Question

HW on Credit Models 1. Assume a company with total assets of $2,000 issues a zero coupon bond of $1,500 par value and one-year maturity. The risk-free rate of return is 2% and the rate of return on the firm's assets is 5%. The assets return volatility is 36%. a) Calculate the value of the bond using structural model. b) Calculate the expected loss on the bond and present value of expected loss. c) Assume the hazard rate (A) is estimated at 1% and the loss given default (Y) is 0.30. Calculate the probability of default over the year, the expected loss, and the present value of expected loss. 2. Assume the following term structure for a risk-free government debt and corresponding spread for a risky corporate bond. Maturity in years Risk-free zero coupon yield % 1.0 1.2 1.3 1.5 1.6 1.55 1.7 Credit spread % 0.6 0.7 1.0 1.2 1.1 1.25 1.3 2.5 3.0 3.5 a) What is the value of a 3-year 6% semiannual coupon corporate bond of $1,000 par? b) Calculate the present value of expected loss on the corporate bond due to credit risk.

Answer 1

Answer to Problem 2 given in the as below with calculation.

Answer to problem 2a
Maturity in Years	3
Market Rate of Interest	2.80%	(This is addition of Government + Credit spread)
Rate of Interest for Bond	6%
terms of Int Pmnt	Semi annual
Bond Value	$           1,000
Interest Payment half yearly	$                 30
Present value of Bond	$920
Formula for PV is (face Value of Bond / (1+Interest rate/no of times interest is paid)^no of periods*no of times interest is paid))
Present value of Interest	$166
(Similar formula as above is utilised except that instead of face value of bond interest amount is used).
Value of Bond	$1,086
Answer to problem 2b
				PV	PV
Maturity in Years	Risk Free Rate	Credit spread %		As per Risk Free Rate	Corporate Rate	Expected Loss
0.50	1.00%	0.60%		99.50	99.21	(0.29)
1.00	1.20%	0.70%		98.81	98.14	(0.68)
1.50	1.30%	1.00%		98.08	96.65	(1.43)
2.00	1.50%	1.20%		97.07	94.81	(2.26)
2.50	1.60%	1.10%		96.11	93.56	(2.55)
3.00	1.55%	1.25%		95.49	92.05	(3.44)
3.50	1.70%	1.30%		94.27	90.17	(4.10)
			Total	679.34	664.58	(14.76)
Assuming $100 Value of Bond. We need to calculate PV at the various Maturity and interest period to arrive at expected loss
Expected Loss = PV as per Corporate rate (Risk free rate + Credit Spread) - PV as per Risk free interest rate