Option Panels in Pure-jump Settings

We develop parametric inference procedures for large panels of noisy option data in the setting where the underlying process is of pure-jump type, i.e., evolve only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across observation times. We consider the asymptotic setting in which the cross-sectional dimension of the panel increases to infinity while its time span remains fixed. The information set is further augmented with high-frequency data on the underlying asset. Given a parametric specification for the risk-neutral asset return dynamics, the option prices are nonlinear functions of a time-invariant parameter vector and a time-varying latent state vector (or factors). Furthermore, no-arbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the so-called jump activity index as well as the time-varying jump intensity. We propose penalized least squares estimation in which we minimize L2 distance between observed and model-implied options and further penalize for the deviation of model-implied quantities from their model-free counterparts measured via the highfrequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector can exhibit different rates of convergence depending on the relative informativeness of the high-frequency return data and the option panel.