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Parametric Inference and Dynamic State Recovery from Option Panels

Author

Listed:
  • Torben G. Andersen

    (Northwestern University, NBER, and CREATES)

  • Nicola Fusari

    (Northwestern University)

  • Viktor Todorov

    (Northwestern University)

Abstract

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonparametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model t for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates that the inference procedures work well for empirically realistic model specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying risk premia of extreme events, i.e., jumps, as well as a more exible relation between the risk premia and the level of risk. We show that both extensions provide a significantly improved characterization, both statistically and economically, of observed option prices.

Suggested Citation

  • Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2011. "Parametric Inference and Dynamic State Recovery from Option Panels," CREATES Research Papers 2012-11, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-11
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    References listed on IDEAS

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    More about this item

    Keywords

    Option Pricing; Inference; Risk Premia; Jumps; Latent State Vector; Stochastic Volatility; Specification Testing; Stable Convergence.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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