Question

Credit risk measures using the structural model: assume a company has the following characteristics.

Time t value of the firm’s assets:   At = $3,000

Expected return on assets: u = 0.06 per year

Risk-free rate: r = 0.03 per year

Face value of the firm’s debt: K = $2,000

Time to maturity of the debt (tenor): T – t = 1 year

Asset return volatility: σ = 0.35 per year

(a) Calculate the probability that the debt will default over the time to maturity.

(b) Calculate the expected loss.

(c) Calculate the present value of the expected loss.

Answer 1

Step1

Calculation of probability

Using scientific calculator

D=N (-C2)

If over the time of maturity there is default in debt

Hence Probability(PD)=70%

Working for financial risk probabaility(PD) is asfollows

e1=In(A/K) +U (T-t)+1/2 ơ^2(T-t) / ơ^√T-t

E2= E1-ơ^√T-t

PE1= ln (3000/2000) + 0.06(1) +1/2 (0.35) ^ 2 (1) / (0.35√1) =2.034

Now

PE2=2.034-0.35√1= 1.7

D=N (-C2)

D= N (-1.7)

D= 1-N (1.7)

D=1-0.3

D= 0.7

D=70%

Step2

Calculation of loss

Probability referred as PD=70% and face value of debt=2000

Rest is for time value of asset

Hence function used

Again on your calculator

calculate expected loss

Expected loss=Kn(-c2)-Ae^u(T-t)*N(-Pe1)

2000*0.7-3000*e^0.06(1)* N (2.034)

-1785.50-3185.50*(2-N (2.034)

Hence loss will be

$318

Step3

Present value of expected loss

D1= ln (3000/2000) + 0.03 (1) + 1/2 (0.35) ^ 2 (1) / (0.35√1)

Hence value of d1=1.4177

Therefore D2=1.4177-0.35√1

D2 value will arrive=1.0677

Now present value of expected loss

2000*e^-0.03*0.66-3000*0.323

$231