Credit Spread Analysis

Jack Gordon, a fixed income analyst for Omega Bank PLC, is evaluating an AA corporate bond for inclusion in the bank’s portfolio. The $100 par, 3.50%, annual pay, 5 year bond is currently priced with a credit spread of 135 bps over the benchmark par rate of 2%. Calculate the bond’s CVA implied in its market price.

Solution

VND for the bond = present value of bond’s cash flows using benchmark YTM.

value of the risky bond using credit spread = 2% benchmark rate + 1.35% credit spread = 3.35% as YTM:

In our earlier discussion on the computation of CVA, we assumed zero volatility for benchmark rates. We now introduce volatility in future 1 period benchmark rates using the binomial tree framework.

Figure 26.3 shows a three year benchmark interest rate tree. Numbers in parentheses in each node indicate the probability for that node (note that probabilities add up to 100% for each period).

Figure 26.3: Benchmark Interest Rate Tree

We use our standard backward induction process to value a risky bond given the benchmark rate tree. Recall that for a binomial interest rate tree, the probability of up = probability of down = 0.5. Because the rates in the tree are benchmark rates, the value obtained is the bond’s VND.

We illustrate the computation of VND using the following example.

For a 3 year, annual pay, 4% coupon, $100 par corporate bond using the interest rate tree in Figure 26.3, calculate the VND for the bond and the exposure for each year.

Solution

The completed tree is shown as follows:

Given a 4% coupon, the cash flow at the end of three years is 104. The value at the bottom node in Year 2 = 104 / 1.04825 = $99.21. The value of bottom node in Year 1 is calculated as the present value of the average of the two values in Year 2 plus the coupon.

Using the same procedure for Year 0, the VND for the bond is $97.24.

exposure for Year t

exposure for Year 1 = (0.5)(98.30) + (0.5)(94.02) + 4 = $100.16

exposure for Year 2 = (0.25)(93.92) + (0.5)(97.02) + (0.25)(99.21) + 4 = $100.79

exposure for Year 3 = $104 (no need to calculate!)

Once the exposure for each period is calculated, given an estimated unconditional probability of default and a recovery rate, we use the same method discussed earlier to calculate the CVA for the bond.