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Options _ Caps_ Floors and More

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					Options, Caps, Floors and
 More Complex Swaps
   The Nature of Options on
   Financial Futures
 An option is an agreement between two parties
  in which one gives the other the right, but not
  the obligation, to buy or sell a specific asset at a
  set price for a specified period of time.
 The buyer of an option pays a premium for the
  opportunity to decide whether to carry out the
  transaction (exercise the option) when it is
  beneficial.
 The option seller (option writer) receives the
  initial option premium and is obligated to carry
  out the transaction if and when the buyer
  exercises the option.
Two Types of Options
 Call option
    The buyer of the call has the right to buy the underlying
     asset at a specific strike price for a set period of time.
    The seller of the call option is obligated to deliver the
     underlying asset to the buyer when the buyer exercises
     the option.
 Put option
    The buyer has the right to sell the underlying asset at a
     specific strike price for a set period of time.
    The seller of a put option is obligated to buy the
     underlying asset when the put option buyer exercises
     the option.
  Options Versus Futures
 In a futures contract, both parties are obligated
  to carry out the transaction
 An option contract gives the buyer (holder) the
  right, but not the obligation, to buy or sell an
  asset at some specified price:
      call option, the right to buy
      put option, the right to sell
 Exercise or strike price:
      the price at which the transaction takes place
 Expiration date:
      the last day on which the option can be used
   Option Valuation
 Theoretical Value of the option:
   Vo    = max( Va - E, 0)

   Va     = Market price of the asset
   E      = Strike or exercise price


 Example:
    Option to buy a house at $100,000
    If market value is $120,000:
     V0 = max( 120,000 - 100,000, 0) = 20,000
    If market value is 80,000:
     V0 = Ø
Options, Market Prices and
Strike Prices
 As long as there is some time to expiration, it is
  possible for the market value of the option to be
         greater than its theoretical value.

              Call Options                      Put Options
 Out of the Money                  Out of the Money
    Market price < Strike price       Market price > Strike price
 At the Money                      At the Money
    Market price = Strike price       Market price = Strike price
 In the Money                      In the Money
    Market price > Strike price       Market price < Strike price
Option Value: Time and Volatility

  The longer the period of time to expiration, the
   greater the value of the option:
      more time in which the option may have value
      the further away is the exercise price, the further
       away you must pay the price for the asset
  The greater the possibility of extreme outcomes,
   the greater the value of the option
      volatility
 Options on 90-Day
                                                  Each option's price, labeled the
 Eurodollar Futures,                               premium, reflects the consensus
                                                   view of the value of the position.
 June 29, 1998                                    Intrinsic value equals the dollar value
                                                   of the difference between the current
               Option Premiums*
                                                   market price of the underlying
                     Calls              Puts       Eurodollar future and the strike price
Strike Price Sept.        Dec.    Sept.      Dec.  or zero, whichever is greater.
9375            0.56     0.54      0.00     0.03  The time value of an option equals
9400            0.32     0.29      0.01     0.07   the difference between the option
9425            0.09     0.03      0.03     0.11
9450            0.02     0.01      0.21     0.35   price and the intrinsic value.
9475            0.00     0.00      0.44     0.58  In the case of the September call at
9500            0.00     0.00      0.69     0.80   93.75, the premium equals $1,400,
Friday volume: 25,987 calls; 13,297 puts           so the time value of the option is
Open interest: Friday, 1,192,154 calls; 885,495
puts                                               zero.
90-Day Eurodollar Futures Prices (Rates), June 29,
1998.
    September 1998: 94.31 (5.69%)
    December 1998: 94.26 (5.74%)
Face value of futures contract is $1,000,000.
Premium is stated as a percent, where 0.01 equals
1 basis point. Each basis point is worth $25 per
contract.
   Option Premiums
 The option premium equals the intrinsic value of the
  option plus the time value:
      premium = intrinsic value + time value
 The intrinsic value and premium for call options with the
  same expiration but different strike prices, decreases as
  the strike price increases.
      the higher is the strike price, the greater is the price the call
       option buyer must pay for the underlying futures contract at
       exercise
 The time value of an option increases with the length of
  time until option expiration
      the market price has a longer time to reach a profitable level
       and move favorably
   Profit or Loss in a Futures Position


                 +   Buy Eurodollar futures       Sell Eurodollar futures
 Loss or Profit 




                                              0

                            Price of Futures when purchased
                 -

                           Value of the Asset --------->
Buying or Selling a Futures Position

  Institutional traders buy and sell futures
   contracts to hedge positions in the cash market.
  As the futures price increases, corresponding
   futures rates decrease.
  Both buyers and sellers can lose an unlimited
   amount
       Given the historical range of futures price
        movements and the short-term nature of the
        futures contracts, actual prices have not varied all
        the way to zero or 100.
  Trading Call Options
 Buying a call option
   the buyer’s profit equals the eventual futures
    price minus the strike price and the initial call
    premium
   compared with a pure long futures position, the
    buyer of a call option on the same futures
    contract faces less risk of loss if futures prices fall
    yet realizes the same potential gains if prices
    increase
 Selling a call option
   the seller’s profit is a maximum of the premium
    less the eventual futures price minus the strike
    price
   compared with a pure short futures position, the
    seller of a call option faces less potential gain if
    futures prices fall yet realizes the same potential
    losses if prices increase
 Trading Put Options
 Buying a put option
   a put option limits losses to the option premium,
    while a pure futures sale exhibits greater loss
    potential
   comparable to the direct short sale of a futures
    contract, the buyer of a put option faces less risk of
    loss if futures prices increase yet realizes the same
    potential gains if prices fall
 Selling a put option
   a put option limits gains to the option premium,
    while a pure futures sale exhibits greater gain
    potential
   comparable to pure long futures position, the buyer
    of a put option faces less potential gain if futures
    prices increase yet realizes the same potential loss
    if prices fall
  Profit or Loss in an Option Position
                         Buy Call Option               Buy Put Option
              +
                              E   E+P                     E+P   E
 Loss or Gain 




                                                  0
                                   Premium Paid

                            Premium Received
                         Write Call Option             Write Put Option


                                                  0
                              E   E+P                     E+P   E
              -
                             Value of the Asset --------->
                   E - exercise or strike price       P - Price of the asset
The Use of Options on Futures
By Commercial Banks
 Commercial banks can use financial futures
  options for the same hedging purposes as
  they use financial futures.
 Managers must first identify the bank’s
  relevant interest rate risk position.
  Positions That Profit From
  Rising Interest Rates
 Suppose that a bank would be adversely
  affected if the level of interest rates increases.
 This might occur because the bank has a
  negative GAP or a positive duration gap, or
  simply anticipates issuing new CDs in the near
  term.
 A bank has three alternatives that should reduce
  the overall risk associated with rising interest
  rates:
     sell financial futures contracts directly
     sell call options on financial futures
     buy put options on financial futures
   Profit and Loss Potential on Futures,
   Options on Futures Positions, and
   Basic Interest Rate Swaps
Generate Profits if Futures Rates Rise
Transaction                      Potential Profit                Potential Loss
Sell financial futures                  Unlimited               Unlimited
Sell call options on futures            Limited to call premium Unlimited
Buy put options on futures              Unlimited               Limited to put premium
Generate Profits if Futures Rates Fall
Transaction                      Potential Profit                Potential Loss
Buy financial futures                   Unlimited                Unlimited
Buy call options on futures             Unlimited                Limited to call premium
Sell put options on futures             Limited to put premium   Unlimited
Generate Profits if Floating Rates Rise: Basic Interest Rate Swap
Transaction                       Potential Profit        Potential Loss
Pay fixed rate, receive floating rate   Unlimited                Unlimited
Generate Profits if Floating Rates Fall. Basic Interest Rate Swaps
Transaction                       Potential Profit       Potential Loss
Pay floating rate, receive fixed rate Unlimited                Unlimited
NOTE: Profits and losses are limited when futures rates equal 0 % and 100%
Futures versus Options Positions

 A final important distinction is the cash flow
  requirement of each type of position.
      The buyer of a call or put option must
       immediately pay the premium.
      There are no margin requirements for long
       positions.
      The seller of a call or put option immediately
       receives the premium, but must post initial
       margin and is subject to margin calls because
       the loss possibilities are unlimited.
      All futures positions require margin.
   Using Options on Futures to
   Hedge Borrowing Costs
 Borrowers in the commercial loan market and mortgage
  market often demand fixed-rate loans.
 How can a bank agree to make fixed-rate loans when it
  has floating-rate liabilities?
      The bank initially finances the loan by issuing a $1 million
       3-month Eurodollar time deposit.
      After the first three months, the bank expects to finance
       the loan by issuing a series of 3-month Eurodollar
       deposits timed to coincide with the maturity of the
       preceding deposit.


6/98             9/98           12/98          3/99              6/99
                        Loan yield 8.0%
 Issue 3m        Issue 3m      Issue 3m        Issue 3m
Euro 5.5%         Euro ?        Euro ?           Euro?
      Using Futures to
      Hedge Borrowing Costs
3-Month Eurodollar Cash and Futures Rates
June 29, 1998                   Initial Basis
3-month cash rate = 5.50%       Dec. contract: 5.74% - 5.50% = 0.24%
Dec 98 futures rate = 5.74%     Mar. contract: 5.69% - 5.50% = 0.19%
Mar 99 futures rate = 5.69%     Jun. contract: 5.72% - 5.50% = 0.22%
Jun 99 futures rate = 5.72%
September 28, 1998
3-month cash rate = 5.95%
Dec 98 futures rate = 6.21%
December 28, 1998
3-month cash rate = 5.30%
Mar. 99 futures rate = 5.60%
March 29, 1999
3-month cash rate = 7.41%
Jun. 99 futures rate = 7.20%
Using Futures to Hedge Borrowing Costs
   Date      Cash Market                      Futures Market                      Basis
   6/29/98   Bank issues $1 million in 3-   Bank sells 1 Dec ’98 Eurodollar future at
             month Eurodollars at 5.50%.    5.74%; 1 Mar. ’99 Eurodollar future at
                                            5.69%; 1 Jun. ’98 Eurodollar future at
                                            5.72%.
   9/28/98 Bank issues 1 million in 3-month Bank buys 1 Dec. ’98 Eurodollar        0.26%
            Eurodollars at 5.95%.           future at 6.21%.
            Opportunity loss = 45 x $25 =   Profit = 47 x $25 = $1,175
            $1,125
   12/28/98 Bank issues $1 million in 3-    Bank buys 1 Mar. ’99 Eurodollar        0.30%
            month Eurodollars at 5.30%.     future at 5.60%.
            Opportunity gain = 20 x $25 =   Loss = 9 x $25 = $225
            $500
   3/29/99 Bank issues $1 million in 3-     Bank buys 1 Jun. ’99 Eurodollar        0.06%
            month Eurodollars at 7.14%.     future at 7.20%
            Opportunity loss = 164 x $25 =  Profit = 148 x $25 = $3,700
            $4,100
   Effective Cost of Borrowing
             Eurodollar Issue Date            Cost = initial cash rate - Basis
             6/29/98                          5.50%
             9/28/98                          5.50% 2 (0.26% - 0.24%)             = 5.48%
             12/28/98                         5.50% 2 (0.30% - 0.19%)             = 5.39%
             3/29/99                          5.50% 2 (0.06% - 0.22%)             = 5.66%
                                                      Average                       5.51%
   Hedging with Options on Futures

 A participant who wants to reduce the risk associated
  with rising interest rates can buy put options on financial
  futures.
      The purchase of a put option essentially places a cap on
       the bank’s borrowing cost.
      If futures rates rise above the strike price plus the premium
       on the option, the put will produce a profit that offsets
       dollar for dollar the increased cost of cash Eurodollars.
      If futures rates do not change much or decline, the option
       may expire unexercised and the bank will have lost a
       portion or all of the option premium.
Profit   A. Buy: December 1998 Put Option; Strike Price= 94.25
                                                                                     Profit Diagrams for
                                                                                     Put Options on
                     (6.21%)
                    F1 = 93.79      94.25
                                                                                     Eurodollar Futures,
    0                                                             Futures
                                                                  Prices
                                                                                     January 6, 1998
                                      94.26 = Futures Price (F)
                           94.14
20.11                     (5.86%)
                                                                            Profit                                              =
                                                                                      B. Buy: March 1999 Put Option; Strike Price 94.25*
Loss
                                                    94.25*
         C. Buy: June 1999 Put Option; Strike Price =                                                                    (5.60%)
Profit                                                                                                         94.25 F1 = 94.40            Futures
                                                                                0
                                                                                                                                           Prices
                                                                                                                 F = 94.31
               (7.20%)                                                                                94.01
            F1 = 92.80              94.25                         Futures 20.24                      (5.99%)
    0
                                                                  Prices
                                     F = 94.28                             Loss
                          93.87
20.38                    (6.13%)

Loss
 Buying Put Options On Eurodollar
 Futures To Hedge Borrowing Costs

3-Month Eurodollar Futures Rates and Put Option Premiums for the 94.25 Strike Price
June 29, 1998                                 Option Premiums
December 1998 futures rate = 5.74%             December 1998 Put at 94.25 = 0.11
March 1999 futures rate = 5.69%                March 1999 Put at 94.25 = 0.24
June 1999 futures rate = 5.72%                 June 1999 Put at 94.25 = 0.38
September 28, 1998
3-month cash rate = 5.95%                      December 1998 Put at 94.25 = 0.51
December 1998 futures rate = 6.21%
December 28, 1.998
3-month cash rate = 5.30%                      March 1999 Put at 94.25 = 0.12
March 1999 futures rate = 5.60%
March 29, 1999
3-month cash rate = 7.14%                      June 1999 Put at 94.25 = 1.45
June 1999 futures rate = 7.20%
    Buying Put Options On Eurodollar Futures
    To Hedge Borrowing Costs
Date        Cash Market                                Put Options
6/29/98     Bank issues $1 million in 3-month          Bank buys one December 1998 put on Eurodollar
            Eurodollars at 5.50%                       futures with strike = 94.25 for 0.11; one March 1999
                                                       put on Eurodollar futures with strike = 94.25 for 0.24;
                                                       one June 1999 put on Eurodollar futures with strike =
                                                       94.25 for 0.38.
9/28/98     Bank issues $1 million in 3-month          December 1998 Eurodollar futures rate = 6.21 Bank
            Eurodollars at 5.95%                       sells December 1998 put option for 0.51;
            Opportunity loss = 45 x $25 = $1,125       receives $1,275 [ in value = +0.40]
12/28/98    Bank issues $1 million in 3-month          March 1999 Eurodollar futures rate = 5.60%; Bank
            Eurodollars at 5.30%.                      sells March 1999 put option for 0.12;
            Opportunity gain = 20 X $25 = $500         receives $300 [ in value = -0.12]
3/29/99     Bank issues $1 million in 3-month          June 1999 Eurodollar futures rate = 7.20%; Bank sells
            Eurodollars at 7.14%                       June 1999 put option for 1.45;
            Opportunity loss = 164 x $25 = $4,100      receives $3,625 [ in value +1.07]



Effective Cost of Borrowing
Eurodollar Issue Date *     Cost = Initial cash rate -  in value of cash -  in value of option

6/29/98                        5.50%
9/28/98                        5.50% + 0.45% - 0.40%                                                  = 5.55%
12/28/98                       5.50% - 0.20% + 0.12%                                                  = 5.42%
3/29/99                        5.50% + 1.64% - 1.07%                                                  = 6.07%
                               Average                                                                  5.64%
INTEREST RATE CAPS, FLOORS
AND COLLARS
 The purchase of a put option on Eurodollar futures
  essentially places a cap on the bank's borrowing
  cost.
 The advantage of a put option is that for a fixed price,
  the option premium, the bank can set a cap on its
  borrowing costs, yet retain the possibility of benefiting
  from rate declines.
 If the bank is willing to give up some of the profit
  potential from declining rates, it can reduce the net
  cost of insurance by accepting a floor, or minimum
  level, for its borrowing cost.
Interest Rate Caps and Floors
 Interest rate cap
    an agreement between two counterparties that
     limits the buyer's interest rate exposure to a
     maximum rate
    the cap is actually the purchase of a call
     option on an interest rate
 Interest rate floor
    an agreement between two counterparties that
     limits the buyer's interest rate exposure to a
     minimum rate
    the floor is actually the purchase of a put
     option on an interest rate
Interest Rate Cap
 A series of consecutive long call options (caplets) on
  a specific interest rate at the same strike rate.
 To establish a Rate Cap:
      the buyer selects an interest rate index
      a maturity over which the contract will be in place
      a strike (exercise) rate that represents the cap rate and
       a notional principal amount
 By paying an up-front premium, the buyer then locks-
  in this cap on the underlying interest rate.
•The buyer of a cap                                Dollar Payout
receives a cash                                  (3-month LIBOR        A. Cap= Long Call Option on 3-Month LIBOR   1C
                                                  =6%)x Notional
payment from the                                 Principal Amount
seller.
The payoff is the
maximum of 0 or 3-
month LIBOR minus
6% times the
notional principal
amount.
. Rate B. Cap Payoff: Strike Rate =6 Percent*
                                                                                                                        3-Month
                                                                                                                        LIBOR
                                                                                            6 Percent
6 Percent
                                                    Floating
                                                    Rate
                                                                                   •If 3-month LIBOR
                                                                                   exceeds 6%, the buyer
                                                                                   receives cash from the
                                                                                   seller and nothing
                                                                                   otherwise.
                Value        Value       Value        Value         Value          •At maturity, the cap
                Date         Date        Date         Date          Date           expires.
                                      Time
 The Pros and Cons of Buying a Cap
 Similar to those of buying any option.
 The bank as buyer of a cap can set a maximum (cap)
  rate on its borrowing costs.
 It can also convert a fixed-rate loan to a floating rate
  loan.
      it gets protection from rising rates and retains the benefits
       if rates fall.
 The primary negative to the buyer is that a cap requires
  an up-front premium payment.
      The premium on a cap that is at the money or in the
       money in a rising rate environment can be high.
   Establishing a Floor
 A bank borrower can establish a floor by selling a call
  option on Eurodollar futures.

 The seller of a call receives the option premium, but agrees
  to sell to the call option buyer the underlying Eurodollar
  futures at the agreed strike price upon exercise.

 A floor exists because any opportunity gain in the cash
  market from borrowing at lower rates will be offset by the
  loss on the sold call option.
      In essence, the bank has limited its maximum borrowing
       cost, but also established a floor borrowing cost.

 The combination of setting a cap rate and floor rate is
  labeled a collar.
•A buyer can establish a
minimum interest Dollar Payout                                         A. Floorlet=Long Put Option on 3-Month LIBOR
rate by buying a LIBOR)233-month +P
                      (6%
floor on an interest Principal Notional
                               Amount
rate index.
The buyer of the floor
receives a cash payment
equal to the greater of
zero the product of 6
percent minus 3-month
LIBOR and a notional
principal amount..
   Rate                          f
                    B. Floor Payof: Strike Rate= 6 Percent*                                                           3-Month
                                                                                                                      LIBOR
                                                                               Floating
                                                                                          6 Percent
                                                                               Rate
                                                                                     •Thus, if 3-m LIBOR
6 Percent                                                                            exceeds 6 %, the buyer
                                                                                     of a floor at 6%
                                                                                     receives nothing.
                                                                                     •The buyer is only paid
                                                                                     if 3-m LIBOR is less
            Value             Value           V alue          V alue      Value      than 6%
            Date              Date             Date            Date       Date
                                           Time
Interest Rate Floor
 A series of consecutive floorlets at the same
  strike rate
 To establish a floor, the buyer of an interest
  rate floor selects
      an index
      a maturity for the agreement
      a strike rate
      a notional principal amount
 By paying a premium, the buyer of the floor,
  or series of floorlets, has established a
  minimum rate on its interest rate exposure.
  The Pros and Cons of Buying a Floor

 The benefits are similar to those of any put
  option
 A floor protects against falling interest rates
  while retaining the benefits of rising rates
 The primary negative is that the premium may
  be high on an at the money or in the money
  floor, especially if the consensus forecast is that
  interest rates will fall in the future.
Interest Rate Collar and Reverse
Collar
 The purchase of an interest rate collar is actually the
  simultaneous purchase of an interest rate cap and
  sale of an interest rate floor on the same index for the
  same maturity and notional principal amount.
      The cap rate is set above the floor rate.
 The objective of the buyer of a collar is to protect
  against rising interest rates.
      The purchase of the cap protects against rising rates
       while the sale of the floor generates premium income.
 A collar creates a band within which the buyer’s
  effective interest rate fluctuates.
Zero Cost Collar
 Designed to establish a collar where the
  buyer has no net premium payment.
 Requires choosing different cap and floor
  rates such that the premiums are equal.
 The benefit is the same as any collar with
  zero up-front cost.
 The negative is that the band within which the
  index rate fluctuates is typically small and the
  buyer gives up any real gain from falling
  rates.
Reverse Collar
 Buying an interest rate floor and
  simultaneously selling an interest rate cap.
 The objective is to protect the bank from
  falling interest rates.
     The buyer selects the index rate and matches
      the maturity and notional principal amounts for
      the floor and cap.
 Buyers can construct zero cost reverse
  collars when it is possible to find floor and
  cap rates with the same premiums that
  provide an acceptable band.
                      A . C aps/Floors
  Term
 C aps
            B id
              6.00%
                   O ffer   B id
                              7.00%
                                    O f er             B id
                                                            8.00%
                                                                     O ffer
                                                                                                  Caps and Floors
  1 y ear
 2 y ears
             2
             27
                    6
                    34
                             1
                             3
                                     2
                                    10
                                                        1
                                                        1
                                                                           2
                                                                           5
                                                                                                   Premium Cost
 3 y ears    66     75      17      26                  1                 10               •First column in each section
 5 y ears   166    181      62      77                  18                33               indicates the term, subsequent
 7 y ears   280    302      124     146                 47                69               columns indicate the premiums.
10 y ears   462    492      233     263                107               137               For the caps, strike rates are 6,
 Floors       4.50%           5.25%                         6.00%                          7, and 8 %.
  1 y ear    1      2        1       5                  37                41
                                                                                           •For the floors, the strike rates
 2 y ears    1      8       17      24                  85                92
                                                                                           are 4.50, 5.25, and 6%. The bid
                                                                                           premium -- option seller
 3 y ears    9      18      41      50                 138               147               receives offer premium --
 5 y ears    34     49      101     116                250               265               option buyer pays.
 7 y ears    66     88      165     187                362               384
10 y ears   120    150      262     292                517               547

                                   6.10%
   3-month                                                                                  e
                                                                          B. Eurodollar Futur s
   Eurodollar                      5.90%
   futures rates
   consensus
   forecast is that                5.70%
                                                                                                                                                             Today
   3-month                                                                                                                                                   Last Week
   LIBOR will                      5.50%
   rise over time.
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   The Size of Cap and Floor Premiums are
   Determined by a Wide Range of Factors
 The relationship between the strike rate and the prevailing 3-
  month LIBOR
      premiums are highest for in the money options and
       lower for at the money and out of the money options
 Premiums increase with maturity.
      The option seller must be compensated more for
       committing to a fixed-rate for a longer period of time.
 Prevailing economic conditions, the shape of the yield curve,
  and the volatility of interest rates.
      upsloping yield curve -- caps will be more expensive
       than floors.
      the steeper is the slope of the yield curve, ceteris
       paribus, the greater are the cap premiums.
      floor premiums reveal the opposite relationship.
       Protecting Against
       Falling Interest Rates
 Assume that a bank is asset sensitive such that the bank's
  net interest income will decrease if interest rates fall.
      Essentially the bank holds loans priced at prime +1% and
       funds the loans with a 3-year fixed-rate deposit at 5.75%.
 Three alternative approaches to reduce risk associated
  with falling rates:
        1) entering into a basic interest rate swap to
         pay 3-month LIBOR and
         receive a fixed rate
        2) buying an interest rate floor
        3) buying a reverse collar
                                       Floating Rate      Bank Swap Terms:
Aggregate Balance Sheet Risk of Loss
                                          Loans           Pay LIBOR, Receive 5.96%
                                               Prime +100  3-m LIBOR
                                                                             Swap
                                           Bank                           Counterparty
Using a Basic Swap to Hedge


                                               Fixed 5.75 5.96% Fixed
                                        Deposits
                                                         Current Rates      Rates Fall        Rates Rise
From Falling Rates




                                                           Constant      100 Basis Points   100 Basis Points
                                                         PRIME 8.50%     PRIME 7.50%        PRIME 9.50%
                                                         LIBOR 5.70%     LIBOR 4.70%        LIBOR 6.70%
                                        Balance Sheet
                                           Flows:
                                        Loan                   9.50%           8.50%             10.50%
                                        Deposit               (5.75%)         (5.75%)            (5.75%)
                                        Spread                 3.75%           2.75%              4.75%

                                         Interest Rate
                                         Swap Flows:
                                        Fixed                  5.96%           5.96%              5.96%
                                        Floating              (5.70%)         (4.70%)            (6.70%)
                                        Spread                 0.26%           1.26%             (0.74%)
                                        Margin                 4.01%           4.01%              4.01%
                                    Floating Rate      Floor Terms:
Buying a Floor on a 3-month LIBOR      Loans           Buy a 5.7% floor on 3m LIBOR
to Hedge Aggregate Balance Sheet            Prime +100
Risk of Loss from Falling Rates                                              Swap
                                        Bank              Receive when
                                                                         Counterparty
                                                       3-m LIBOR< 5.7%
                                            Fixed 5.75                   Fee: (.29%) /yr
                                      Deposits
                                                      Current Rates      Rates Fall        Rates Rise
                                                        Constant      100 Basis Points   100 Basis Points
                                                      PRIME 8.50%     PRIME 7.50%        PRIME 9.50%
                                                      LIBOR 5.70%     LIBOR 4.70%        LIBOR 6.70%
                                      Balance Sheet
                                         Flows:
                                     Loan                   9.50%           8.50%             10.50%
                                     Deposit               (5.75%)         (5.75%)            (5.75%)
                                     Spread                 3.75%           2.75%              4.75%

                                      Floor Flows:
                                     Payout                 0.00%           1.00%              0.00%
                                     Fee Amort.            (0.29%)         (0.29%)            (0.29%)
                                     Spread                (0.29%)          0.71%             (0.29%)
                                     Margin                 3.46%           3.46%              4.46%
                                                              Strategy: Buy a Floor on a 3-m

Aggregate Balance Sheet Risk of Loss
                                Floating Rate                 LIBOR at 5.2%, sell a Cap on 3-m
                                   Loans                      LIBOR at 6.2%
Buying a Reverse Collar to Hedge
                                        Prime +100             Pay when
                                                           3-m LIBOR>6.2%                   Swap
                                        Bank                  Receive when               Counterparty
                                             Fixed 5.75     3-m LIBOR<5.2%
                                                                                         Prem: (.10%) /yr
                                       Deposits
                                                          Current Rates      Rates Fall        Rates Rise
From Falling Rates




                                                            Constant      100 Basis Points   100 Basis Points
                                                          PRIME 8.50%     PRIME 7.50%        PRIME 9.50%
                                                          LIBOR 5.70%     LIBOR 4.70%        LIBOR 6.70%
                                          Balance Sheet
                                             Flows:
                                         Loan                   9.50%           8.50%             10.50%
                                         Deposit               (5.75%)         (5.75%)            (5.75%)
                                         Spread                 3.75%           2.75%              4.75%
                                         Reverse Collar
                                            Flows:
                                         Payout                 0.00%           0.50%             (0.50%)
                                         Premium                0.10%           0.10%              0.10%
                                         Spread                (0.29%)          0.71%             (0.29%)
                                         Margin                 3.85%           3.35%              4.35%
   Protecting Against
   Rising Interest Rates
 Assume that the bank has made 3-year fixed rate term
  loans at 9%, funded via 3-month Eurodollar deposits for
  which it pays the prevailing LIBOR - 0.25%.
      The bank is liability sensitive, it is exposed to loss from
       rising interest rates
 Three strategies to hedge this risk:
       1) enter a basic swap to pay 6% fixed-
          rate and receive 3-month LIBOR
       2) buy a cap on 3-month LIBOR with a
          5.70% strike rate
       3) buy a collar on 3-month LIBOR
                                       Floating Rate            Strategy:
Aggregate Balance Sheet Risk of Loss
                                          Loans                 Receive 3-m LIBOR, Pay 6.0%
                                                  Fixed 9.0%
                                                                     6.0% Fixed
                                                                                               Swap
                                           Bank
                                                                                            Counterparty
Using a Basic Swap to Hedge



                                         3-m LIBOR - 0.25%           3-m LIBOR

                                         Deposits
                                                        Current Rates       Rates Fall         Rates Rise
From Rising Rates




                                                          Constant       100 Basis Points    100 Basis Points
                                        Balance Sheet   LIBOR 5.70%      LIBOR 4.70%         LIBOR 6.70%
                                           Flows:
                                       Loan                     9.00%          9.00%               9.00%
                                       Deposit                 (5.45%)        (4.45%)             (6.45%)
                                       Spread                   3.55%          4.55%               2.55%

                                        Interest Rate
                                        Swap Flows:
                                       Fixed                   (6.00%)        (6.00%)             (6.00%)
                                       Floating                 5.70%          4.70%               6.70%
                                       Spread                  (0.30%)        (1.30%)             (0.70%)
                                       Margin                   3.25%          3.25%               3.25%
                                     Floating Rate
                                                                Strategy: Buy a Cap
Hedge Aggregate Balance Sheet Risk
Buying a Cap on 3-month LIBOR to        Loans
                                                                on 3m LIBOR at 5.7%
                                               Fixed 9.0%
                                                              Receive when               Swap
                                         Bank
                                                            3-m LIBOR> 5.7%          Counterparty
                                       3-m LIBOR - 0.25%                             Fee: (.45%) /yr
of Loss from Rising Rates


                                       Deposits
                                                      Current Rates      Rates Fall        Rates Rise
                                                        Constant      100 Basis Points   100 Basis Points
                                      Balance Sheet   LIBOR 5.70%     LIBOR 4.70%        LIBOR 6.70%
                                         Flows:
                                     Loan                    9.00%          9.00%              9.00%
                                     Deposit                (5.45%)        (4.45%)            (6.45%)
                                     Spread                  3.55%          4.55%              2.55%

                                          Cap
                                         Flows:
                                     Payout                  0.00%          0.00%              1.00%
                                     Fee Amort.             (0.45%)        (0.45%)            (0.45%)
                                     Spread                 (0.45%)        (0.45%)             0.55%
                                     Margin                  3.10%          4.10%              3.10%
                                     Floating Rate           Strategy: Buy a Cap at 6.2%
Using a Collar on 3-Month LIBOR to
Hedge Aggregate Balance Sheet Risk
                                        Loans                and Sell a Floor at 5.2%
                                               Fixed 9.0%  Receive when
                                                        3-m LIBOR>6.2%      Swap
                                        Bank
                                                             Pay when   Counterparty
                                       3-m LIBOR - 0.25% 3-m LIBOR<5.2% Fee: (.10%) /yr
of Loss From Rising Rates


                                       Deposits
                                                      Current Rates      Rates Fall        Rates Rise
                                                        Constant      100 Basis Points   100 Basis Points
                                      Balance Sheet   LIBOR 5.70%     LIBOR 4.70%        LIBOR 6.70%
                                         Flows:
                                     Loan                    9.00%          9.00%              9.00%
                                     Deposit                (5.45%)        (4.45%)            (6.45%)
                                     Spread                  3.55%          4.55%              2.55%

                                         Collar
                                         Flows:
                                     Payout                  0.00%          0.00%              1.00%
                                     Fee Amort.             (0.10%)        (0.10%)            (0.10%)
                                     Spread                 (0.10%)        (0.60%)             0.40%
                                     Margin                  3.45%          3.95%              2.95%
Interest Rate Swaps With Options
 To obtain fixed-rate financing, a firm with access to capital markets has
   a variety of alternatives:
       Issue option-free bonds directly
       Issue floating-rate debt that it converts via a basic swap to
        fixed-rate debt
       Issue fixed-rate callable debt, and combine this with an
        interest rate swap with a call option and a plain vanilla or basic
        swap
 Investors demand a higher rate for callable bonds to compensate for the
   risk the bonds will be called
       the call option will be exercised when interest rates fall, and
        investors will receive their principal back when similar
        investment opportunities carry lower yields
       the issuer of the call option effectively pays for the option in
        the form of the higher initial interest rate
Interest Rate Swap with a Call Option

 A swap with a call option is like a basic swap
  except that the call option holder (buyer) has
  the right to terminate the swap after a set
  period of time.
 Specifically, the swap party that pays a fixed-
  rate and receives a floating rate has the
  option to terminate a callable swap prior to
  maturity of the swap.
      This option may, in turn, be exercised only
       after some time has elapsed.
   Issue fixed-rate debt with an 8-
    year maturity
                                                          Callable Swap:
   Dealer spread: 0.10%                                  An Example
Cash Market Alternatives                             Strategy involves three steps
   8-year fixed rate debt: 8.50%                     implemented simultaneously:
   8-year callable fixed-rate debt: 8.80%            1) issues callable debt at 8.80%
   6-month floating-rate debt: LIBOR                 2) enters into a callable swap
                                                          paying LIBOR and
Interest Rate Swap Terms                                  receiving 8.90%
   Basic Swap: 8-year swap without options:          3) enters into a basic swap
     pay 8.55% fixed; receive LIBOR                       paying 8.55%, receiving
     pay LIBOR; receive 8.45%                             LIBOR.
   Callable Swap: 8-year swap,
                          callable after 4 yrs:
     pay LIBOR; receive 8.90% fixed
     pay 9.00% fixed; receive LIBOR
Net Borrowing Cost after Option Exercise              Net Cost of Borrowing
  Pay:                                                  After Option Exercise in 4 Yrs
  cash rate + callable swap rate + basic swap rate      Basic swap:
          [8.80% + LIBOR + 8.55%]                         pay 8.55%; receive LIBOR
  Receive: callable swap rate + basic swap rate         New floating-rate debt:
              – [8.90% + LIBOR]                           pay LIBOR +/- ?
  Net Pay =8.45%                                        Net cost = 8.55% +/- spread to LIBOR
Interest Rate Swap with a Put Option

  A put option gives the holder of a putable
   swap the right to put the security back to the
   issuer prior to maturity
      with a putable bond an investor can get
       principal back after a deferment period
      option value increases when interest rates rise
      investors are willing to accept lower yields
  With a putable swap, the party receiving the
   fixed-rate payment has the option of
   terminating the swap after a deferment
   period, and will likely do so when rates
   increase.
          Callable Swap: An Example
  Putable Bond: 8-yr bond, putable after 4 yrs: 8.05%
  Putable Swap: 8-yr swap, putable after 4 yrs:
        pay LIBOR; receive 8.20% fixed
        pay 8.30% fixed; receive LIBOR
Strategy involves three steps implemented simultaneously:
1) issue putable debt at 8.05%
2) enter into a putable swap to pay LIBOR and receive 8.20%
3) enter into a basic swap to pay 8.55% and receive LIBOR

      Net Cost of Borrowing With a Putable Swap for 4 Years
        Pay: Put bond rate + Put swap rate + Basic swap rate
               [8.05% + LIBOR + 8.55%]
        Receive: Put swap rate + Basic swap rate
               - [ 8.20% + LIBOR]
          Net cost = 8.40%
      Net Cost of Borrowing After Option Exercise in 4 Yrs
        Basic swap: pay 8.55%; receive LIBOR
        New floating-rate debt: pay LIBOR +/- ?
          Net cost = 8.55% +/- spread to LIBOR

				
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