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A Simple Time-Consistent Model For The Forward Density Process

Author

Listed:
  • HENRIK HULT

    (Department of Mathematics, KTH Royal Institute of Technology, SE 100 44, Stockholm, Sweden)

  • FILIP LINDSKOG

    (Department of Mathematics, KTH Royal Institute of Technology, SE 100 44, Stockholm, Sweden)

  • JOHAN NYKVIST

    (Department of Mathematics, KTH Royal Institute of Technology, SE 100 44, Stockholm, Sweden)

Abstract

In this paper, a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of n options and a forward contract are expressed as time-varying functions of an (n + 1)-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrate that the model provides a good fit to option price data.

Suggested Citation

  • Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A Simple Time-Consistent Model For The Forward Density Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-29.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500489
    DOI: 10.1142/S0219024913500489
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    Keywords

    Option pricing; mixture models;

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