Exam Question about Credit spread

[Johannes]

Dear David,

I am currently doing some practice exams and I can't solve the question below. Can you please explain it to me?

A credit-spread option has a notional amount of $50 million with a maturity of one year. The underlying security is a 10-year, semi-annual bond with a 7% coupon and a $1,000 face value. The current spread is 120 bp against 10-year Treasuries. The option is a European option with a strike of 130 bp. If at expiration, Treasury yields have moved from 6% to 6.3% and the credit-spread has widened to 150 bp, what will be the payout to the buyer of this credit-spread option?

A) $587,352
B) $611,893
C) $622,426
D) $639,023

Thanks in advance for your help,

Johannes

 

[David Harper CFA FRM]

Hi Johannes,

I entered it into the pre-existing credit-spread XLS. See third tab here. Or direct to XLS is here:

Note it has two ways to solve, the 2nd (following de Servigny) uses duration, which we aren't given here.
The first gives result of $622,4xx based on the idea of pricing the bond @ strike versus bond @ actual:
Bond at strike = PV(6.3% + 1.3% yield, ....) subtract
Bond at actual = PV (6.3% + 1.5% yield,....) = 1.245% * 50 notional.

Let me know if you disagree (b/c i left it as a third solution in the xls). thanks!

David