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First American bank case solution : A case of credit default swaps (cds).
Citation preview
First American Bank: Credit Default Swaps
SUNWOO HWANG*
* KDI School of Public Policy and Management, Hoegi-ro 87, Dongdaemun-gu, Seoul, 130-868, Korea.
HBS Case Study
Introduction
3
Charles Bank International
(CBI)
First American Bank (FAB)
(A rump sum or) periodic payment
Protection Buyer Protection Seller
Payment
Pricing the CDS spread
5
The fair value of the CDS spread is the number that sets the initial value of the CDS contract to zero.
V = (PV Payoff) – s(PV Spread) =
where
s: spread: present value of a dollar paid at time t
: marginal default rate from now to year t : survival probability until the end of year t
f: recovery rate (see exhibit 14)r: risk-free interest rate (See Exhibit 8. Treasury STRIP yields)
The 1st Issue
Solution
Kittal had to determine the semi-annual fee to be charged to CBI for the default swap
- Pricing a CDS
Pricing the CDS spread (cont.)
6
But, how to compute the marginal probability of d(t)? Apply the Merton model and, in turn, compute the fair value of CDS spread using the marginal probability.
In the Black-Scholes model, N(d2) is also the probability of exercising the call, or that the bond will not default. Conversely, 1 – N(d2) = N(-d2) is the risk-neutral probability of default.
where
* N(.) is the cumulative distribution function for the standard normal distribution
S: Market value of the CEU’s asset = $6.8 + $4.1 = $10.9bnK: Strike price or the face value of the bond = FV(Current market value of the bond)
: Time to maturity or duration = 4.2 years: Implied volatility = 49.9%
Parameters Computation
Pricing the CDS spread (cont.)
7
The fair value of the CDS spread is the number that sets the initial value of the CDS contract to zero. We compute it using the default probability and recovery rate.
Probability (%)Risk-free Int. Rate
Discount Factor P
V(t)
Payoff Payments Spread payments
Yeart
Default.k(t)
SurvivalS(t)
Expectedk(t)x(1-f)
PVExpectedsxS(t-1)
PV
0.5 0.0514 0.9486 1.47% 0.9927 0.0093 0.0092 0.0093 0.0092
1 0.0488 0.8998 2.14% 0.9788 0.0088 0.0086 0.0088 0.0086
1.5 0.0463 0.8536 2.67% 0.9607 0.0083 0.0080 0.0083 0.0080
2 0.0439 0.8097 3.20% 0.9380 0.0079 0.0074 0.0079 0.0074
Total 0.0332 0.0332
CDS spread = 92.52bp!!
Pricing the CDS spread
Solution to the Second Issue
9
To hedge its risk exposure to the credit event occurrence of CEU, FAB may issue a credit-linked note (CLN), which is structured security that combine a credit derivative with a regular bond.
The 2nd Issue
Solution
Kittal needed to ensure that First American Bank could hedge its end of the default swap by selling off the credit exposure in the form of another default swap or through another means.
Credit Default Swap
Regular Bond+Credit-Linked
Note=
Option Bond
Some of the principal amount are able to be used to cover the loss given default.
Structured Product
Accounting interpretation
10
The note is a liability on the bank’s balance sheet.
B/S (CapEx
Unlimited)
B/S (Charles Bank International)
B/S (First American
Bank)
$100m $100m
Asset Liability Asset Liability Asset Liability
$50m $50m
$100m
$50m
$50m
Cash
Debit Credit
$50m
Credit-Risk Hedged Loan
Debit Credit
$50m
CLN Structure
11
CLNs are notes with an embedded short position in a CDS on CEU. In a CLN, the buyer of protection transfers credit risk to an investor via an intermediary bond-issuing entity, which can be the buyer itself or a special purpose vehicle (SPV).
CapExUnlimited
(CEU)
Charles Bank International
(CBI)
First American
Bank (FAB)
Investor 1
Investor 2
Investor N-1
Investor N
…
Top-rated Asset
Contingent Payment
$ 50m
$ 50m$ 5
0m
R’ R1LIBOR +
R1+R2
LIB
OR
+R
2
CLN (Top-rated
Asset in trust + CRS)
SPVOR
Contingent Payment
Source: Financial Risk Manager Handbook, Jorion, P., Wiley, 5th edition, 2009.
CLN Structure (cont.)
12
The investor’s initial funds are placed in a top-rated investment that pays LIBOR plus a spread of R2. The FAB or SPV takes a short position in a credit default swap, for an additional annual receipt of R1. The annual payment to the investors is then LIBOR + R1 + R2.
Source: Financial Risk Manager Handbook, Jorion, P., Wiley, 5th edition, 2009.
CapExUnlimited
(CEU)
Charles Bank International
(CBI)
First American
Bank (FAB)
Investor 1
Investor 2
Investor N-1
Investor N
…
Top-rated Asset
Contingent Payment
$ 50m
$ 50m$ 5
0m
R’ R1LIBOR +
R1+R2
LIB
OR
+R
2
CLN (Top-rated
Asset in trust + CRS)
SPVOR
Contingent Payment
Additional Remarks
- Investors receive a high coupon but will lose some of the principal if CEU defaults on its debt.
- This structure achieves its goal of reducing the bank’s exposure if CEU defaults.
- In this case, because the note is a liability of the bank, the investor is exposed to a default of either ECU or of the bank FAB.
13
Pros and Cons
Attractiveness
- Relative to a regular investment in, say, a note issued by the government of the United States, this structure may carry a higher yield if the CDS spread is greater than the bond yield spread.
- This structure may also be attractive to investors who are precluded from investing directly in derivatives.