Market Calibration Problem and the Implied Structure of the Black-Cox Bond Model
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.2166Keywords:
Modelo de Black-Cox, volatilidad implícita, arbitraje, Black-Cox model, implied volatility, arbitrageAbstract
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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