York UniversityADMS 4504

The credit risk on a 4-year $100 par value 5% annual coupon payment corporate bond can be expressed by an annual probability of default 1% and a recovery rate of 36%. The risk-free yield curve is flat at 2% across maturities. Calculate the credit spread and credit valuation adjustment (CVA) for this bond.

 

Answer:

(i). Credit spread: 0.0064

(ii). CVA: 2.239

Step-by-step explanation

(i). Credit spread is given by the formula:

(1 - Recovery rate) x (default probability)

Given that:

Recovery rate: 36%

Default rate:     1%

For simplicity converts the percentages into decimal representations which will be given as:

Recovery rate: 36/100 = 0.36

Default rate. :  1/100    = 0.01

Credit spread = (1 - 0.36) x (0.01)

                        =0.64 x 0.01

                        =0.0064

(ii). CVA = Risk free value - True value 

      ° Risk free value:

     Rfv  = Xe^-rT). 

Where:

T = maturity date 

r = risk free interest rate 

X =Payoff at T

In our case herein:

T = 4 years 

r. = 5%

X =100

100^(4x0.05)

100^0.2

 = 2.5118

True value:

T = Xe^(r+s)T

 We realize it is similar to the risk free value but has an adjustment for credit spread denoted as's'

Given that our 's' = 0.0064

T = 100 ^( 0.05+0.0064)x4

   100^0.2256

   = 4.7512

CAV = 2.5118 - 4.7512 

           = -2.239

 We take the absolute figure 

CAV = 2.239