Projection of the two-dimensional Black-Scholes equation for options with underlying stock and strike prices in two different currencies



Título del documento: Projection of the two-dimensional Black-Scholes equation for options with underlying stock and strike prices in two different currencies
Revista: Revista mexicana de física
Base de datos: PERIÓDICA
Número de sistema: 000460872
ISSN: 0035-001X
Autores: 1
1
Instituciones: 1Universidad Autónoma Metropolitana, Departamento de Matemáticas Aplicadas y Sistemas, Ciudad de México. México
Año:
Periodo: Ene-Feb
Volumen: 68
Número: 1
País: México
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico, teórico
Resumen en inglés The two-variable Black-Scholes equation is used to study the option exercise price of two different currencies. Due to the complexity of dealing with several variables, reduction methods have been implemented to deal with these problems. This paper proposes an alternative reduction by using the so-called Zwanzig projection method to one-dimension, successfully developed to study the diffusion in confined systems. In this case, the option price depends on the stock price and the exchange rate between currencies. We assume that the exchange rate between currencies will depend on the stock price through some model that bounds such dependence, which somehow influences the final option price. As a result, we find a projected one-dimensional Black-Scholes equation similar to the so-called Fick-Jacobs equation for diffusion on channels. This equation is an effective Black-Scholes equation with two different interest rates, whose solution gives rise to a modified Black-Scholes formula. The properties of this solution are shown and were graphically compared with previously found solutions, showing that the corresponding difference is bounded
Disciplinas: Física y astronomía
Palabras clave: Física,
Difusión en canales,
Potencial entrópico
Keyword: Ecuación de Black-Scholes,
Physics,
Diffusion in channels,
Entropic potential,
Black-Scholes equation
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