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Valoración de derivados europeos con mixtura de distribuciones Weibull
[Valuation for European derivatives with mixture-Weibull distributions]

Author

Listed:
  • Molina Barreto, Andrés Mauricio
  • Jiménez Moscoso, José Alfredo

Abstract

The Black-Scholes valuation model for European options is widely used in the stock markets due to its easy implementation. However, the model is not accurate for different assets whose dynamics do not follow those of a lognormal distribution, so it is necessary to investigate new distributions to price different options written on various underlying assets. Several researchers have worked on new valuation formulas, assuming different distributions for either the price of the underlying asset or for the return of the same. This paper presents two methods for European derivatives valuation, one of them, modifying the formula using a Weibull distribution with two parameters given by Savickas (2002) adding two new parameters (scale and location), and another assuming that the underlying distribution is a Weibull mixture. Comparisons are also presented with these models against existing models such as the Black-Scholes model and Savickas with a simple Weibull distribution.

Suggested Citation

  • Molina Barreto, Andrés Mauricio & Jiménez Moscoso, José Alfredo, 2014. "Valoración de derivados europeos con mixtura de distribuciones Weibull [Valuation for European derivatives with mixture-Weibull distributions]," MPRA Paper 118572, University Library of Munich, Germany, revised 08 Aug 2014.
  • Handle: RePEc:pra:mprapa:118572
    as

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    File URL: https://mpra.ub.uni-muenchen.de/118572/1/Molina-Jimenez.pdf
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    References listed on IDEAS

    as
    1. José Alfredo Jiménez & Viswanathan Arunachalam & Gregorio Manuel Serna, 2014. "Option pricing based on the generalised Tukey distribution," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 3(3), pages 191-221.
    2. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 211-239, June.
    3. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    4. Robert Savickas, 2005. "Evidence On Delta Hedging And Implied Volatilities For The Black‐Scholes, Gamma, And Weibull Option Pricing Models," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(2), pages 299-317, June.
    5. Robert Savickas, 2002. "A Simple Option‐Pricing Formula," The Financial Review, Eastern Finance Association, vol. 37(2), pages 207-226, May.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Weibull distribution; mixture of Weibull; valuation; European options;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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