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Valuación de opciones asiáticas versus opciones europeas con tasa de interés estocástica

  • Ambrosio Ortiz Ramírez [1] ; María Teresa V. Martínez Palacios [1]
    1. [1] Instituto Politécnico Nacional

      Instituto Politécnico Nacional

      México

  • Localización: Contaduría y administración, ISSN 0186-1042, ISSN-e 2448-8410, Vol. 61, Nº. 4, 2016, págs. 629-648
  • Idioma: español
  • DOI: 10.1016/j.cya.2016.06.002
  • Títulos paralelos:
    • Pricing of average value options versus European options with stochastic interest rate
  • Enlaces
  • Resumen
    • español

      Este trabajo propone una metodología para obtener el precio de una opción asiática con subyacente promedio mediante simulación Monte Carlo. Se supone que la tasa de interés es conducida por un proceso de reversión a la media de tipo Vasicek y CIR con parámetros calibrados por máxima verosimilitud. La simulación incluye el remuestreo cuadrático, el cual reduce el uso de recursos computacionales; en particular, el método mejora la generación de la matriz de varianza-covarianza. La metodología propuesta se aplica en la valuación de opciones sobre el precio de AMXL. Los resultados muestran que al comparar los precios de opciones europeas —tanto simulados como con los publicados por MexDer— con sus contrapartes asiáticas, los precios de opciones asiáticas son menores en el caso de opciones de compra y de venta dentro del dinero. Para opciones de venta, los precios simulados fueron menores en todos los casos. Asimismo se encontró que la diferencia se incrementa conforme el plazo al vencimiento de la opción aumenta.

    • English

      This paper proposes a methodology to obtain the price of an Asian option with underlying average through Monte Carlo simulation. It is assumed that the interest rate is driven by a mean reversion process of Vasicek and CIR type with parameters calibrated by maximum likelihood. The simulation includes the quadratic resampling which reduces the use of computational resources, in particular the method improves the generation of variance covariance matrix. The proposed methodology is applied in the valuation of options on the price of AMXL. The results show that by comparing prices of European options, with both simulated and published by MexDer with their Asian counterparts, Asian options prices are lower in the case of call and put options in the money. For put options simulated prices were lower in all cases. Moreover, it was also found that the difference increases as the time to maturity of the option increases.

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