Generalized Transform Analysis for Asset Pricing and Parameter Estimation

Abstract

In this paper, we extend the existing generalized transform analysis in a way that allows us to propose a novel GMM approach for estimating asset pricing models. Our methodology is capable of incorporating a broad class of assets within both reduced-form and structural models, while avoiding the drawbacks of competing approaches. To formulate moment conditions, we derive expressions for moments involving transform-based asset prices. Our theory yields analytically tractable expressions for exact moments and an additionally computationally efficient strategy to obtain approximate moments, whose convergence we establish under standard conditions. Exact and approximate moments induce exact and approximate GMM estimators, respectively, for which we discuss asymptotic properties. Finally, we exemplify and numerically support our methodology with a worked-out estimation problem involving equity options.

Keywords: standard transforms, generalized transforms, asset pricing, GMM estimation

JEL Classification: C32, C51, C58, G12, G13