http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 frm chapter 22 credit derivatives...
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http://pluto.huji.ac.il/~mswiener/zvi.html
972-2-588-3049FRM
Chapter 22Credit Derivatives
Following P. Jorion 2001
Financial Risk Manager Handbook
Zvi Wiener slide 2Credit Derivatives
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.
Zvi Wiener slide 3Credit Derivatives
Credit Derivatives
Bond insurance
Letter of credit
Credit derivatives on organized exchanges:
TED spread = Treasury-Eurodollar spread
(Futures are driven by AA type rates).
Zvi Wiener slide 4Credit Derivatives
Types of Credit Derivatives
Underlying credit (single or a group of entities)
Exercise conditions (credit event, rating, spread)
Payoff function (fixed, linear, non-linear)
Zvi Wiener slide 5Credit Derivatives
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%
Zvi Wiener slide 6Credit Derivatives
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.
A - buyer B - sellerpremium
Contingent payment
Reference asset
Zvi Wiener slide 7Credit Derivatives
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.
Zvi Wiener slide 8Credit Derivatives
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
Zvi Wiener slide 9Credit Derivatives
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).
Zvi Wiener slide 10Credit Derivatives
Total Return Swap (TRS)
A - buyer B - sellerPayment tied to reference asset
Payment tied to reference rate
Reference asset
Zvi Wiener slide 11Credit Derivatives
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
Zvi Wiener slide 12Credit Derivatives
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
Zvi Wiener slide 13Credit Derivatives
Credit Spread OptionPut type
Payment = Max(S-K, 0)*Duration*Notional
Call type
Payment = Max(K-S, 0)*Duration*Notional
Zvi Wiener slide 14Credit Derivatives
ExampleA 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
Zvi Wiener slide 15Credit Derivatives
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.
Zvi Wiener slide 16Credit Derivatives
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.
Zvi Wiener slide 17Credit Derivatives
Credit Linked Note
Credit swap buyer
investor
AAA asset
CLN =
AAA note +
Credit swap
par
L+X+Y
Contingent payment
Xbp
Contingent payment
par LIBOR+Y
Asset backed securities can be very dangerous!
Zvi Wiener slide 18Credit Derivatives
Types of Credit Linked Note
Type Maximal Loss
Asset-backed Initial investment
Compound Credit Amount from the first default
Principal Protection Interest
Enhanced Asset Return Pre-determined
Zvi Wiener slide 19Credit Derivatives
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
Zvi Wiener slide 20Credit Derivatives
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
Zvi Wiener slide 21Credit Derivatives
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
Zvi Wiener slide 22Credit Derivatives
FRM 2000-39 Credit RiskA 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
Zvi Wiener slide 23Credit Derivatives
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
Zvi Wiener slide 24Credit Derivatives
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
Zvi Wiener slide 25Credit Derivatives
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
Zvi Wiener slide 26Credit Derivatives
Example: Credit Default Swap
CDS on a $10M two-year agreement.
A – protection buyer agrees to pay to
B – protection seller a fixed annual fee in exchange for protection against default of 2-year bond XYZ.
The payout will be Notional*(100-B) where B is the price of the bond at expiration, if the credit event occurs.
XYZ is now A rated with YTM=6.6%, while T-note trades at 6%.
Zvi Wiener slide 27Credit Derivatives
Actuarial Method
1Y 1% probability of default
2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%
Starting Ending state TotalState A B C DA 0.90 0.07 0.02 0.01 1.00B 0.05 0.90 0.03 0.02 1.00C 0 0.10 0.85 0.05 1.00D 0 0 0 1.00 1.00
Zvi Wiener slide 28Credit Derivatives
Actuarial Method
1Y 1% probability of default
2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%
If the recovery rate is 60%, the expected costs are
1Y: 1%*(100%-60%) = 0.4%
2Y: 1.14%*(100%-60%) = 0.456%
Annual cost (no discounting):
800,42$%)60%100(2
%14.1%110$
M
Zvi Wiener slide 29Credit Derivatives
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
Zvi Wiener slide 30Credit Derivatives
Equity Price Method
Following the Merton’s model (see chapter 21) the fair value of the Put is
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
)()( 21 dNKedNVPut rT
)(
11
1dNS
V
V
Put