Closed-Form Asymptotics for Local Volatility Models

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 recently developed in [7, 8, 10] for short time asymptotic expansions of heat kernels, and obtain a family of general explicit closed form approximate 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