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Parametric vs. non-parametric methods for estimating option implied risk-neutral densities: the case of the exchange rate Mexican peso – US dollar

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  • Guillermo Benavides Perales

    () (Banco de México, Dirección General de Investigación Económica and Tecnológico de Monterrey, Campus Ciudad de México.)

  • Israel Felipe Mora Cuevas

    (University of Essex)

Abstract

This research paper presents statistical comparisons between two methods that are commonly used to estimate option implied Risk-Neutral Densities (RND). These are: 1) mixture of lognormals (MXL); and, 2) volatility function technique (VFT). The former is a parametric method whilst the latter is a non-parametric approach. The RNDs are extracted from over-thecounter European-style options on the Mexican Peso–US Dollar exchange rate. The non-parametric method was the superior one for out-of-sample evaluations. The implied mean, median and mode were, in general, statistically different between the competing approaches. It is recommended to apply the VFT instead of the MXL given that the former has superior accuracy and it can be estimated when there is a relatively short crosssection of option exercise price range. The results have implications for financial investors and policy makers given that they could use the information content in options to analyze market’s perceptions about the future expected variability of the financial asset under study.

Suggested Citation

  • Guillermo Benavides Perales & Israel Felipe Mora Cuevas, 2008. "Parametric vs. non-parametric methods for estimating option implied risk-neutral densities: the case of the exchange rate Mexican peso – US dollar," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 33-52, May.
  • Handle: RePEc:ere:journl:v:xxvii:y:2008:i:1:p:33-52
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    References listed on IDEAS

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    1. Peter Hördahl & David Vestin, 2005. "Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia," Review of Finance, Springer, vol. 9(1), pages 97-137, March.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
    4. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    5. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    6. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    7. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. Peter Christoffersen & Stefano Mazzotta, 2004. "The Informational Content of Over-the-Counter Currency Options," CIRANO Working Papers 2004s-16, CIRANO.
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    Citations

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    Cited by:

    1. Guillermo Benavides Perales, 2012. "Central Bank Exchange Rate Interventions and Market Expectations: The Case of México During the Financial Crisis 2008-2009," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, October.

    More about this item

    Keywords

    currency option implied volatility; exchange rate; parametric methods; non-parametric methods; risk-neutral densities;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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