In the Merton model of risky debt, suppose we define which gives the volatility of the value of the risky debt Also, we denote the credit spread by s( d), where s( d) Y() r Show that (Merton, 1974) Give the financial interpretation to each of the above results ( d) aV V 9A...

1 The Merton model is a widely used model in finance that describes the relationship between a companys debt and its underlying risk factors The model ...

In the Merton model of risky debt, suppose we define which gives the volatility of the value

Question:

In the Merton model of risky debt, suppose we define

(;d) = aV V 9A

which gives the volatility of the value of the risky debt. Also, we denote the credit spread by s(τ ; d), where s(τ ; d) = Y(τ) − r. Show that (Merton, 1974)

(a) (b) (c) s - = d s 2 s r 1 1 zov (t; d) > 0; N'(d) 2 N (d) ov -ov (t; d) > 0, where d -(t; d) < 0. O =