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American Option Valuation with Particle Filters

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Numerical Methods in Finance

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 12))

Abstract

A method to price American–style option contracts in a limited information framework is introduced. The pricing methodology is based on sequential Monte Carlo techniques, as presented in Doucet, de Freitas, and Gordon’s text Sequential Monte Carlo Methods in Practice, and the least–squares Monte Carlo approach of Longstaff and Schwartz (Rev Financ Stud 14:113–147, 2001). We apply this methodology using a risk–neutralized version of the square–root mean–reverting model, as used for European option valuation by Heston (Rev Financ Stud 6:327–343, 1993). We assume that volatility is a latent stochastic process, and we capture information about it using particle filter based “summary vectors.” These summaries are used in the exercise/hold decision at each time step in the option contract period. We also benchmark our pricing approximation against the full–state (observable volatility) result. Moreover, posterior inference, utilizing market–observed American put option prices on the NYSE Arca Oil Index, is made on the volatility risk premium, which we assume is a constant parameter. Comparisons on the volatility risk premium are also made in terms of time and observability effects, and statistically significant differences are reported.

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Notes

  1. 1.

    Note that these positivity constraints for the square–root mean–reverting model are also satisfied under the risk–neutral measure.

  2. 2.

    The references in [58] also provide additional background on American option valuation with stochastic volatility.

  3. 3.

    The vega of more exotic options (e.g., options on spreads) may not necessarily be positive. See [39] for additional discussion.

  4. 4.

    Additional details about the data set/data analysis will be available in Sect. 5; the discussion here is only meant to be illustrative.

  5. 5.

    Although these are small simulation sample sizes relative to large–scale Monte Carlo experiments, they are suitable for our illustrative purposes.

  6. 6.

    See http://www.nyse.com for additional details on the NYSE Euronext index options.

  7. 7.

    We used the last 1,000 draws, as opposed to the last accepted draw, to compute simulation-based distributional summaries. The results are also robust across longer iteration lengths.

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Acknowledgements

The author gratefully acknowledges the suggestions of the Editors and two anonymous referees. Their insights have significantly improved the content of this work.

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Authors and Affiliations

  1. Department of Treasury, Office of the Comptroller of the Currency (OCC), 250 E Street SW, Washington, DC, 20219, USA

    Bhojnarine R. Rambharat

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  1. Bhojnarine R. Rambharat
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Correspondence to Bhojnarine R. Rambharat .

Editor information

Editors and Affiliations

  1. Dept. Operations Research &, Financial Engineering, Princeton University, Charlton Street, Princeton, 08544, New Jersey, USA

    René A. Carmona

  2. Centre INRIA Bordeaux Sud-Ouest, Institut de Mathématiques, Université Bordeaux I, Cours de la Libération 351, Talence Cedex, 33405, France

    Pierre Del Moral

  3. Centre INRIA Bordeaux Sud-Ouest, Institut de Mathématiques, Université Bordeaux I, cours de la Libération 351, Talence Cedex, 33405, France

    Peng Hu

  4. EDF Recherche et Développement, Avenue Générale de Gaulle 1, Clamart, 92140, France

    Nadia Oudjane

Additional information

MSC code: 62F15, 62L15, 91G20, 91G60, 91G70

Disclaimer: The views expressed in this paper are solely those of the author and neither reflect the opinions of the OCC nor the U.S. Department of the Treasury.

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Rambharat, B.R. (2012). American Option Valuation with Particle Filters. In: Carmona, R., Del Moral, P., Hu, P., Oudjane, N. (eds) Numerical Methods in Finance. Springer Proceedings in Mathematics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25746-9_2

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