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Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox = Market Calibration Problem and the Implied Structure of the Black-Cox Bond Model

Listed author(s):
  • Sukhomlin, Nikolay


    (Departamento de Física, Universidad Autónoma de Santo Domingo (República Dominicana), CEREGMIA, Université des Antilles et de la Guyane (France))

  • Santana Jiménez, Lisette Josefina


    (Grupo de Investigación en Econofísica, Universidad Autónoma de Santo Domingo (República Dominicana))

Registered author(s):

    El principal resultado de este artículo consiste en la resolución del problema inverso del modelo de Black-Cox (1976), usando el método propuesto por Sukhomlin (2007). Se parte del enfoque retrógrado (backward) para obtener una expresión exacta de la volatilidad implícita en función de parámetros cuantificables con datos de mercado y de variables conocidas. Se descubre la existencia de dos valores de la volatilidad para un activo subyacente en el modelo referido, lo que indica que las asunciones tradicionales no lo definen de manera unívoca. Se encuentra la causa de que el modelo de Black-Cox contenga dos valores de la volatilidad. Además, se lleva a cabo una simulación, afín de verificar, numéricamente, que la expresión obtenida para la volatilidad es la inversión de la fórmula que representa la probabilidad de que la firma no alcance un nivel de insolvencia antes del tiempo de madurez de la deuda. Finalmente, se resuelve el problema de calibración de mercado desde el punto de vista directo (forward), encontrándose una expresión que resulta de mayor utilidad para los agentes de mercado. The main result of this paper consists in the resolution of the inverse problem for the Black-Cox (1976) model, using the method proposed by Sukhomlin (2007). Based on the backward approach, we obtain an exact expression of the implied volatility expressed as a function of quantifiable market parameters and known variables. We discover the existence of two values of the volatility for an underlying asset, in the referred model, which means that the model's traditional assumptions do not define it univocally. We find the cause that the Black-Cox model contains two values of the volatility. Besides, we carry out a simulation in order to verify, numerically, that our volatility expression is in fact the inversion of the formula that represents the probability that the firm has not reached the reorganization boundary before the debt expires. Finally, we solve the market calibration problem from the forward approach, finding an expression that is more useful for market agents.

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    Article provided by Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration in its journal Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration.

    Volume (Year): 10 (2010)
    Issue (Month): 1 (December)
    Pages: 73-98

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    Handle: RePEc:pab:rmcpee:v:10:y:2010:i:1:p:73-98
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    1. Jean-Pierre Fouque & George Papanicolaou & Ronnie Sircar & Knut Solna, 2004. "Maturity cycles in implied volatility," Finance and Stochastics, Springer, vol. 8(4), pages 451-477, November.
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    12. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
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