Valuación de opciones asiáticas con precio de ejercicio flotante igual a la media aritmética: un enfoque de control óptimo estocástico

• Autores: María Teresa V. Martínez Palacios, Ambrosio Ortiz Ramírez, José Francisco Martínez-Sánchez
• Localización: Revista Mexicana de Economía y Finanzas (REMEF): nueva época, ISSN-e 2448-6795, ISSN 1665-5346, Vol. 12, Nº. 4, 2017, págs. 389-404
• Idioma: español
• DOI: 10.21919/remef.v12i4.240
• Títulos paralelos:
  • Pricing Asian Options with Floating Exercise Price Equal to the Arithmetic Mean: An Optimal Stochastic Control Approach
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• Resumen
  • español

    En esta investigación se caracteriza la prima de una opción de venta asiática de tipo europeo con precio de ejercicio flotante igual a la media aritmética, mediante el análisis de solución a un problema de control óptimo estocástico en tiempo continuo, que modela el proceso de toma de decisiones de consumo-inversión de un consumidor racional en un horizonte finito de planeación con fecha final estocástica. La prima obtenida es una ecuación diferencial parcial de segundo orden que corresponde a la ecuación de Black-Scholes-Merton, con la diferencia de que esta se establece con fundamentos de racionalidad económica. Asimismo, se resuelve analíticamente la ecuación diferencial parcial de Hamilton-Jacobi-Bellman que optimiza el problema de control ´optimo estocástico planteado.

  • English

    This research characterizes the premium of a European-type +Asian put option with floating exercise price equal to the arithmetic mean, through the solution analysis to a stochastic optimal control problem in continuous time, that models the decision-making process of consumption-investment of a rational consumer in a finite horizon of planning with stochastic terminal date. The premium obtained is a partial differential equation of second order corresponding to the Black-Scholes-Merton equation, with the difference that this is established with fundamentals of economic rationality. Also, the Hamilton-Jacobi-Bellman partial differential equation is solved, which optimizes the stochastic optimal control problem.

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