A SIMPLE TIME-CONSISTENT MODEL FOR THE FORWARD DENSITY PROCESS

Henrik Hult (), Filip Lindskog () and Johan Nykvist ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 08, 1-29

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.

Keywords: Option pricing; mixture models (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0219024913500489

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