Inference for Option Panels in Pure-Jump Settings, Econometric Theory
We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves 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 the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span remains fixed. The information set is augmented with high-frequency data on the underlying asset. Given a para- metric 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 min- imize the L2 distance between observed and model-implied options. In addition, we penalize for the deviation of the model-implied quantities from their model-free counterparts, obtained from the high-frequency returns. We derive the joint asymp- totic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vec- tor exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.
Torben Andersen, Nicola Fusari, Viktor Todorov, Rasmus Varneskov
Andersen, Torben, Nicola Fusari, Viktor Todorov, and Rasmus Varneskov. 2019. Inference for Option Panels in Pure-Jump Settings. Econometric Theory. 35(5): 901–942.