One of the most widely used option valuation procedures among practitioners is a version of Black-Scholes in which implied volatilities are smoothed across strike prices and maturities. A growing body of empirical evidence suggests that this ad hoc approach performs quite well. It has previously been argued that such a procedure works because it amounts to a sophisticated interpolation tool. We show that this is the case in a formal, asymptotic sense. In addition, we conduct some simulations which allow us to examine the importance of the sample size, the order of the polynomial, and the recalibration frequency in controlled settings. We also apply the ABS approach to daily S&P 100 index options to show that the procedure outperforms the Black-Scholes formula in valuing actual option prices out-of-sample.