May 15

Credit spread option - Practice question (Par 4 difficulty)

by David Harper, CFA, FRM, CIPM

Assume:

A firm buys a one-year European credit spread option with USD notional of $100 million.

The underlying is a corporate bond with a 10-year maturity paying a 5% semiannual coupon. The Treasury yield curve is (unrealistically) flat at 4% for all maturities and will remain flat going forward.

The corporate bond's current spread is 100 basis points; the option's strike spread is also 100 basis points.

Assume that, one year later (when the spread option expires, and the bond has maturity of 9 years), the spread widens to 200 basis points.

Question:

(i) If the buyer does receive a payout (i.e., as the spread widened), is the option a put or call?
(ii) What is payout given by the credit spread option?
(iii) If the option premium was 20 basis point, what is the net payout to the buyer (neglecting time value of money)
(iv) Bonus: Can we also solve the payout in terms of DURATION?

(don't peek until you try)

Answer:

(i)
The payoff of a credit-spread PUT = Duration * Notional * MAX[0, Credit spread - Strike spread]. Therefore, the buyer of a put profits on spread widening and the buyer of a call profits on spread narrowing.

(ii)
See the EditGrid below.

The bond price at strike spread is conveniently its par: 4% Treasury + 1% strike spread = 5%. Since the coupon is 5%, the bond must price at par.

Compare to bond price @ 4% + 2%. The price of a 6% YTM bond = $93.12 (n = 18 because 9 years remain!)

The 6.88% decline implies a $6.88 million payout.

(iii)
20 basis point premium implies $200,000 premium. Net of payout = $6.68 million.

(iv)
See below for duration approach. The duration one year forward is 7+ (note: Meissner assume duration at start for convenience). So, under duration approach, (gross) payout is $7+ million. But we cannot expect an exact match. Why?