and Scholes proposed a valuation model that gives a "fair price" for an option assuming the price fluctuates according to geometric Brownian motion (GBM). They provided a continuous-time trading method allowing the investor to buy and sell the asset in order to "replicate" the option's payoff. But why require a strong stochastic assumption on the price fluctuations? In this talk we'll consider a new method for evaluating the price of options and other derivatives that makes worst-case assumptions, that is where the asset's price path may be chosen by a (constrained) adversary. We show that the Black Scholes model is recovered even under such pessimistic assumptions.