Black Scholes Merton option pricing theory

Firm s assets evolve randomly. The probability of a firm default is determined using the Black Scholes Merton option pricing theory. 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

The theory of options was developed in the assumption of market equilibrium. The first option pricing model was proposed by Black and Scholes (1973) and then by Merton (1973), in which they did not consider dividend payments. Authors as Schwartz (1975) include dividend payments into valuation model and also consider the possibility of exercising the option before the maturity... 

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