### Abstract

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.

Original language | English |
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Place of Publication | Aarhus |

Publisher | Aarhus Universitet |

Number of pages | 31 |

Publication status | Published - 2018 |

Externally published | Yes |

Series | Creates Research Paper |
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Number | 2018-4 |

### Keywords

- Inference
- Jump activity
- Large data sets
- Nonlinear factor model
- Options
- Panel data
- Stable convergence
- Stochastic jump intensity

## Cite this

Andersen, T. G., Fusari, N., Todorov, V., & Varneskov, R. T. (2018).

*Option Panels in Pure-jump Settings*. Aarhus Universitet. Creates Research Paper, No. 2018-4 http://econ.au.dk/fileadmin/site_files/filer_oekonomi/Working_Papers/CREATES/2018/rp18_04.pdf