New measures of stock return volatility are developed to increase the precision of stock option price estimates. With Bayesian statistical methods, volatility estimates for a given stock are developed using prior information on the cross-sectional patterns in return volatilities for groups of stocks sorted on size, financial leverage, and trading volume. Call option values computed with the Bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility, standard historical volatility, or even the actual ex post volatility that occurred during each option's life. Although the Bayesian methods produce biased call price estimators, they do reduce the systematic tendency of standard pricing approaches to overprice (underprice) options on high (low) volatility stocks. Little bias improvement is observed with respect to the time to maturity and moneyness of the call options.