Part 2

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• Part 2 Exotic swap products
• Asset swaps
• Total return swaps
• Forward swaps
• Cancellable swaps and swaptions
• Spread-lock interest rate swaps
• Constant maturity swaps
• Credit default swaps
• Equity-linked swaps

2
Asset swaps

• Combination of a defaultable bond with an
  interest rate swap.
• B pays the notional amount upfront to acquire
  the asset swap package.

LIBOR sA
A
B
The asset swap spread sA is adjusted to ensure
that the asset swap package has an initial value
equal to the notional.
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• Asset swaps are more liquid than the underlying
  defaultable bond.
• The Asset Swap may be transacted at the time of
  the security purchase or added to a bond already
  owned by the investor.
• An asset swaption gives B the right to enter
  an asset swap package at some future date T at a
  predetermined asset swap spread sA.

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Example

1. An investor believes CAD rates will rise over the
   medium term. They would like to purchase CAD
   50million 5yr Floating Rate Notes.
2. There are no 5yr FRNs available in the market in
   sufficient size. The investor is aware of XYZ Ltd
   5yr 6.0 annual fixed coupon Bonds currently
   trading at a yield of 5.0. The bonds are
   currently priced at 104.38.
3. The investor can purchase CAD 50million Fixed
   Rate Bonds in the market for a total
   consideration of CAD 51,955,000 plus any accrued
   interest. They can then enter a 5 year Interest
   Rate Swap (paying fixed) with the Bank as follows

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Notional CAD 50,000,000
Investor Pays 6.0 annual Fixed (the coupons on the bond)
Investor Receives LIBOR plus say 50bp
Up front Payment The Bank Pays CAD 1,955,000 plus accrued bond interest to investor
The upfront payment compensates the investor for
any premium paid for the bonds. Likewise, if the
bonds were purchased at a discount, the investor
would pay the discount amount to the Bank. This
up front payment ensures that the net position
created by the Asset Swap is the same as a FRN
issued at par so that the initial outlay by the
investor is CAD 50million.
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Pricing

• From the investors viewpoint, the net cash flows
  from the Bond plus the Asset Swap are the same as
  the cash flows from a Floating Rate Note.
• The yield on the Asset Swap (in the example LIBOR
  plus 50bp), will depend upon the relationship
  between the Bond yield and the Swap Yield for
  that currency. When converting a fixed rate bond
  to floating rate, LOWER swap rates relative to
  bond yields will result in HIGHER Asset Swap
  yields. When converting FRNs to fixed rate,
  HIGHER swap rates relative to bond yields will
  result in HIGHER Asset Swap yields.
• Remark It is a common mistake to assume that the
  yield over LIBOR on the Asset Swap (50bp in the
  example above) is merely the difference between
  the Bond Yield (5) and the 5yr Swap yield. It is
  necessary to price the Asset Swap using a
  complete Interest Rate Swap pricing model.

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Target Market Any investor purchasing or holding
interest bearing securities. The Asset Swap can
either be used to create synthetic securities
unavailable in the market, or as an overlay
interest rate management technique for existing
portfolios. Many investors use Asset Swaps to
"arbitrage" the credit markets, as in many
instances synthetic FRNs or Bonds produce premium
yields compared to traditional securities issued
by the same company.
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Total return swap
Exchange the total economic performance of a
specific asset for another cash flow. A
commercial bank can hedge all credit risk on a
loan it has originated. The counterparty can gain
access to the loan on an off-balance sheet basis,
without bearing the cost of originating, buying
and administering the loan.
total return of asset
Total return receiver
Total return payer
LIBOR Y bp
Total return comprises the sum of interests, fees
and any change-in-value payments with respect to
the reference asset.
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The payments received by the total return
receiver are

• 1. The coupon of the bond (if there were one
  since the last payment date Ti - 1)
• The price appreciation
  of the underlying bond
• C since the last payment (if there were only).
• 3. The recovery value of the bond (if there were
  default).

The payments made by the total return receiver
are

• 1. A regular fee of LIBOR sTRS
• The price depreciation
  of bond C since the last
• payment (if there were only).
• 3. The par value of the bond C if there were a
  default in the meantime).

The coupon payments are netted and swaps
termination date is earlier than bonds maturity.
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Some essential features

• 1. The receiver is synthetically long the
  reference asset without having to fund the
  investment up front. He has almost the same
  payoff stream as if he had invested in risky bond
  directly and funded this investment at LIBOR
  sTRS.
• The TRS is marked to market at regular intervals,
  similar to a futures contract on the risky bond.
  The reference asset should be liquidly traded to
  ensure objective market prices for making to
  market (determined using a dealer poll
  mechanism).
• The TRS allows the receiver to leverage his
  position much higher than he would otherwise be
  able to (may require collateral). The TRS spread
  should not be driven by the default risk of the
  underlying asset but also by the credit quality
  of the receiver.

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Used as a financing tool

• The receiver wants financing to invest 100
  million in the reference bond. It approaches the
  payer (a financial institution) and agrees to the
  swap.
• The payer invests 100 million in the bond. The
  payer retains ownership of the bond for the life
  of the swap and has much less exposure to the
  risk of the receiver defaulting.
• The receiver is in the same position as it would
  have been if it had borrowed money at LIBOR
  sTRS to buy the bond. He bears the market risk
  and default risk of the underlying bond.

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Motivation of the receiver

• 1. Investors can create new assets with a
  specific maturity not currently available in the
  market.
• 2. Investors gain efficient off-balance sheet
  exposure to a desired asset class to which they
  otherwise would not have access.
• 3. Investors may achieve a higher leverage on
  capital ideal for hedge funds. Otherwise,
  direct asset ownership is on on-balance sheet
  funded investment.
• 4. Investors can reduce administrative costs via
  an off-balance sheet purchase.
• 5. Investors can access entire asset classes by
  receiving the total return on an index.

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Motivation of the payer

• The payer creates a hedge for both the price
  risk and default risk of the reference asset.
• A long-term investor, who feels that a
  reference asset in the portfolio may widen in
  spread in the short term but will recover later,
  may enter into a total return swap that is
  shorter than the maturity of the asset. This
  structure is flexible and does not require a sale
  of the asset (thus accommodates a temporary
  short-term negative view on an asset).

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• Forward swaps
• Forward swaps are executed now but begin at a
  preset future date.
• They allow asset and liability managers to
  implement their view of the yield curve. Two
  examples
• Corporations may wish to lock into forward
  rates in the belief that they will be lower than
  the spot rate at a future date but at the same
  time may wish to leave their liabilities floating
  at an attractive lower rate for a period.
• Municipalities have used them to lock in rates
  for future debt refinancing.
• Suppose a corporation wants to enter into a swap
  beginning one years time for a period of 4 years
  (one-year-by-four-year swap), the swap house will
  have to enter into two offsetting swaps
  immediately to hedge its position.

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• Swaptions
• Product nature
• The buyer of a swaption has the right to enter
  into an interest rate swap by some specified
  date. The swaption also specifies the maturity
  date of the swap.
• The buyer can be the fixed-rate receiver (put
  swaption) or the fixed-rate payer (call
  swaption).
• The writer becomes the counterparty to the swap
  if the buyer exercises.
• The strike rate indicates the fixed rate that
  will be swapped versus the floating rate.
• The buyer of the swaption either pays the
  premium upfront or can be structured into the
  swap rate.

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• TARGET MARKET
• Investors with floating rate assets may wish
  to buy Receiver Swaptions which will convert
  their assets from floating to fixed when rates
  fall below the strike.
• This strategy is similar to a Floor. While
  under a Floor the investor remains floating but
  with a guaranteed minimum level, here the asset
  is converted to a fixed rate.
• The option can also be used as a speculative
  instrument for investors who believe fixed rates
  will fall.

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• Hedge against cash flow uncertainties
• Used to hedge a portfolio strategy that uses an
  interest rate swap but where the cash flow of the
  underlying asset or liability is uncertain.
• Uncertainties come from (i) callability, eg, a
  callable bond or mortgage loan, (ii) exposure to
  default risk.
• Example
• Consider a S L Association entering into a
  4-year swap in which it agrees to pay 9 fixed
  and receive LIBOR.
• The fixed rate payments come from a portfolio
  of mortgage pass-through securities with a
  coupon rate of 9. One year later, mortgage
  rates decline, resulting in large prepayments.
• The purchase of a put swaption with a strike
  rate of 9 would be useful to offset the
  original swap position.

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Management of callable debt
Three years ago, XYZ issued 15-year fixed rate
callable debt with a coupon rate of 12.
-3 0 2
12
original bond issue
today
bond call date
bond maturity
Strategy
The issuer sells a two-year receiver option on a
10-year swap, that gives the holder the right,
but not the obligation, to receive the fixed
rate of 12.
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Call monetization
By selling the swaption today, the company has
committed itself to paying a 12 coupon for the
remaining life of the original bond. The
swaption was sold in exchange for an upfront
swaption premium received at date 0.
Company XYZ
Swap Counterparty
Swaption Premium
Pay 12 Coupon
Bondholders
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Call-Monetization Cash Flow Swaption Expiration
Date
Interest Rates ³ 12
Company XYZ
Swap Counterparty
Pay 12 Coupon
Bondholders
Interest Rates lt 12
LIBOR
Company XYZ
Swap Counterparty
12
Pay FRN Coupon at LIBOR
New Bondholders
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Disasters for the issuer
The fixed rate on a 10-year swap was below
12 in two years but its debt refunding rate in
the capital market was above 12 (due to
credit deterioration) The company would be
forced either to enter into a swap that it does
not want or liquidate the position at a
disadvantage and not be able to refinance its
borrowing profitably.
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Cancellable Swap

• One of the counterparties has the right to
  terminate the transaction on a predetermined date
  at no cost.
• If the client is the payer of the fixed rate and
  he (counterparty) has the right to cancel the
  swap, the rate paid will be higher (lower) than
  that paid under a plain vanilla Swap.
• Usually, it is Bermudan (cancellable on more than
  one date).
• A pre-agreed fixed cancellation fee can be paid
  to the client upon termination.

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Use of cancellable swaps
Assume that the following bond is available in
the secondary market
Terms of the callable bond
Issue Date 1 July 2001 Maturity 1 July 2011
(10 years) Coupon 7.00 pa annual Call
provisions Callable at the option of the issuer
commencing 1 July 2006 (5 years) and annually
thereafter on each coupon date. Initially
callable at a price of 101 decreasing by 0.50
each year and thereby callable at par on 1
July 2008 and each coupon date thereafter. Bond
price Issued at par
An investor purchases the bond and enters into
the following swap to convert the fixed rate
returns from the bond into floating rate payments
priced off LIBOR.
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Terms of the cancellable swap
Final Maturity 1 July 2011 Fixed
coupon Investor pays 7.00 pa annually (matching
the bond coupon). Floating coupon Investor
receives 6 months LIBOR 48 bps pa Swap
Termination Investor has the right to terminate
the swap commencing 1 July 2005 and each
anniversary of the swap. On each termination
date, the investor pays the following fee to
the swap counterparty Date Fee () 1
July 2006 1.00 1 July 2007 0.50 1 July
2008 to 1 July 2010 0.00
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• The swap combines a conventional interest rate
  swap (investor pays fixed rate and receives
  LIBOR) with a receiver swaption purchased by the
  investor to receive fixed rates (at 7.00 pa) and
  pay floating (at LIBOR plus 48 bps).
• The swaption is a Bermudan style exercise. The
  investor can exercise the option on any annual
  coupon date commencing 1 July 2006 (triggering a
  5 year interest rate swap) and 1 July 2010
  (triggering a 1 year interest rate swap).
• There are no initial cash flows under this swap.
  The only initial cash flow is the investment by
  the investor in the underlying bonds.

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The investors cash flow on each interest payment
date will be as follows
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If the bond is called, then the investor is paid
101 of the face value of the bond by the issuer
(assuming call on 1 July 2006). The investor
passes 1 to the dealer for the right to trigger
the swaption and cancel the original 10 year
interest rate swap. This effectively gives the
investor back 100 of its initial investment.
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• The pricing of the overall transaction
  incorporate
• Interest rate swap rate.
• Pricing of the swaption purchased by the
  investor.
• The value of the swaption may be embedded in the
  fixed rate.

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Rationale for doing these transactions

• There is a limited universe of non-callable
  fixed rate bonds.
• When interest rates decrease below the coupon,
  the bond is called. The investor is left with an
  out-of-the-money interest rate swap position
  (the swap fixed rate is above market rates).
• The swap is expensive to reverse, creating
  losses for investors. Puttable swaps are
  structured as a means of mitigating the
  potential loss resulting from early redemption
  of the asset swap.

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Callable debt management
In August 1992 (two years ago), a corporation
issued 7-year bonds with a fixed coupon rate of
10 payable semiannually on Feb 15 and Aug 15 of
each year. The debt was structured to be
callable (at par) offer a 4-year deferment
period and was issued at par value of 100
million. In August 1994, the bonds are
trading in the market at a price of 106,
reflecting the general decline in market
interest rates and the corporations recent
upgrade in its credit quality.
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Question
The corporate treasurer believes that the current
interest rate cycle has bottomed. If the bonds
were callable today, the firm would realize a
considerable savings in annual interest expense.
Considerations The bonds are still in their
call protection period. The treasurers fear is
that the market rate might rise considerably
prior to the call date in August
1996. Notation T 3-year Treasury yield that
prevails in August, 1996 T BS refunding rate
of corporation, where BS is the company
specific bond credit spread T SS prevailing
3-year swap fixed rate, where SS stands for
the swap spread
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Strategy I. Sell a receiver swaption at a strike
rate of 9.5 expiring in
two years. Initial cash flow Receive 2.50
million (in-the-money swaption) August 1996
decisions Gain on refunding (per settlement
period) 10 percent (T BS) if T BS lt 10
percent, 0
if T BS ³ 10 percent. Loss on unwinding the
swap (per settlement period) 9.50 percent
(T SS) if T SS lt 9.50 percent,
0 if T SS ³ 9.50
percent . With BS 1.00 percent SS 0.50
percent, these gains and losses in 1996 are
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Gain on Refunding
Gains
If BS goes up
T
9
If SS goes down
Losses
Loss on selling receiver swaption
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Net Gain
Gains
T
9
If SS goes down or BS goes up
Losses
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Comment on the strategy By
selling the receiver swaption, the company has
been able to simulate the sale of the embedded
call feature of the bond, thus fully monetizing
that option. The only remaining uncertainty is
the basis risk associated with unanticipated
changes in swap and bond spreads.
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Strategy II. Enter an off-market forward swap as
the fixed rate payer Agreeing to pay 9.5
(rather than the at-market rate of 8.55) for a
three-year swap, two years forward. Initial
cash flow Receive 2.25 million since the the
fixed rate is above the at-market rate. Assume
that the corporations refunding spread remains
at its current 100 bps level and the 3-year swap
spread over Treasuries remains at 50 bps, then
the annual reduction in interest rate expense
after refunding 10 - (T 1.0) if
the firm is able to refund 0
if it is not. The gain (or loss) on
unwinding the swap is the fixed rate at that
time T 0.5 - 9.5. The two effects offset
each other, given the assumed spreads. The
corporation has effectively sold the embedded
call option for 2.25m.
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Gains and losses August
1996 decisions Gain on refunding (per
settlement period) 10 percent (T BS) if
T BS lt 10 percent, 0
if T BS ³ 10 percent. Gain (or
loss) on unwinding the swap (per settlement
period) - 9.50 percent (T SS) if T SS
lt 9.50 percent, (T SS) 9.50 percent
if T SS ³ 9.50 percent. Assuming that BS
1.00 percent, SS 0.50 percent, these gains and
losses in 1996 are
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Callable Debt Management with a Forward Swap
Gain on Refunding
Gain on Unwinding Swap
Gains
If BS goes up
T
9
If SS goes down
Losses
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Net Gain
Gains
T
9
If SS goes down or BS goes up
Losses
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Comment on the
strategy Since the company stands to gain in
August 1996 if rates rise, it has not fully
monetized the embedded call options. This is
because a symmetric payoff instrument (a forward
swap) is used to hedge an asymmetric payoff
(option) problem.
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• Spread-lock interest rate swaps
• Enables an investor to lock in a swap spread and
  apply it to
• an interest rate swap executed at some point in
  the future.
• The investor makes an agreement with the bank on
• swap spread, (ii) a Treasury rate.
• The sum of the rate and swap spread equals the
  fixed rate paid by the investor for the life of
  the swap, which begins at the end of the three
  month (say) spread-lock.
• The bank pays the investor a floating rate. Say,
  3-month LIBOR.

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Example

• The current 5yr swap rate is 8 while the 5yr
  benchmark government bond rate is 7.70, so the
  current spread is 30bp an historically low level.
  
• A company is looking to pay fixed using an
  Interest Rate Swap at some point in the year. The
  company believes however, that the bond rate will
  continue to fall over the next 6 months. They
  have therefore decided not to do anything in the
  short term and look to pay fixed later.
• It is now six months later and as they predicted,
  rates did fall. The current 5 yr bond rate is now
  7.40 so the company asks for a 5 yr swap rate
  and is surprised to learn that the swap rate is
  7.90. While the bond rate fell 30bp, the swap
  rate only fell 10bp. Why?

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• Explanations
• The swap spread is largely determined by demand
  to pay or receive fixed rate.
• As more parties wish to pay fixed rate, the
  "price" increases, and therefore the spread over
  bond rates increases.
• It would appear that as the bond rate fell,
  more and more companies elected to pay fixed,
  driving the swap spread from 30bp to 50bp.
• While the company has saved 10bp, it could have
  used a Spread-lock to do better.

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• When the swap rate was 8 and the bond yield
  7.70, the company could have asked for a six
  month Spread-lock on the 5yr Swap spread.
• While the spot spread was 30bp, the 6mth
  forward Spread was say 35bp.
• The company could "buy" the Spread-lock for six
  months at 35bp. At the end of the six months,
  they can then enter a swap at the then 5yr bond
  yield plus 35bp, in this example a total of
  7.75. The Spread-lock therefore increases the
  saving from 10bp to 25bp.

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• A Spread-lock allows the Interest Rate Swap user
  to lock in the forward differential between the
  Interest Rate Swap rate and the underlying
  Government Bond Yield (usually of the same or
  similar tenor).
• The Spread-lock is not an option, so the buyer is
  obliged to enter the swap at the maturity of the
  Spread-lock.

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CONSTANT MATURITY SWAP

• An Interest Rate Swap where the interest rate on
  one leg is reset periodically but with reference
  to a market swap rate rather than LIBOR.
• The other leg of the swap is generally LIBOR but
  may be a fixed rate or potentially another
  Constant Maturity Rate.
• Constant Maturity Swaps can either be single
  currency or Cross Currency Swaps. The prime
  factor therefore for a Constant Maturity Swap is
  the shape of the forward implied yield curves.

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EXAMPLE Investors perspective

• The GBP yield curve is currently positively
  sloped with the current 6mth LIBOR at 5.00 and
  the 3yr Swap rate at 6.50, the 5yr swap at 8.00
  and the 7yr swap at 8.50.
• The current differential between the 3yr swap and
  6mth LIBOR is therefore 150bp.
• The investor is unsure as to when the expected
  flattening will occur, but believes that the
  differential between 3yr swap and LIBOR (now
  150bp) will average 50bp over the next 2 years.

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In order to take advantage of this view, the
investor can use the Constant Maturity Swap.
They can enter the following transaction for 2
years  
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• Each six months, if the 3yr Swap rate is less
  than 105bp, the investor will receive a net
  positive cashflow, and if the differential is
  greater than 105bp, pay a net cashflow.
• As the current spread is 150bp, the investor will
  be required to pay 45bp for the first 6 months.
  It is clear that if the investor is correct and
  the differential does average 50bp over the two
  years, this will result in a net flow of 55bp to
  the investor.
• The advantage is that the timing of the narrowing
  within the 2 years is immaterial, as long as the
  differential averages less than 105bp, the
  investor "wins".

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Example Corporate perspective

• A Swedish company has recently embraced the
  concept of duration and is keen to manage the
  duration of its debt portfolio.
• In the past, the company has used the Interest
  Rate Swap market to convert LIBOR based funding
  into fixed rate and as swap transactions mature
  has sought to replace them with new 3, 5 and 7yr
  swaps.
• The debt duration of the company is therefore
  quite volatile as it continues to shorten until
  new transactions are booked when it jumps higher.

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The Constant Maturity Swap can be used to
alleviate this problem. If the company is
seeking to maintain duration at the same level as
say a 5 year swap, instead of entering into a 5
yr swap, they can enter the following Constant
Maturity swap  
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• The tenor of the swap is not as relevant, and in
  this case could be for say 5 years. The
  "duration" of the transaction is almost always at
  the same level as a 5yr swap and as time goes by,
  the duration remains the same unlike the
  traditional swap.
• So here, the duration will remain around 5yrs for
  the life of the Constant Maturity Swap,
  regardless of the tenor of the transaction.
• The tenor however, may have a dramatic effect on
  the pricing of the swap, which is reflected in
  the premium or discount paid (in this example a
  discount of 35bp).

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Credit default swaps
The protection seller receives fixed periodic
payments from the protection buyer in return for
making a single contingent payment covering
losses on a reference asset following a default.
140 bp per annum
protection seller
Credit event payment (100 ? recovery rate) only
if credit event occurs
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Protection seller earns investment income with
no funding cost gains customized, synthetic
access to the risky bond Protection
buyer hedges the default risk on the reference
asset 1. Very often, the bond tenor is longer
than the swap tenor. In this way, the
protection seller does not have exposure to the
full market risk of the bond. 2. Basket default
swap - gain additional yield by selling
default protection on several assets.
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A bank lends 10mm to a corporate client at L
65bps. The bank also buys 10mm default
protection on the corporate loan for
50bps. Objective achieved maintain
relationship reduce credit risk on a new loan
Default Swap Premium
Corporate Borrower
Interest and Principal
Financial House
If Credit Event obligation (loan)
Bank
Default Swap Settlement following Credit Event of
Corporate Borrower
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Funding cost arbitrage Credit default swap
Lender to the AAA-rated Institution
A-rated institution as Protection Seller
AAA-rated institution as Protection Buyer
LIBOR-15bps as funding cost
50bps annual premium
funding cost of LIBOR 50bps
coupon LIBOR 90bps
BBB risky reference asset
Lender to the A-rated Institution
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• The combined risk faced by the Protection Buyer
• default of the BBB-rated bond
• default of the Protection Seller on the
  contingent payment
• The AAA-rated Protection Buyer creates a
  synthetic AA-asset with
• a coupon rate of LIBOR 90bps - 50bps LIBOR
  40bps.
• This is better than LIBOR 30bps, which is the
  coupon rate of a
• AA-asset (net gains of 10bps).

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For the A-rated Protection Seller, it gains
synthetic access to a BBB-rated asset with
earning of net spread of
50bps - (LIBOR 90bps) - (LIBOR 50bps)
10bps
the A-rated Protection Seller earns 40bps if it
owns the BBB asset directly
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In order that the credit arbitrage works, the
funding cost of the default protection seller
must be higher than that of the default
protection buyer.
Example
Suppose the A-rated institution is the Protection
buyer, and assume that it has to pay 60bps for
the credit default swap premium (higher premium
since the AAA-rated institution has lower
counterparty risk). The net loss of spread
(60 - 40) 20bps.
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Supply and demand drive the price
Credit Default Protection Referencing a 5-year
Brazilian Eurobond (May 1997)
Chase Manhattan Bank 240bps Broker
Market 285bps JP Morgan 325bps
It is very difficult to estimate the recovery
rate upon default.

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Credit default exchange swaps
Two institutions that lend to different regions
or industries can diversify their loan portfolios
in a single non-funded transaction - hedging the
concentration risk on the loan portfolios.
contingent payments are made only if credit
event occurs on a reference asset periodic
payments may be made that reflect the different
risks between the two reference loans
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Counterparty risk
Before the Fall 1997 crisis, several Korean banks
were willing to offer credit default protection
on other Korean firms.
40 bp
US commercial bank
Korea exchange bank
LIBOR 70bp
Hyundai (not rated)
Political risk, restructuring risk and the risk
of possible future war lead to potential high
correlation of defaults.

Advice Go for a European bank to buy the
protection.
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Risks inherent in credit derivatives
counterparty risk counterparty could renege
or default legal risk - arises from ambiguity
regarding the definition of default liquidity
risk thin markets (declines when markets become
more active) model risk probabilities of
default are hard to estimate
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Market efficiencies provided by credit
derivatives
1. 2. 3.
Absence of the reference asset in the negotiation
process - flexibility in setting terms that meet
the needs of both counterparties. Short sales of
credit instruments can be executed with
reasonable liquidity - hedging existing exposure
or simply profiting from a negative credit view.
Short sales would open up a wealth of arbitrage
opportunities. Offer considerable flexibilities
in terms of leverage. For example, a hedge fund
can both synthetically finance the position of a
portfolio of bank loans but avoid the
administrative costs of direct ownership of the
asset.
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Auto-Cancellable Equity Linked Swap
Contract Date June 13, 2003 Effective Date
June 18, 2003 Termination Date The earlier of
(1) June 19, 2006 and (2) the Settlement Date
relating to the Observation Date on which the
Trigger Event takes place (maturity
uncertainty).
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Trigger Event The Trigger Event is deemed to
be occurred when the closing price of the
Underlying Stock is at or above the Trigger Price
on an Observation Date. Observation Dates 1.
Jun 16, 2004, 2. Jun 16, 2005, 3. Jun 15, 2006
Settlement Dates With respect to an
Observation Date, the 2nd business day after such
Observation Date.
72
Underlying Stock HSBC (0005.HK) Notional HKD
83,000,000.00 Trigger Price HK95.25
Party A pays For Calculation Period 1 4
3-month HIBOR 0.13, For Calculation Period 5
12 3-month HIBOR - 0.17
Party B pays On Termination Date, 8 if the
Trigger Event occurred on Jun 16, 2004 16 if
the Trigger Event occurred on Jun 16, 2005 24
if the Trigger Event occurred on Jun 15, 2006
or 24 if the Trigger Event occurred on Jun 15,
2006 or 0 if the Trigger Event never occurs.
Final Exchange Applicable only if the Trigger
Event has never occurred Party A pays Notional
Amount Party B delivers 1,080,528 shares of the
Underlying Stock
Interest Period Reset Date 18th of Mar, Jun,
Sep, Dec of each year Party B pays Party A an
upfront fee of HKD1,369,500.00 (i.e. 1.65 on
Notional) on Jun 18, 2003.
73
Model Formulation

• This swap may be visualized as an auto
  knock-out equity forward with terminal payoff
• 1,080,528 x terminal stock price
  - Notional.
• Modeling of the equity risk The stock price
  follows the trinomial random walk. The clock
  of the stock price trinomial tree is based on
  trading days. When we compute the drift rate of
  stock and equity discount factor, one year
  is taken as the number of trading days in a year.
  
• The net interest payment upon early termination
  is considered as knock-out rebate. The
  contribution of the potential rebate to the swap
  value is given by the Net Interest Payment
  times the probability of knock-out.
• The Expected Net Interest Payment is calculated
  based on todays yield curve. Linear
  interpolation on todays yield curve is used to
  find the HIBOR at any specific date. The
  dynamics of interest rate movement has been
  neglected for simplicity since only Expected Net
  Interest Payment (without cap or floor feature)
  appears as rebate payment.

74
Quanto version
Underlying Stock HSBC (0005.HK) Notional USD
10,000,000.00 Trigger Price HK95.25
Party A pays For Calculation Period 1 4
3-month LIBOR For Calculation Period 5 12
3-month LIBOR - 0.23,
Party B pays On Termination Date, 7 if the
Trigger Event occurred on Jun 16, 2004 14 if
the Trigger Event occurred on Jun 16, 2005 21
if the Trigger Event occurred on Jun 15, 2006
or 0 if the Trigger Event never occurs.
75
Final Exchange Applicable only if the Trigger
Event has never occurred Party A pays Notional
Amount Party B delivers Number of Shares of the
Underlying Stock
Number of Shares Notional x USD-HKD Spot
Exchange Rate on Valuation Date / Trigger Price
Interest Period Reset Date 18th of Mar, Jun,
Sep, Dec of each year
Party B pays Party A an upfront fee of
USD150,000.00 (i.e. 1.5 on Notional) on Jun 18,
2003.
76
Model Formulation

• By the standard quanto prewashing technique,
  the drift rate of the HSBC stock in US currency
  rHK - qS - r sS sF ,

where rHK riskfree interest rate of HKD
qS dividend yield of stock r
correlation coefficient between stock price
and exchange rate sS annualized volatility
of stock price sF annualized volatility of
exchange rate

• Terminal payoff (in US dollars)
• Notional / Trigger Price (HKD) x terminal
  stock price (HKD) - Notional.

• The exchange rate F does not enter into the
  model since the payoff in US dollars does not
  contain the exchange rate. The volatility of F
  appears only in the quanto-prewashing formula.

77
Worst of two stocks
Contract Date June 13, 2003 Effective Date June
18, 2003
Underlying Stock The Potential Share with the
lowest Price Ratio with respect to each of the
Observation Dates.
Price Ratio In respect of a Potential Share, the
Final Share Price divided by its Initial Share
Price.
Final Share Price Closing Price of the Potential
Share on the Observation Date
Party A pays For Calculation Period 1 4
3-month HIBOR 0.13, For Calculation Period 5
12 3-month HIBOR - 0.17,
78
Party B pays On Termination Date, 10 if the
Trigger Event occurred on Jun 16, 2004 20 if
the Trigger Event occurred on Jun 16, 2005 30
if the Trigger Event occurred on Jun 15, 2006
or 0 if the Trigger Event never occurs.
Final Exchange Applicable only if the Trigger
Event has never occurred Party A pays Notional
Amount Party B delivers Number of Shares of the
Underlying Stock as shown above
Interest Period Reset Date 18th of Mar, Jun,
Sep, Dec of each year
Party B pays Party A an upfront fee of
HKD1,369,500.00 (i.e. 1.65 on Notional) on Jun
18, 2003.