Analytical Option Pricing for Time Dependent Quadratic Local Volatility Models

In this note we develop accurate analytical pricing formulas for time dependent quadratic local volatility models. We derive a set of exact simple analytical expressions for option prices when parameters are constant and provide novel and simpler proofs to already exisiting results. We then build a general framework for deriving analytical expansions for time dependent local volatility models and use these to deduce averaging formulas which enable us to transform any time-dependent quadratic volatility model onto an equivalent constant parameter one. We show the accuracy of these methods through numerical examples