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

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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 =

Give the financial interpretation to each of the above results.

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