This study derives approximate valuation formulas for basket options and Asian options under the jump-diffusion process. To obtain an approximation for options prices under the jump-diffusion process, we extend the Taylor expansion method developed by Ju N. (2002) under the diffusion process. We show that the Taylor expansion method, suggested in this study, provides better pricing performance as compared to log-normal or four-moment methods. The performance improvement using the Taylor expansion method increases as the time to maturity increases. In addition, our numerical analysis shows that jump effects become significant when the expected jump sizes take large negative values. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 31:830–854, 2011