### Abstract

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 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 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 asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.

Original language | English |
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Journal | Econometric Theory |

Volume | 35 |

Issue number | 5 |

Pages (from-to) | 901-942 |

Number of pages | 42 |

ISSN | 0266-4666 |

DOIs | |

Publication status | Published - Oct 2019 |

Externally published | Yes |

## Cite this

Andersen, T. G., Fusari, N., Todorov, V., & Varneskov, R. T. (2019). Inference for Option Panels in PURE-Jump Settings.

*Econometric Theory*,*35*(5), 901-942. https://doi.org/10.1017/S0266466618000373