Symbolically, the Merton model stipulates that firm asset follows a geometric Brownian motion

The equity value of a firm satisfies the call option condition

where E is the market value of firm equity, F is the synthesis of firm liabilities, acting as option’s strike price, V is the firm’s asset value, r is the instantaneous risk-free rate, N(.) is the cumulative standard normal distribution function. In addition, d₁ and d₂ are defined, respectively, as

and

The distance to default DD can be calculated as

where μ is an estimate of the expected annual return of the firm’s assets. The corresponding implied default likelihood, DLI, is then defined as: