Transcript Credit Derivatives

Swaps
Zvi Wiener
02-588-3049
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Interest Rate Swaps: Concept
• An agreement between 2 parties to exchange
periodic payments calculated on the basis of
specified interest rates and a notional amount.
•Plain Vanilla Swap
Fixed rate
B
A
Floating rate
Based on a presentation of Global Risk Strategy Group of Deutsche Bank
Credit Derivatives
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IRS
• In a standard IRS, one leg consists of fixed
rate payments and the other depends on the
evolution of a floating rate.
• Typically long dated contracts: 2-30 years
• Sometimes includes options, amortization,
etc.
• Interest compounded according to different
conventions (eg 30/360, Act/Act. Act/360, etc.)
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IRS Origins
AAA wants to borrow in floating and BBB
wants to borrow in fixed.
Fixed
Floating
AAA
7.00%
LIBOR+5bps
BBB
8.50%
LIBOR+85bps
difference
1.5%
0.8%
Net differential 70bps = 0.7%
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Comparative Advantage
7.4%
7.0%
AAA
Libor
BBB
Libor+85bp
Cost of funds for AAA=Libor - 40bp (45bps saved)
Cost of funds for BBB=8.25% (25bps saved)
Swap rate = 7.40%
Swap rate is the fixed rate which is paid against
receiving Libor.
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Basic terms of IRS
• Notional amount
• Fixed rate leg
• Floating rate leg
• Calculated period
• Day count fraction
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Basic terms of IRS
• Payer and receiver - quoted relative to fixed
interest (i.e. payer = payer of fixed rate)
• buyer = payer, seller =receiver
• Short party = payer of fixed, (buyer)
• Long party = receiver of fixed, (seller)
• Valuation = net value NOT notional!!
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Various swaps
• Coupon swaps - fixed against floating.
• Basis or Index swaps - exchange of two
streams both are computed using floating IR.
• Currency swap - interest payments are
denominated in different currencies.
• Asset swap - to exchange interest received
on specific assets.
• Term swap maturity more then 2 years.
• Money Market swap - less then 2 years.
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Payments
Fixed payment =
(notional)(Fixed rate)(fixed rate day count convention)
Floating payment =
(notional)(Float. rate)(float. rate day count convention)
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Time Value of Money
• present value PV = CFt/(1+r)t
• Future value FV = CFt(1+r)t
• Net present value NPV = sum of all PV
-PV
5
5
5
5
105
4
5
105
PV  

t
5
(
1

r
)
(
1

r
)
t 1
t
5
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Credit Derivatives
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Swap Pricing
A swap is a series of cash flows.
An on-market swap has a Net Present Value of
zero!
PV(Fixed leg) + PV(Floating leg) = 0
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Pricing
• Floating leg is equal to notional amount at
each day of interest rate settlement (by
definition of LIBOR).
• Fixed leg can be valued by standard NPV,
since the paid amount is known.
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Credit Derivatives
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Credit Derivatives
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Forward starting swaps
• interest starts accruing at some date in the
future.
• Valuation is similar to a long swap long and
a short swap short.
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• Zero coupon swap (reinvested payments)
• Amortizing swap (decreasing notional)
• Accreting swap (increasing notional)
• Rollercoaster (variable notional)
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Amortizing swap
Decreasing notional affects coupon payments
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Unwinding an existing swap
• Enter into an offsetting swap at the
prevailing market rate.
• If we are between two reset dates the
offsetting swap will have a short first period
to account for accrued interest.
• It is important that floating payment dates
match!!
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Unwinding
8%
A
LIBOR
B
6%
A
LIBOR
C
Net of the two offsetting swaps is 2% for the
life of the contract. (sometimes novation)
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Risks of Swaps
• Interest rate risk - value of fixed side may
change
• Credit risk - default or change of rating of
counterparty
• Mismatch risk - payment dates of fixed and
floating side are not necessarily the same
• Basis risk and Settlement risk
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Credit risk of a swap contract
Default of counterparty (change of rating).
Exists when the value of swap is positive
Frequency of payments reduces the credit risk,
similar to mark to market.
Netting agreements.
Credit exposure changes during the life of a
swap.
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Duration of a swap
• Fixed leg has a long duration (approximately).
• Short leg has duration about time to reset.
Duration is a measure of price sencitivity to
interest rate changes (approximately is equal to
average time to payment).
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IRS Markets
Daily average volume of trade (notional)
1995
1998
2001
$63B
$155B
$331B
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Mark to market
• daily repricing
• collateral
• adjustments
• reduces credit exposure
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Reasons to use swaps by firms
• Lower cost of funds
• Home market effects
• Comparative advantage of highly rated firms
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Credit Derivatives
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Credit Derivatives
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Credit Derivatives
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FRM-GARP 00:47
Which one of the following deals has the
largest credit exposure for a $1,000,000 deal
size. Assume that the counterparty in each
deal is a AAA-rated bank and there is no
settlement risk.
A. Pay fixed in an interest rate swap for 1 year
B. Sell USD against DEM in a 1 year forward
contract.
C. Sell a 1-year DEM Cap
D. Purchase a 1-year Certificate of Deposit
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FRM-GARP 00:47
Which one of the following deals has the
largest credit exposure for a $1,000,000 deal
size. Assume that the counterparty in each
deal is a AAA-rated bank and there is no
settlement risk.
A. Pay fixed in an interest rate swap for 1 year
B. Sell USD against DEM in a 1 year forward
contract.
C. Sell a 1-year DEM Cap
D. Purchase a 1-year Certificate of Deposit
Credit Derivatives
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slide 31
Global Derivatives Markets 1999
Exchange traded $13.5T
IR contracts
11,669
Futures
7,914
Options
3,756
FX contracts
59
Futures
37
Options
22
Stock-index contr. 1,793
Futures
334
Options
1,459
World GDP in 99 = 30,000B
All stocks and bonds = 70,000
Liquidation value = 2,800B
Credit Derivatives
Zvi Wiener
Source
BIS
OTC Instruments $88T
IR contracts
60,091
FRAs
6,775
Swaps
43,936
Options
9,380
FX contracts
14,344
Forwards
9,593
Swaps
2,444
Options
2,307
Equity-linked contr. 1,809
Forw. and swaps
283
Options
1,527
Commodity contr. 548
Others
11,408
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Global Derivatives Markets 2001
Exchange traded $23.5T
IR contracts
21,614
Futures
9,137
Options
12,477
FX contracts
89
Futures
66
Options
23
Stock-index contr. 1,838
Futures
295
Options
1,543
Credit Derivatives
Zvi Wiener
Source
BIS
OTC Instruments $111T
IR contracts
77,513
FRAs
7,737
Swaps
58,897
Options
10,879
FX contracts
16,748
Forwards
10,336
Swaps
3,942
Options
2,470
Equity-linked contr. 1,881
Forw. and swaps
320
Options
1,561
Commodity contr. 598
Others
14,375
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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.
Credit Derivatives
Zvi Wiener
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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%
Credit Derivatives
Zvi Wiener
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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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Zvi Wiener
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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
Zvi Wiener
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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
Credit Derivatives
Zvi Wiener
slide 52
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
Credit Derivatives
Zvi Wiener
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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
Credit Derivatives
Zvi Wiener
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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
Credit Derivatives
Zvi Wiener
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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
Credit Derivatives
Zvi Wiener
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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
Credit Derivatives
Zvi Wiener
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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%
Credit Derivatives
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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
Credit Derivatives
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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
Credit Derivatives
Zvi Wiener
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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 )
Credit Derivatives
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