Árboles binomiales para la valoración de opciones sobre procesos derivados de la ecuación diferencial estocástica autónoma
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Keywords
Ecuaciones diferenciales estocásticas, árboles binomiales, probabilidades de transición, valoración de opciones.
Resumen
En este trabajo se propone una recombinación en árboles binomiales multiplicativageneralizada para la ecuación autónoma, en términos de la condición inicial y del producto entre saltos no constantes hacia arriba y hacia abajo delproceso discretizado. Se presenta de manera formal una técnica para encontrarlas probabilidades de transición dinámicas considerando los dos primeros momentos del proceso solución de la ecuación diferencial, los cuales incorporanel factor de crecimiento y la volatilidad en términos de los parámetrosy del proceso subyacente a lo largo de su ramificación. Se muestran algunosresultados numéricos experimentales de valoración de opciones Europeas parael proceso log–normal y para los procesos de reversión a la media con ruidoaditivo y ruido proporcional para diferentes fechas de expiración.
MSC: 91Gxx, 91G80
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Referencias
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