what is the merton model 
the merton model is a mathematical formula that stock analysts and commercial loan officers among others can use to judge a corporation s risk of credit default named for economist robert c merton who proposed it in 1974 the merton model assesses the structural credit risk of a company by modeling its equity as a call option on its assets formula for the merton modele v t n d 1 k e r t n d 2 where d 1 ln v t k r v 2 2 t v t and d 2 d 1 v t e theoretical value of a company s equity v t value of the company s assets in period t k value of the company s debt t current time period t future time period r risk free interest rate n cumulative standard normal distribution e exponential term i e 2 7183 standard deviation of stock returns begin aligned e v tn left d 1 right ke r delta t n left d 2 right textbf where d 1 frac ln frac v t k left r frac sigma v 2 2 right delta t sigma v sqrt delta t text and d 2 d 1 sigma v sqrt delta t text e theoretical value of a company s equity v t text value of the company s assets in period t text k value of the company s debt text t current time period text t future time period text r risk free interest rate text n cumulative standard normal distribution text e exponential term left i e text 2 7183 right sigma text standard deviation of stock returns end aligned e vt n d1 ke r tn d2 where d1 v t lnkvt r 2 v2 t andd2 d1 v t e theoretical value of a company s equityvt value of the company s assets in period tk value of the company s debtt current time periodt future time periodr risk free interest raten cumulative standard normal distributione exponential term i e 2 7183 standard deviation of stock returns 