We obtain new closed-form pricing formulas for contingent claims when the
asset follows a Dupire-type local volatility model. To obtain the formulas we
use the Dyson-Taylor commutator method re- cently developed in [7, 8, 10] for
short time asymptotic expansions of heat kernels, and obtain a family of
general explicit closed form approx- imate solutions for both the pricing
kernel and derivative price. We also perform analytic as well as a numerical
error analysis, and compare our results to other known methods.