Managing Fixed-Income

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• Managing Fixed-Income
• Positions with OTC Derivatives

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• Hedging with OTC Derivatives
• Hedging a Series of Cash FlowsOTC Caps and
  Floors
• Financing Caps and Floors Collars and Corridors
• Other Interest Rate Derivatives
• Hedging Currency Positions with Currency Options

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3

• Hedging with OTC Derivatives

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Forward Rate Agreements (FRA)

• A forward rate agreement, FRA, requires a cash
  payment or provides a cash receipt based on the
  difference between a realized spot rate such as
  the LIBOR and a pre-specified rate.
• For example, the contract could be based on a
  specified rate of Rk 6 (annual) and the
  3-month LIBOR (annual) in 5 months and a notional
  principal, NP (principal used only for
  calculation purposes) of 10,000,000.

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Forward Contracts and Forward Rate Agreements
(FRA)

• In five months the payoff would be
• If the LIBOR at the end of five months exceeds
  the specified rate of 6, the buyer of the FRA
  (or long position holder) receives the payoff
  from the seller.
• If the LIBOR is less than 6, the seller (or
  short position holder) receives the payoff from
  the buyer.

6
Forward Contracts and Forward Rate Agreements
(FRA)

• If the LIBOR were at 6.5, the buyer would be
  entitled to a payoff of 12,267 from the seller
• If the LIBOR were at 5.5, the buyer would be
  required to pay the seller 12,297.

7
Forward Contracts and Forward Rate Agreements
(FRA)

• In general, a FRA that matures in T months and is
  written on a M-month LIBOR rate is referred to as
  a T x (TM) agreement.
• Thus, in this example the FRA is a 5 x 8
  agreement.
• At the maturity of the contract (T), the value of
  the contract, VT is

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Forward Contracts and Forward Rate Agreements
(FRA)

• FRAs originated in 1981 amongst large London
  Eurodollar banks that used these forward
  agreements to hedge their interest rate exposure.
  
• Today, FRAs are offered by banks and financial
  institutions in major financial centers and are
  often written for the banks corporate customers.
  
• They are customized contracts designed to meet
  the needs of the corporation or financial
  institution.

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Forward Contracts and Forward Rate Agreements
(FRA)

• FRAs are used by corporations and financial
  institutions to manage interest rate risk in the
  same way as financial futures are used.
• Different from financial futures, FRAs are
  contracts between two parties and therefore are
  subject to the credit risk of either party
  defaulting.
• The customized FRAs are also less liquid than
  standardized futures contracts.
• The banks that write FRAs often takes a position
  in the futures market to hedge their position or
  a long and short position in spot money market
  securities to lock in a forward rate.
• As a result, in writing the FRA, the specified
  rate Rk is often set equal to the rate implied on
  a futures contract.

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Forward Contracts and Forward Rate Agreements
(FRA)

• Example
• Suppose Kendall Manufacturing forecast a cash
  inflow of 10,000,000 in 2 months that it is
  considering investing in a Sun National Bank CD
  for 90 days.
• Sun National Banks jumbo CD pays a rate equal to
  the LIBOR.
• Currently such rates are yielding 5.5.
• Kendall is concerned that short-term interest
  rates could decrease in the next 2 months and
  would like to lock in a rate now.

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Forward Contracts and Forward Rate Agreements
(FRA)

• Example
• As an alternative to hedging its investment with
  Eurodollar futures, Sun National suggests that
  Kendall hedge with a Forward Rate Agreement with
  the following terms
• FRA would mature in 2 months (T) and would be
  written on a 90-day (3-month) LIBOR (T x (TM)
  2 x 5 agreement
• NP 10,000,000
• Contract rate Rk 5.5
• Day count convention 90/365
• Cagle would take the short position on the FRA,
  receiving the payoff from Sun National if the
  LIBOR were less than Rk 5.5
• Sun National would take the long position on the
  FRA, receiving the payoff from Cagle if the LIBOR
  were greater than Rk 5.5

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Forward Contracts and Forward Rate Agreements
(FRA)

• The exhibit slide shows Kendalls FRA receipts or
  payments and cash flows from investing the
  10,000,000 cash inflow plus or minus the FRA
  receipts or payments at possible LIBORs of 5,
  5.25, 5, 5.75, and 6.
• As shown, Kendall is able to earn a hedged rate
  of return of 5.5 from its 10,000,000 investment.

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Forward Contracts and Forward Rate Agreements
(FRA)
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Interest Rate Call

• An interest rate call, also called a caplet,
  gives the buyer a payoff on a specified payoff
  date if a designated interest rate, R, such as
  the LIBOR, rises above a certain exercise rate,
  Rx.
• On the payoff date
• If the designated rate is less than Rx, the
  interest rate call expires worthless.
• If the rate exceeds Rx, the call pays off the
  difference between the actual rate and Rx, times
  a notional principal, NP, times the fraction of
  the year specified in the contract, ?.

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Interest Rate Call

• Example
• Given an interest rate call with a designated
  rate of LIBOR, Rx 6, NP 1,000,000, time
  period of 180 days, and day-count convention of
  actual/360, the buyer would receive a 5,000
  payoff on the payoff date if the LIBOR were 7

Payoff Max.07-.06, 0(180/360)(1,000,000)
Payoff 5,000
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Interest Rate Call

• Hedging Use
• Interest rate call options are often written by
  commercial banks in conjunction with futures
  loans they plan to provide to their customers.
• The exercise rate on the option usually is set
  near the current spot rate, with that rate often
  being tied to the LIBOR.

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Hedging a Future Loan Rate with an OTC Interest
Rate Call

• Example
• Suppose a construction company plans to finance
  one of its project with a 10,000,000 90-day
  loan from Sun Bank, with the loan rate to be set
  equal to the LIBOR 100 BP when the project
  commences 60 day from now.
• Furthermore, suppose that the company expects
  rates to decrease in the future, but is concerned
  that they could increase.

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Hedging a Future Loan Rate with an OTC Interest
Rate Call

• Example
• To obtain protection against higher rates,
  suppose the company buys an interest rate call
  option from Sun Bank for 20,000 with the
  following terms
• Exercise rate 7
• Reference rate LIBOR
• Time period applied to the payoff 90/360
• Notional principal 10,000,000
• Payoff made at the maturity date on the loan (90
  days after the options expiration)
• Interest rate calls expiration T 60 days
  (time of the loan)
• Interest rate call premium of 20,000 to be paid
  at the options expiration with a 7 interest
  Cost 20,000(1 (.07)(60/360)) 20,233

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Hedging a Future Loan Rate with an OTC Interest
Rate Call

• Example
• The exhibit slide shows the company's cash flows
  from the call, interest paid on the loan, and
  effective interest costs that would result given
  different LIBORs at the starting date on the loan
  and the expiration date on the option.
• As shown in Column 6 of the slide, the company
  is able to lock in a maximum interest cost of
  8.016 if the LIBOR is 7 or greater at
  expiration, and still benefit with lower rates if
  the LIBOR is less than 7.

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Hedging a Future Loan Rate with an OTC Interest
Rate Call
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Interest Rate Put

• An interest rate put, also called a floorlet,
  gives the buyer a payoff on a specified payoff
  date if a designated interest rate, R, is below
  the exercise rate, Rx.
• On the payoff date
• If the designated rate (or reference rate) is
  more than Rx, the interest rate put expires
  worthless.
• If the reference rate is less than Rx, the put
  pays the difference between Rx and the actual
  rate times a notional principal, NP, times the
  fraction of the year, ?, specified in the
  contract.

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Interest Rate Put

• Hedging Use
• A financial or non-financial corporation that is
  planning to make an investment at some future
  date could hedge that investment against interest
  rate decreases by purchasing an interest rate put
  from a commercial bank, investment banking firm,
  or dealer.

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Hedging a CD Rate with an OTC Interest Rate Put

• Example
• Suppose the ABC manufacturing company was
  expecting a net cash inflow of 10,000,000 in 60
  days from its operations and was planning to
  invest the excess funds in a 90-day CD from Sun
  Bank paying the LIBOR.
• To hedge against interest rate decreases
  occurring 60 days from the now, suppose the
  company purchases an interest rate put
  (corresponding to the bank's CD it plans to buy)
  from Sun Bank for 10,000.

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Hedging a CD Rate with an OTC Interest Rate Put

• Example
• Suppose the put has the following terms
• Exercise rate 7
• Reference rate LIBOR
• Time period applied to the payoff ? 90/360
• Day Count Convention 30/360
• Notional principal 10 million
• Payoff made at the maturity date on the CD (90
  days from the options expiration)
• Interest rate puts expiration T 60 days
  (time of CD purchase)
• Interest rate put premium of 10,000 to be paid
  at the options expiration with a 7 interest
  Cost 10,000(1 (.07)(60/360)) 10,117

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Hedging a CD Rate with an OTC Interest Rate Put

• Example
• As shown in the exhibit slide, the purchase of
  the interest rate put makes it possible for the
  ABC company to earn higher rates if the LIBOR is
  greater than 7 and to lock in a minimum rate of
  6.993 if the LIBOR is 7 or less.

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Hedging a CD Rate with an OTC Interest Rate Put
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Hedging a CD Rate with an OTC Interest Rate Put

• Example
• If 60 days later the LIBOR is at 6.5, then the
  company would receive a payoff (90 day later at
  the maturity of its CD) on the interest rate put
  of 12,500
• The 12,500 payoff would offset the lower (than
  7) interest paid on the companys CD of
  162,500
• At the maturity of the CD, the company would
  therefore receive CD interest and an interest
  rate put payoff equal to 175,000

12,500 (10,000,000).07 - .065(90/360)
162,500 (10,000,000)(.065)(90/360)
175,000 162,500 12,500
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Hedging a CD Rate with an OTC Interest Rate Put

• Example
• With the interest-rate puts payoffs increasing
  the lower the LIBOR, the company would be able to
  hedge any lower CD interest and lock in a hedged
  dollar return of 175,000.
• Based on an investment of 10,000,000 plus the
  10,117 costs of the put, the hedged return
  equates to an effective annualized yield of
  6.993
• On the other hand, if the LIBOR exceeds 7, the
  company benefits from the higher CD rates.

6.993 (4)(175,000)/10,000,000 10,117
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Cap

• A popular option offered by financial
  institutions in the OTC market is the cap.
• A plain-vanilla cap is a series of European
  interest rate call optionsa portfolio of
  caplets.

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Cap

• Example
• A 7, 2-year cap on a 3-month LIBOR, with a NP of
  100,000,000, provides, for the next 2 years, a
  payoff every 3 months of (LIBOR -
  .07)(.25)(100M) if the LIBOR on the reset date
  exceeds 7 and nothing if the LIBOR equals or is
  less than 7.
• Note Typically, the payoff does not occur on the
  reset date, but rather on the next reset date.

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Cap

• Uses
• Caps are often written by financial institutions
  in conjunction with a floating-rate loan and are
  used by buyers as a hedge against interest rate
  risk.

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Cap

• A company with a floating-rate loan tied to the
  LIBOR could lock in a maximum rate on the loan by
  buying a cap corresponding to its loan.
• At each reset date, the company would receive a
  payoff from the caplet if the LIBOR exceeded the
  cap rate, offsetting the higher interest paid on
  the floating-rate loan on the other hand, if
  rates decrease, the company would pay a lower
  rate on its loan whereas its losses on the caplet
  would be limited to the cost of the option.
• Thus, with a cap, the company is able to lock in
  a maximum rate each quarter, and yet still
  benefit with lower interest costs if rates
  decrease.

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Floor

• A plain-vanilla floor is a series of European
  interest rate put optionsa portfolio of
  floorlets.

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Floor

• Example
• A 7, 2-year floor on a 3-month LIBOR, with a NP
  of 100,000,000, provides for the next 2 years a
  payoff every 3 months of (.07 -
  LIBOR)(.25)(100M) if the LIBOR on the reset date
  is less than 7 and nothing if the LIBOR equals
  or exceeds 7.

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Floor

• Uses
• Floors are often purchased by investors as a tool
  to hedge their floating-rate investment against
  interest rate declines.
• Thus, with a floor, an investor with a
  floating-rate security is able to lock in a
  minimum rate each period, and yet still benefit
  with higher yields if rates increase.

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• Hedging a Series of Cash Flows OTC Caps and
  Floors

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Hedging a Series of Cash Flows OTC Caps and
Floors

• We have examined how a strip of Eurodollar
  futures puts can be used to cap the rate paid on
  a floating-rate loan, and how a strip of
  Eurodollar futures calls can be used to set a
  floor on a floating-rate investment.
• Using such exchange-traded options to establish
  interest rate floors and ceiling on floating rate
  assets and liabilities, though, is subject to
  hedging risk.
• As a result, many financial and non-financial
  companies looking for such interest rate
  insurance prefer to buy OTC caps or floors that
  can be customized to meet their specific needs.

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Hedging a Series of Cash Flows OTC Caps and
Floors

• Financial institutions typically provide caps and
  floors with
• Terms that range from 1 to 5 years
• Monthly, quarterly, or semiannual reset dates
• LIBOR as the reference rate
• Notional principal and the reset dates that often
  match the specific investment or loan
• Settlement dates that usually come after the
  reset dates

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Hedging a Series of Cash FlowsOTC Caps and
Floors

• In cases where a floating-rate loan (or
  investment) and cap (or floor) come from the same
  financial institution, the loan and cap (or
  investment and floor) are usually treated as a
  single instrument so that when there is a payoff,
  it occurs at an interest payment (receipt) date,
  lowering (increasing) the payment (receipt).
• The exercise rate is often set so that the cap or
  floor is initially out of the money, and the
  payments for these interest rate products are
  usually made up front, although some are
  amortized.

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Floating Rate Loan Hedged with an OTC Cap

• Example
• Suppose the Diamond Development Company borrows
  50 million from Commerce Bank to finance a
  2-year construction project.
• Suppose
• The loan is for 2 years
• The loan starts on March 1 at a known rate of 8
• The loan rate resets every three months6/1, 9/1,
  12/1, and 3/1at the prevailing LIBOR plus 150
  bp.

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Floating Rate Loan Hedged with an OTC Cap

• In entering this loan agreement, suppose the
  company is uncertain of future interest rates and
  therefore would like to lock in a maximum rate,
  but still benefit from lower rates if the LIBOR
  decreases.

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Floating Rate Loan Hedged with an OTC Cap

• To achieve this, suppose the company buys a cap
  corresponding to its loan from Commerce Bank for
  150,000, with the following terms
• The cap consist of seven caplets with the first
  expiring on 6/1/Y1 and the others coinciding with
  the loans reset dates.
• Exercise rate on each caplet 8
• NP on each caplet 50,000,000
• Reference Rate LIBOR
• Time period to apply to payoff on each caplet
  90/360. (Typically the day count convention is
  defined by the actual number of days between
  reset date.)
• Payment date on each caplet is at the loans
  interest payment date, 90 days after the reset
  date.
• The cost of the cap 150,000 it is paid at
  beginning of the loan, 3/1/Y1.

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Floating Rate Loan Hedged with an OTC Cap

• On each reset date, the payoff on the
  corresponding caplet would be
• With the 8 exercise rate (sometimes called the
  cap rate), the Diamond Company would be able to
  lock in a maximum rate each quarter equal to the
  cap rate plus the basis points on the loan, 9.5,
  but still benefit with lower interest costs if
  rates decrease.
• This can be seen in the exhibit slide, where the
  quarterly interests on the loan, the cap payoffs,
  and the hedged and unhedged rates are shown for
  different assumed LIBORs at each reset date on
  the loan.

Payoff (50,000,000) (MaxLIBOR - .08,
0)(90/360)
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Floating Rate Loan Hedged with an OTC Cap
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Floating Rate Loan Hedged with an OTC Cap

• For the 5 reset dates from 12/1/Y1 to the end of
  the loan, the LIBOR is at 8 or higher.
• In each of these cases, the higher interest on
  the loan is offset by the payoff on the cap,
  yielding a hedged rate on the loan of 9.5 (the
  9.5 rate excludes the 150,000 cost of the cap
  the rate is 9.53 with the cost included).
• For the first 2 reset dates on the loan, 6/1/Y1
  and 9/1/Y1, the LIBOR is less than the cap rate.
  At these rates, there is no payoff on the cap,
  but the rates on the loan are lower with the
  lower LIBORs.

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Floating Rate Asset Hedged with an OTC Floor

• Example
• As noted, floors are purchased to create a
  minimum rate on a floating-rate asset.
• As an example, suppose the Commerce Bank in the
  preceding example wanted to establish a minimum
  rate or floor on the rates it was to receive on
  the 2-year floating-rate loan it made to the
  Diamond Company.

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Floating Rate Asset Hedged with an OTC Floor

• Suppose the bank purchased from another financial
  institution a floor for 100,000 with the
  following terms corresponding to its
  floating-rate asset
• The floor consist of 7 floorlets with the first
  expiring on 6/1/Y1 and the others coinciding with
  the reset dates on the banks floating-rate loan
  to the Diamond Company
• Exercise rate on each floorlet 8
• NP on each floorlet 50,000,000
• Reference Rate LIBOR
• Time period to apply to payoff on each floorlet
  90/360 Payment date on each floorlet is at the
  loans interest payment date, 90 days after the
  reset date
• The cost of the floor 100,000 it is paid at
  beginning of the loan, 3/1/Y1

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Floating Rate Asset Hedged with an OTC Floor

• On each reset date, the payoff on the
  corresponding floorlet would be
• With the 8 exercise rate, Commerce Bank would be
  able to lock in a minimum rate each quarter equal
  to the floor rate plus the basis points on the
  floating-rate asset, 9.5, but still benefit with
  higher returns if rates increase.

Payoff (50,000,000) (Max.08 - LIBOR,
0)(90/360)
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Floating Rate Asset Hedged with an OTC Floor

• In the exhibit slide, Commerce Banks quarterly
  interests received on its loan to Diamond, its
  floor payoffs, and its hedged and unhedged yields
  on its loan are shown for different assumed
  LIBORs at each reset date.

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Floating Rate Asset Hedged with an OTC Floor
51
Floating Rate Asset Hedged with an OTC Floor

• For the first two reset dates on the loan, 6/1/Y1
  and 9/1/Y1, the LIBOR is less than the floor rate
  of 8. At theses rates, there is a payoff on the
  floor that compensates for the lower interest
  Commerce receives on the loan this results in a
  hedged rate of return on the banks loan asset of
  9.5 (the rate is 9.52 with the 100,000 cost of
  the floor included).
• For the five reset dates from 12/1/Y1 to the end
  of the loan, the LIBOR equals or exceeds the
  floor rate. At these rates, there is no payoff
  on the floor, but the rates the bank earns on its
  loan are greater, given the greater LIBORs.

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• Financing Caps and Floors Collars and Corridors

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Collars

• A collar is combination of a long position in a
  cap and a short position in a floor with
  different exercise rates.
• The sale of the floor is used to defray the cost
  of the cap.
• For example, the Diamond Company in the preceding
  case could reduce the cost of the cap it
  purchased to hedge its floating rate loan by
  selling a floor.
• By forming a collar to hedge its floating-rate
  debt, the Diamond Company, for a lower net
  hedging cost, would still have protection against
  a rate movement against the cap rate, but it
  would have to give up potential interest savings
  from rate decreases below the floor rate.

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Collars

• Example
• Suppose the Diamond Company decided to defray the
  150,000 cost of its 8 cap by selling a 7 floor
  for 70,000, with the floor having similar terms
  to the cap
• Effective dates on floorlet reset date on loan
• Reference rate LIBOR
• NP on floorlets 50,000,000
• Time period for rates .25

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Collars

• By using the collar instead of the cap, the
  company reduces its hedging cost from 150,000 to
  80,000, and as shown in the exhibit slide, it
  still locked in a maximum rate on its loan of
  9.5.
• However, when the LIBOR is less than 7, the
  company has to pay on the 7 floor, offsetting
  the lower interest costs it would pay on its
  loan. For example
• When the LIBOR is at 6 on 6/1/Y1, Diamond has to
  pay 125,000 ninety days later on its short floor
  position.
• When the LIBOR is at 6.5 on 9/1/Y1, the company
  has to pay 62,500.
• These payments, in turn, offset the benefits of
  the respective lower interest of 7.5 and 8
  (LIBOR 150 bp) it pays on its floating rate
  loan.

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Collars
57
Collars

• Thus, for LIBORs less than 7, Diamond has a
  floor in which it pays an effective rate of 8.5
  (losing the benefits of lower interest payments
  on its loan) and for rates above 8 it has a cap
  in which it pays an effective 9.5 on its loan.

58
Corridor

• An alternative financial structure to a collar is
  a corridor.
• A corridor is a long position in a cap and a
  short position in a similar cap with a higher
  exercise rate.
• The sale of the higher exercise-rate cap is used
  to partially offset the cost of purchasing the
  cap with the lower strike rate.

59
Corridor

• For example, instead of selling a 7 floor for
  70,000 to partially finance the 150,000 cost
  of its 8 cap, the Diamond company could sell a
  9 cap for say 70,000.
• If cap purchasers believe there was a greater
  chance of rates increasing than decreasing, they
  would prefer the collar to the corridor as a tool
  for financing the cap.

60
Reverse Collar

• A reverse collar is combination of a long
  position in a floor and a short position in a cap
  with different exercise rates. The sale of the
  cap is used to defray the cost of the floor.
• For example, the Commerce Bank in the floor
  example could reduce the 100,000 cost of the 8
  floor it purchased to hedge the floating-rate
  loan it made to the Diamond company by selling a
  cap.
• By forming a reverse collar to hedge its
  floating-rate asset, the bank would still have
  protection against rates decreasing against the
  floor rate, but it would have to give up
  potential higher interest returns if rates
  increase above the cap rate.

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Reverse Collar

• Example
• Suppose Commerce sold a 9 cap for 70,000, with
  the cap having similar terms to the floor.
• By using the reverse collar instead of the floor,
  the company would reduce its hedging cost from
  100,000 to 30,000,
• As shown in the exhibit slide, Commerce would
  lock in an effective minimum rate on its a asset
  of 9.5 and an effective maximum rate of 10.5.

62
Reverse Collar
63
Reverse Corridor

• Instead of financing a floor with a cap, an
  investor could form a reverse corridor by selling
  another floor with a lower exercise rate.

64

• Other Interest Rate Products

65
Other Interest Rate Products

• Caps and floors are one of the more popular
  interest rate products offered by the OTC
  derivative market.
• In addition to these derivatives, a number of
  other interest rate products have been created
  over the last decade to meet the many different
  interest rate hedging needs.
• Many of these products are variations of the
  generic OTC caps and floorsexotic options two
  of these to note are barrier options and
  path-dependent options.

66
Barrier Options

• Barrier options are options in which the payoff
  depends on whether an underlying security price
  or reference rate reaches a certain level.
• They can be classified as either knock-out or
  knock-in options
• Knock-out option is one that ceases to exist once
  the specified barrier rate or price is reached.
• Knock-in option is one that comes into existence
  when the reference rate or price hits the barrier
  level.

67
Barrier Options

• Knock-out and knock-in options can be formed with
  either a call or put and the barrier level can be
  either above or below the current reference rate
  or price when the contract is established
• Down-and-out or up-and-out knock out options
• Up-and-in or down-and-in knock in options

68
Barrier Options

• Barrier caps and floors with termination or
  creation features are offered in the OTC market
  at a premium above comparable caps and floors
  without such features.

69
Barrier Options

• Down-and-out caps and floors are options that
  ceases to exist once rates hit a certain level.
• Example
• A 2-year, 8 cap that ceases when the LIBOR hits
  6.5
• A 2-year, 8 floor that ceases once the LIBOR
  hits 9

70
Barrier Options

• Up-and-in cap and florr is one that becomes
  effective once rates hit a certain level.
• Examples
• A 2-year, 8 cap that that becomes effective when
  the LIBOR hits 9
• A 2-year, 8 floor that become effective when
  rates hit 6.5

71
Path-Dependent Options

• In the generic cap or floor, the underlying
  payoff on the caplet or floorlet depends only on
  the reference rate on the effective date.
• The payoff does not depend on previous rates
  that is, it is independent of the path the LIBOR
  has taken.
• Some caps and floors, though, are structured so
  that their payoff is dependent on the path of the
  reference rate.

72
Path-Dependent Options Average Cap

• An average cap is one in which the payoff depends
  on the average reference rate for each caplet.
• If the average is above the exercise rate, then
  all the caplets will provide a payoff.
• If the average is equal or below, the whole cap
  expires out of the money.

73
Path-Dependent Options Average Cap

• Example
• Consider a one-year average cap with an exercise
  rate of 7 with four caplets.
• If the LIBOR settings turned out to be 7.5,
  7.75, 7, and 7.5, for an average of 7.4375,
  then the average cap would be in the money
  (.074375 - .07)(.25)(NP).
• If the rates, though, turned out to be 7, 7.5,
  6.5, and 6, for an average of 6.75, then the
  cap would be out of the money.

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Path-Dependent Options Q-Cap

• In a cumulative cap (Q-cap), the cap seller pays
  the holder when the periodic interest on the
  accompanying floating-rate loan hits or exceeds a
  specified level.

75
Path-Dependent Options Q-Cap

• Example
• Suppose the Diamond Company in the earlier cap
  example decided to hedge its 2-year floating rate
  loan (paying LIBOR 150bp) by buying a Q-Cap
  from Commerce Bank with the following terms (next
  2 slides)

76
Path-Dependent Options Average Cap

• Q-Cap Terms
• The cap consist of seven caplets with the first
  expiring on 6/1/Y1 and the others coinciding with
  the loans reset dates
• Exercise rates on each caplet 8
• NP on each caplet 50,000,000
• Reference Rate LIBOR
• Time period to apply to payoff on each caplet
  90/360

77
Path-Dependent Options Average Cap

• Q-Cap Terms
• For the period 3/1/Y1 to 12/1/Y1, the caplet will
  payoff when the cumulative interest starting from
  loan date 3/1/Y1 on the companys loan hits 3
  million.
• For the period 3/1/Y2 to 12/1/Y2, the caplet will
  payoff when the cumulative interest starting from
  date 3/1/Y2 on the companys loan hits 3
  million.
• Payment date on each caplet is at the loans
  interest payment date, 90 days after the reset
  date.
• The cost of the cap 125,000 it is paid at
  beginning of the loan, 3/1/Y1.

78
Path-Dependent Options Q-Cap

• The exhibit slide shows the quarterly interest,
  cumulative interests, Q-cap payments, and
  effective interests for assumed LIBORs.
• In the Q-caps first protection period, 3/1/Y1 to
  12/1/Y1, Commerce Bank will pay the Diamond
  Company on its 8 caplet when the cumulative
  interest hits 3 million.
• The cumulative interest hits the 3 million limit
  on reset date 9/1/Y1, but on that date the 9/1/Y1
  caplet is not in the money.
• On the following reset date, though, the caplet
  is in the money at the LIBOR of 8.5. Commerce
  would, in turn, have to pay Diamond 62,500 (90
  days later) on the caplet, locking in a hedged
  rate of 9.5 on Diamonds loan.

79
Path-Dependent Options Q-Cap

• In the second protection period, 3/1/Y2 to
  12/1/Y2, the assumed LIBOR rates are higher.
• The cumulative interest hits the 3 million limit
  on reset date 9/1/Y1. The caplet on that date and
  the caplet on the next reset date (12/1/Y1) are
  in the money.
• As a result, with the caplet payoffs, Diamond is
  able to obtained a hedged rate of 9.5 for the
  last 2 payment periods on its loan.

80
Path-Dependent Options Q-Cap
81
Path-Dependent Options Q-Cap

• When compared to a standard cap, the Q-cap
  provides protection for the 1-year protection
  periods, whereas the standard cap provides
  protection for each period (quarter).
• As shown in the next exhibit slide, a standard 8
  cap provides more protection than the Q-cap,
  capping the loan at 9.5 from date 12/1/Y1 to the
  end of the loan and providing a payoff on 5 of
  the 7 caplets for a total payoff of 687,500.
• In contrast, the Q-cap pays on only 3 of the 7
  caplets for a total payoff of only 500,000.
• Because of its lower protection limits, a Q-cap
  cost less than a standard cap.

82
Path-Dependent Options Q-Cap
83
Exotic Options

• Q-caps, average caps, knock-in options, and
  knock-out options are sometimes referred to as
  exotic options.
• Exotic option products are nongeneric products
  that are created by financial engineers to meet
  specific hedging needs and return-risk profiles.

84
Exotic Options

• Chooser Option Option that gives the holder the
  right to choose whether the option is a call or a
  put after a specified period of time.
•  
• Bermudan Option An option in which early
  exercise is restricted to certain dates.
•  
• Forward Start Option An option that will start
  at some time in the future.
•  
• Trigger Option An option that depends on another
  index that is, whether the option is in the
  money depends on value of another index.

85
Exotic Options

• Asian Option An option in which the payoff
  depends on the average price of the underlying
  asset during some part of the options life
  Call IV MaxSav X,0 put IV MaxX -
  Sav,0.
• Lookback Option An option in which the payoff
  depends on the minimum or maximum price reached
  during the life of the option.
•  
• Binary Option An option with a discontinuous
  payoff such as a payoff or nothing. For example
  If the price is equal or less than X, the option
  pays nothing if the price exceeds X, the option
  pays a fixed amount.
•  
• Compound Option is an option on an option Call
  on a call, call on put, put on put, and put on
  call.

86
Exotic Options

• Caption An option on a cap.
• Floortion An option on a floor.
•  
• Yield Curve Option An option between two points
  on a yield curve. For example, a yield curve
  with a exercise equal to 200 basis point on the
  difference between the yields on two-year and
  10-year notes Payoff Max(YTM10 YTM2) .02,
  0NP.