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; Israel Felipe Mora Cuevas

doi:10.29105/ensayos27.1-2

Autores/as

Guillermo Benavides Perales
Israel Felipe Mora Cuevas

DOI:

https://doi.org/10.29105/ensayos27.1-2

Palabras clave:

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

Resumen

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.

Clasificación JEL: C14, C52, F31, G13.

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Citas

Abadir, K. M., and Rockinger, M. (2003). “Density functionals, with an option-pricing application.” Econometric Theory. Vol. 19, pp. 778- 811. Bahra, B. (1997). “Implied Risk Neutral Probability Density Functions from Options Prices: Theoryand Application.” Bank of England. Workingpaper No. 66. DOI: https://doi.org/10.1017/S0266466603195047

Bliss, R., and Panigirtzoglou, N. (2000). “Testing the Stability of Implied Probability Density Functions.” Bank of England. ISSN 1368-5562. DOI: https://doi.org/10.2139/ssrn.230786

Breeden, D., and Litzenberger, R. (1978). “Prices of State-Contingent Claims Implicit in Option Prices.” The Journal of Business. Vol. 51, pp. 621-51. DOI: https://doi.org/10.1086/296025

Bu, R., and Hadri, K. (2007). “Estimating option implied risk-neutral densities using spline and hypergeometric functions.” The Econometrics Journal. Vol. 10, pp. 216-244. DOI: https://doi.org/10.1111/j.1368-423X.2007.00206.x

Castrén, O. (2005). “Estimating and Analyzing Currency Options Implied Risk-Neutral Density Functions for the Largest New EU Member Status.” European Central Bank. Workingpaper No. 440. February. DOI: https://doi.org/10.2139/ssrn.648001

Christoffersen, P., and Mazzotta, S. (2004). “The Informational Content of Over-the-Counter Currency Options.” European Central Bank. Working paper No. 366. DOI: https://doi.org/10.2139/ssrn.506202

Clews, R., Panigirtzoglou, N., and Proudman, J. (2000). “Recent Developments in Extracting Information from Option Markets.” Bank of England Quarterly Bulletin. February.

Cooper, N., and Talbot, J. (1999). “The Yen/Dollar Exchange Rate in 1998: Views from Options Markets.” Bank of England. Working paper.

Díaz de León, A., and Casanova, M. E. (2004). “Expectativas del Mercado Implícitas en los Precios de Instrumentos Derivados: Aplicaciones al Mercado Cambiario y Petrolero.” Banco de México. Documento de investigación No. 2004-01. DOI: https://doi.org/10.36095/banxico/di.2004.01

Diebold, F. X., and Mariano, R. S. (1995). “Comparing Predictive Accuracy.” Journal of Business and Economic Statistics. Vol. 13, pp. 253-263. DOI: https://doi.org/10.1080/07350015.1995.10524599

Garman, M. B., and Kohlhagen, S. W. (1983). “Foreign Currency Option Values.” Journal of International Money and Finance. Vol. 2, pp. 231-37. May. DOI: https://doi.org/10.1016/S0261-5606(83)80001-1

Hördahl, P., and Vestin, D. (2003). “Interpreting implied risk-neutral densities: the role of risk premia.” European Central Bank. Workingpaper No. 274. DOI: https://doi.org/10.2139/ssrn.407730

Hull, J. (2003). “Options, Futures and Other Derivatives.” 5th. Edition. Prentice Hall.

Liu, X., Shackelton, M., Taylor, S., and Xinzhong, X. (2004). “Closed-form Transformations from Risk-Neutral to Real-world Distributions.” Lancaster University. Working paper. DOI: https://doi.org/10.2139/ssrn.424420

Malz, A. M. (1997a). “Option-implied Probability Distributions and Currency Excess Returns.” Federal Reserve Bank of New York. Staff Reports, No. 32. DOI: https://doi.org/10.2139/ssrn.943500

Malz, A. M. (1997b). “Estimating the Probability Distribution of the Future Exchange Rate from Option Prices.” Journal of Derivatives. Vol. 5, pp. 18-36. DOI: https://doi.org/10.3905/jod.1997.407988

Mc Manus, D. J. (1999). “The Information Content of Interest Rate Futures Options.” Bank of Canada. Workingpaper No. 99-15.

Melick, W. R., and Thomas C. P. (1997). “Recovering an Asset’s Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis.” Journal of Financial and Quantitative Analysis. Vol. 32, pp. 91-115. DOI: https://doi.org/10.2307/2331318

Micu, M. (2004). “Extracting Expectations from Currency Option Prices: A Comparison of Methods.” Bank of International Settlements. Working paper. September.

Ritchey, R. J. (1990). “Call Option Valuation for Discrete Normal Mixtures.” Journal of Financial Research. Vol. XIII, No. 4, pp. 285-96. DOI: https://doi.org/10.1111/j.1475-6803.1990.tb00633.x

Rubinstein, M. (1994). “Implied Binomial Trees.” Journal of Finance. Vol. 49, pp. 771-818. July. DOI: https://doi.org/10.1111/j.1540-6261.1994.tb00079.x

Shimko, D. (1993). “Bounds of Probability.” Risk. Vol. 6, pp. 33-7. April. Taylor, S. J. (2005). “Asset Price Dynamics, Volatility, and Prediction.” Princeton University Press.