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Inference For Option Panels In Pure-Jump Settings

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  • Andersen, Torben G.
  • Fusari, Nicola
  • Todorov, Viktor
  • Varneskov, Rasmus T.

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.

Suggested Citation

  • Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor & Varneskov, Rasmus T., 2019. "Inference For Option Panels In Pure-Jump Settings," Econometric Theory, Cambridge University Press, vol. 35(5), pages 901-942, October.
  • Handle: RePEc:cup:etheor:v:35:y:2019:i:05:p:901-942_00
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    Cited by:

    1. Hounyo, Ulrich & Varneskov, Rasmus T., 2020. "Inference for local distributions at high sampling frequencies: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 215(1), pages 1-34.

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