Characteristic Function-Based Factor Modeling of Affine Jump-Diffusions using Options

We develop a framework to analyze option markets using factor modeling techniques, offering a novel method to study how many and which risk factors drive the price process of a single asset. We exploit information contained in option prices to construct observations on the characteristic function of the returns on the underlying asset, without having to specify a parametric model. Our asymptotic setting is one in which the number of observed options, with varying strikes, tends to infinity. We establish consistency and asymptotic normality of the option-based log-characteristic function estimator, and provide a feasible central limit theorem that can be used for testing. Based on this, we prove that principal component analysis is able to extract the factors of affine jump-diffusions. We show in Monte Carlo simulations that our has good finite-sample properties. An empirical application indicates that the main factor driving S&P 500 returns is a stochastic variance process, along with a factor related to left-tail jump risk, and that at least two factors are needed to explain higher-order moments with reasonable accuracy.