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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

  • 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)

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    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.

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    Article provided by Universidad Autonoma de Nuevo Leon, Facultad de Economia in its journal Ensayos Revista de Economia.

    Volume (Year): XXVII (2008)
    Issue (Month): 1 (May)
    Pages: 33-52

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    Handle: RePEc:ere:journl:v:xxvii:y:2008:i:1:p:33-52
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    1. Peter Christoffersen & Stefano Mazzotta, 2004. "The Informational Content of Over-the-Counter Currency Options," CIRANO Working Papers 2004s-16, CIRANO.
    2. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    4. 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, 03.
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    7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    8. Ruijun Bu & Kaddour Hadri, 2007. "Estimating option implied risk-neutral densities using spline and hypergeometric functions," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 216-244, 07.
    9. 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 285-96, Winter.
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