In this paper we use isoelasticity functions as pricing kernels to derive option-pricing bounds. We give call (put) option pricing bounds depending on the bounds of the elasticity of the true pricing kernel by taking the spot stock price (the riskless interest rate) as given. The result potentially gives tighter upper call bound, which previous efforts have found difficult to achieve. We also show how to use the Black-Scholes formula to obtain option pricing bounds under the assumption of lognormaility. Moreover, we show that under our approach, the analysis for DARA (DRRA) bound can be simplified and generalized.