Transcript Management of Financial Risk

Chapter 22
Credit Derivatives
Following P. Jorion 2001
Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Credit Derivatives
From 1996 to 2000 the market has grown from
$40B
to
$810B
Contracts that pass credit risk from one counterparty to
another. Allow separation of credit from other exposures.
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Credit Derivatives
Bond insurance
Letter of credit
Credit derivatives on organized exchanges:
TED spread = Treasury-Eurodollar spread
(Futures are driven by AA type rates).
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Types of Credit Derivatives
Underlying credit (single or a group of entities)
Exercise conditions (credit event, rating, spread)
Payoff function (fixed, linear, non-linear)
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Types of Credit Derivatives
November 1, 2000 reported by Risk
Credit default swaps
45%
Synthetic securitization
26%
Asset swaps
12%
Credit-linked notes
9%
Basket default swaps
5%
Credit spread options
3%
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Credit Default Swap
A buyer (A) pays a premium (single or periodic
payments) to a seller (B) but if a credit event
occurs the seller (B) will compensate the buyer.
premium
B - seller
A - buyer
Contingent payment
Reference asset
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Example
• The protection buyer (A) enters a 1-year credit
default swap on a notional of $100M worth of 10-year
bond issued by XYZ. Annual payment is 50 bp.
• At the beginning of the year A pays $500,000 to the
seller.
• Assume there is a default of XYZ bond by the end
of the year. Now the bond is traded at 40 cents on
dollar.
• The protection seller will compensate A by $60M.
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Types of Settlement
Lump-sum – fixed payment if a trigger event occurs
Cash settlement – payment = strike – market value
Physical delivery – you get the full price in exchange
of the defaulted obligation.
Basket of bonds, partial compensation, etc.
Definition of default event follows ISDA’s Master
Netting Agreement
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Total Return Swap (TRS)
Protection buyer (A) makes a series of payments
linked to the total return on a reference asset. In
exchange the protection seller makes a series of
payments tied to a reference rate (Libor or
Treasury plus a spread).
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Total Return Swap (TRS)
Payment tied to reference asset
B - seller
A - buyer
Payment tied to reference rate
Reference asset
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Example TRS
• Bank A made a $100M loan to company XYZ at a fixed rate
of 10%. The bank can hedge the exposure to XYZ by entering
TRS with counterparty B. The bank promises to pay the
interest on the loan plus the change in market value of the loan
in exchange for LIBOR + 50 bp.
• Assume that LIBOR=9% and by the end of the year the value
of the bond drops from $100 to $95M.
• The bank has to pay $10M-$5M=5M and will receive in
exchange $9+$0.5M=9.5M
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Credit Spread Forward
Payment = (S-F)*Duration*Notional
S – actual spread
F – agreed upon spread
Cash settlement
May require credit line of collateral
Payment formula in terms of prices
Payment =[P(y+F, T)-P(y+S,T)]*Notional
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Credit Spread Option
Put type
Payment = Max(S-K, 0)*Duration*Notional
Call type
Payment = Max(K-S, 0)*Duration*Notional
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Example
A credit spread option has a notional of $100M with a maturity of
one year. The underlying security is a 8% 10-year bond issued by
corporation XYZ. The current spread is 150bp against 10-year
Treasuries. The option is European type with a strike of 160bp.
Assume that at expiration Treasury yield has moved from 6.5% to
6% and the credit spread widened to 180bp.
The price of an 8% coupon 9-year semi-annual bond discounted at
6+1.8=7.8% is $101.276.
The price of the same bond discounted at 6+1.6=7.6% is $102.574.
The payout is (102.574-101.276)/100*$100M = $1,297,237
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Credit Linked Notes (CLN)
Combine a regular coupon-paying note with some
credit risk feature.
The goal is to increase the yield to the investor in
exchange for taking some credit risk.
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CLN
A buys a CLN, B invests the money in a high-
rated investment and makes a short position in a
credit default swap.
The investment yields LIBOR+Ybp, the short
position allows to increase the yield by Xbp, thus
the investor gets LIBOR+Y+X.
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Credit Linked Note
CLN =
Xbp
Credit swap
buyer
par
AAA note +
Credit swap
Contingent payment
par
L+X+Y
investor
Contingent payment
LIBOR+Y
AAA asset
Asset backed securities can be very dangerous!
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Types of Credit Linked Note
Type
Asset-backed
Compound Credit
Principal Protection
Enhanced Asset Return
Credit Derivatives
Maximal Loss
Initial investment
Amount from the first default
Interest
Pre-determined
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FRM 1999-122 Credit Risk (22-4)
A portfolio manager holds a default swap to hedge an AA
corporate bond position. If the counterparty of the default
swap is acquired by the bond issuer, then the default swap:
A. Increases in value
B. Decreases in value
C. Decreases in value only if the corporate bond is
downgraded
D. Is unchanged in value
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FRM 1999-122 Credit Risk (22-4)
A portfolio manager holds a default swap to hedge an AA
corporate bond position. If the counterparty of the default
swap is acquired by the bond issuer, then the default swap:
A. Increases in value
B. Decreases in value – it is worthless (the same default)
C. Decreases in value only if the corporate bond is
downgraded
D. Is unchanged in value
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FRM 2000-39 Credit Risk (22-5)
A portfolio consists of one (long) $100M asset and a default
protection contract on this asset. The probability of default over the
next year is 10% for the asset, 20% for the counterparty that wrote
the default protection. The joint probability of default is 3%.
Estimate the expected loss on this portfolio due to credit defaults
over the next year assuming 40% recovery rate on the asset and 0%
recovery rate for the counterparty.
A. $3.0M
B. $2.2M
C. $1.8M
D. None of the above
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FRM 2000-39 Credit Risk
A portfolio consists of one (long) $100M asset and a default
protection contract on this asset. The probability of default over the
next year is 10% for the asset, 20% for the counterparty that wrote
the default protection. The joint probability of default is 3%.
Estimate the expected loss on this portfolio due to credit defaults
over the next year assuming 40% recovery rate on the asset and 0%
recovery rate for the counterparty.
A. $3.0M
B. $2.2M
C. $1.8M = $100*0.03*(1– 40%) only joint default leads to a loss
D. None of the above
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FRM 2000-62 Credit Risk (22-11)
Bank made a $200M loan at 12%. The bank wants to hedge the
exposure by entering a TRS with a counterparty. The bank promises
to pay the interest on the loan plus the change in market value in
exchange for LIBOR+40bp. If after one year the market value of
the loan decreased by 3% and LIBOR is 11% what is the net
obligation of the bank?
A. Net receipt of $4.8M
B. Net payment of $4.8M
C. Net receipt of $5.2M
D. Net payment of $5.2M
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FRM 2000-62 Credit Risk (22-11)
Bank made a $200M loan at 12%. The bank wants to hedge the
exposure by entering a TRS with a counterparty. The bank promises
to pay the interest on the loan plus the change in market value in
exchange for LIBOR+40bp. If after one year the market value of
the loan decreased by 3% and LIBOR is 11% what is the net
obligation of the bank?
A. Net receipt of $4.8M = [(12%-3%) –(11%+0.4%)]*$200M
B. Net payment of $4.8M
C. Net receipt of $5.2M
D. Net payment of $5.2M
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Pricing and Hedging Credit
Derivatives
1. Actuarial approach – historic default rates
relies on actual, not risk-neutral probabilities
2. Bond credit spread
3. Equity prices – Merton’s model
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Example: Credit Default Swap
CDS on a $10M two-year agreement.
A – protection buyer agrees to pay to
B – protection seller a fixed annual fee in
exchange for protection against default of 2year bond XYZ.
The payout will be Notional*(100-B) where B
is the price of the bond at expiration, if the
credit event occurs.
XYZ is now A rated with YTM=6.6%, while Tnote trades at 6%.
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Actuarial Method
Starting
State
A
B
C
D
Ending state
A
B
C
0.90 0.07 0.02
0.05 0.90 0.03
0
0.10 0.85
0
0
0
Total
D
0.01
0.02
0.05
1.00
1.00
1.00
1.00
1.00
1Y 1% probability of default
2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%
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Actuarial Method
1Y 1% probability of default
2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%
If the recovery rate is 60%, the expected costs are
1Y: 1%*(100%-60%) = 0.4%
2Y: 1.14%*(100%-60%) = 0.456%
Annual cost (no discounting):
1%  1.14%
$10 M
(100 %  60%)  $42,800
2
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Credit Spread Method
Compare the yield of XYZ with the yield of
default-free asset. The annual protection cost is
Annual Cost = $10M (6.60%-6%) = $60,000
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Equity Price Method
Following the Merton’s model (see chapter 21)
the fair value of the Put is
Put  V  N (d1 )  Ke
 rT
 N (d 2 )
The annual protection fee will be the cost of Put
divided by the number of years.
To hedge the protection seller would go short the
following amount of stocks
Put V
1
 1
V S
N (d1 )
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