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A non-parametric inference for implied volatility governed by a Lévy-driven Ornstein–Uhlenbeck process

Author

Listed:
  • Fard, Farzad Alavi

    (RMIT)

  • Pourkhanali, Armin

    (School of Mathematical Sciences, Monash University)

  • Sy, Malick

    (School of Economics, Finance and Marketing, RMIT)

Abstract

We provide a non-parametric method for stochastic volatility modelling. Our method allows the implied volatility to be governed by a general Lévy-driven Ornstein–Uhlenbeck process, the density function of which is hidden to market participants. Using discrete-time observation we estimate the density function of the stochastic volatility process via developing a cumulant M-estimator for the Lévy measure. In contrast to other non-parametric estimators (such as kernel estimators), our estimator is guaranteed to be of the correct type. We implement this method with the aid of a support-reduction algorithm, which is an efficient iterative unconstrained optimisation method. For the empirical analysis, we use discretely observed data from two implied volatility indices, VIX and VDAX. We also present an out-of-sample test to compare the performance of our method with other parametric models.

Suggested Citation

  • Fard, Farzad Alavi & Pourkhanali, Armin & Sy, Malick, 2018. "A non-parametric inference for implied volatility governed by a Lévy-driven Ornstein–Uhlenbeck process," Algorithmic Finance, IOS Press, vol. 7(1-2), pages 15-30.
    • Handle: RePEc:ris:iosalg:0064
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    More about this item

    Keywords

    Non-parametric estimation; stochastic volatility; Ornstein-Uhlenbeck process; acceptance-rejection; out-of-sample;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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