Examinando por Autor "Marin-Sanchez, Freddy H."

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    GARCH-type volatility in the multiplicative quadrinomial tree method: An application to real options
    (Universidad Nacional Autonoma de Mexico, 2020-03-03) Pareja, J.; Marin-Sanchez, Freddy H.; Universidad EAFIT. Departamento de Economía y Finanzas; Research in Spatial Economics (RISE)
    This article applies the multiplicative quadrinomial tree numerical method with non-constant volatility to assess a real option of abandonment, based on an estimate of the conditional volatility for WTI oil commodity prices and their respective equivalence in a GARCH-diffusion model. The methodology refers to the use of an estimate of type GARCH (1,1) and the numerical method through a quadrinomial tree. There are two main findings: 1) when employing the quadrinomial method, the value of the real option turned out to be greater than the value estimated through the traditional multiplicative binomial method, due to underestimation of the real value of volatility that occurs in a specific period according to the latter method; and 2) a methodological contribution that demonstrates plainly way the presence of non-constant conditional volatility as well as being able to value all types of options using stochastic volatility. © 2019 Universidad Nacional Autónoma de México, Facultad de Contaduría y Administración. This is an open access article under the CC BY-NC-SA (https://creativecommons.org/licenses/by-nc-sa/4.0/)
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    Ítem
    GARCH-type volatility in the multiplicative quadrinomial tree method: An application to real options
    (Universidad Nacional Autonoma de Mexico, 2020-03-03) Pareja, J.; Marin-Sanchez, Freddy H.; Universidad EAFIT. Escuela de Ciencias; Modelado Matemático
    This article applies the multiplicative quadrinomial tree numerical method with non-constant volatility to assess a real option of abandonment, based on an estimate of the conditional volatility for WTI oil commodity prices and their respective equivalence in a GARCH-diffusion model. The methodology refers to the use of an estimate of type GARCH (1,1) and the numerical method through a quadrinomial tree. There are two main findings: 1) when employing the quadrinomial method, the value of the real option turned out to be greater than the value estimated through the traditional multiplicative binomial method, due to underestimation of the real value of volatility that occurs in a specific period according to the latter method; and 2) a methodological contribution that demonstrates plainly way the presence of non-constant conditional volatility as well as being able to value all types of options using stochastic volatility. © 2019 Universidad Nacional Autónoma de México, Facultad de Contaduría y Administración. This is an open access article under the CC BY-NC-SA (https://creativecommons.org/licenses/by-nc-sa/4.0/)
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    Ítem
    Quadrinomial Trees to Value Options in Stochastic Volatility Models
    (Institutional Investor Systems, 2019-01-01) Pareja-Vasseur, Julian A.; Marin-Sanchez, Freddy H.; Universidad EAFIT. Departamento de Economía y Finanzas; Research in Spatial Economics (RISE)
    This article describes in detail the multiplicative quadrinomial tree numerical method with nonconstant volatility, based on a system of stochastic differential equations of the GARCH-diffusion type. The methodology allowed for the derivation of the first two moments of the proposed equations to estimate the respective recombination between discrete and continuous processes and, as a result, a numerical methodological proposal is formally presented to value, with relative ease, both real and financial options, when the volatility is stochastic. The main findings showed that in the proposed method, when volatility approaches zero, the multiplicative binomial traditional method is a particular case, and the results are comparable between these methodologies, as well as to the exact solution offered by the Black-Scholes model. Finally, the originality of the methodological proposal is that it allows for the emulation in a simple way of the presence of a nonconstant volatility in the price of the underlying asset, and it can be used to value all kinds of options both in the real world and in risk-neutral situations.
  • No hay miniatura disponible
    Ítem
    Quadrinomial Trees to Value Options in Stochastic Volatility Models
    (Institutional Investor Systems, 2019-01-01) Pareja-Vasseur, Julian A.; Marin-Sanchez, Freddy H.; Universidad EAFIT. Escuela de Ciencias; Modelado Matemático
    This article describes in detail the multiplicative quadrinomial tree numerical method with nonconstant volatility, based on a system of stochastic differential equations of the GARCH-diffusion type. The methodology allowed for the derivation of the first two moments of the proposed equations to estimate the respective recombination between discrete and continuous processes and, as a result, a numerical methodological proposal is formally presented to value, with relative ease, both real and financial options, when the volatility is stochastic. The main findings showed that in the proposed method, when volatility approaches zero, the multiplicative binomial traditional method is a particular case, and the results are comparable between these methodologies, as well as to the exact solution offered by the Black-Scholes model. Finally, the originality of the methodological proposal is that it allows for the emulation in a simple way of the presence of a nonconstant volatility in the price of the underlying asset, and it can be used to value all kinds of options both in the real world and in risk-neutral situations.