Swaps

							            Financial Risk Management
                                       Zvi Wiener
                                             Following
        P. Jorion, Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html     FRM       972-2-588-3049
                                             Swaps
                                      Zvi Wiener
                                      02-588-3049
      http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
http://pluto.huji.ac.il/~mswiener/zvi.html    FRM    972-2-588-3049
           Interest Rate Swaps: Concept
        • An agreement between 2 parties to exchange
        periodic payments calculated on the basis of
        specified interest rates and a notional amount.

        •Plain Vanilla Swap
                               Fixed rate
           A                                                 B
                              Floating rate
Based on a presentation of Global Risk Strategy Group of Deutsche Bank
Swaps                                    Zvi Wiener                      slide 3
                             IRS
        • In a standard IRS, one leg consists of fixed
        rate payments and the other depends on the
        evolution of a floating rate.
        • Typically long dated contracts: 2-30 years
        • Sometimes includes options, amortization,
        etc.
        • Interest compounded according to different
        conventions (eg 30/360, Act/Act. Act/360, etc.)

Swaps                        Zvi Wiener                  slide 4
                 IRS Origins
  AAA wants to borrow in floating and BBB
  wants to borrow in fixed.
                    Fixed         Floating
  AAA               7.00%         LIBOR+5bps
  BBB               8.50%         LIBOR+85bps
  difference        1.5%          0.8%
  Net differential 70bps = 0.7%


Swaps                 Zvi Wiener            slide 5
           Comparative Advantage
                       7.4%
        7.0%                             Libor+85bp
               AAA    Libor        BBB

Cost of funds for AAA=Libor - 40bp (45bps saved)
Cost of funds for BBB=8.25% (25bps saved)
Swap rate = 7.40%
Swap rate is the fixed rate which is paid against
receiving Libor.

Swaps                 Zvi Wiener                slide 6
         Basic terms of IRS
        • Notional amount
        • Fixed rate leg
        • Floating rate leg
        • Calculated period
        • Day count fraction


Swaps               Zvi Wiener   slide 7
                   Basic terms of IRS
        • Payer and receiver - quoted relative to fixed
        interest (i.e. payer = payer of fixed rate)
        • buyer = payer, seller =receiver
        • Short party = payer of fixed, (buyer)
        • Long party = receiver of fixed, (seller)
        • Valuation = net value NOT notional!!


Swaps                         Zvi Wiener              slide 8
                    Various swaps
        • Coupon swaps - fixed against floating.
        • Basis or Index swaps - exchange of two
        streams both are computed using floating IR.
        • Currency swap - interest payments are
        denominated in different currencies.
        • Asset swap - to exchange interest received
        on specific assets.
        • Term swap maturity more then 2 years.
        • Money Market swap - less then 2 years.
Swaps                       Zvi Wiener                 slide 9
                     Payments
Fixed payment =
(notional)(Fixed rate)(fixed rate day count convention)

Floating payment =
(notional)(Float. rate)(float. rate day count convention)




Swaps                    Zvi Wiener               slide 10
                 Time Value of Money
        • present value PV = CFt/(1+r)t

        • Future value FV = CFt(1+r)t

        • Net present value NPV = sum of all PV

           -PV     5         5   5            5    105
                         4
                               5        105
                 PV                 
                      t 1 (1  rt ) (1  r5 ) 5
                                    t



Swaps                            Zvi Wiener              slide 11
Swaps   Zvi Wiener   slide 12
                      Swap Pricing
        A swap is a series of cash flows.
        An on-market swap has a Net Present Value
        of zero!
        PV(Fixed leg) + PV(Floating leg) = 0




Swaps                       Zvi Wiener              slide 13
                          Pricing
        • Floating leg is equal to notional amount at
        each day of interest rate settlement (by
        definition of LIBOR).
        • Fixed leg can be valued by standard NPV,
        since the paid amount is known.




Swaps                        Zvi Wiener                 slide 14
Swaps   Zvi Wiener   slide 15
Swaps   Zvi Wiener   slide 16
               Forward starting swaps
        • interest starts accruing at some date in the
        future.
        • Valuation is similar to a long swap long and
        a short swap short.




Swaps                        Zvi Wiener                  slide 17
        • Zero coupon swap (reinvested payments)
        • Amortizing swap (decreasing notional)
        • Accreting swap (increasing notional)
        • Rollercoaster (variable notional)




Swaps                        Zvi Wiener            slide 18
                  Amortizing swap




        Decreasing notional affects coupon payments




Swaps                      Zvi Wiener             slide 19
           Unwinding an existing swap
        • Enter into an offsetting swap at the
        prevailing market rate.
        • If we are between two reset dates the
        offsetting swap will have a short first period
        to account for accrued interest.
        • It is important that floating payment dates
        match!!

Swaps                        Zvi Wiener                  slide 20
                       Unwinding
                             8%
              A           LIBOR            B

                             6%
              A           LIBOR            C

        Net of the two offsetting swaps is 2% for the
        life of the contract. (sometimes novation)

Swaps                       Zvi Wiener              slide 21
                     Risks of Swaps
        • Interest rate risk - value of fixed side may
        change
        • Credit risk - default or change of rating of
        counterparty
        • Mismatch risk - payment dates of fixed and
        floating side are not necessarily the same
        • Basis risk and Settlement risk


Swaps                        Zvi Wiener                  slide 22
          Credit risk of a swap contract
        Default of counterparty (change of rating).
        Exists when the value of swap is positive
        Frequency of payments reduces the credit risk,
        similar to mark to market.
        Netting agreements.
        Credit exposure changes during the life of a
        swap.

Swaps                       Zvi Wiener             slide 23
                  Duration of a swap

        • Fixed leg has a long duration (approximately).
        • Short leg has duration about time to reset.


        Duration is a measure of price sencitivity to
        interest rate changes (approximately is equal to
        average time to payment).

Swaps                        Zvi Wiener                 slide 24
                      IRS Markets
        Daily average volume of trade (notional)
        1995       1998      2001
        $63B       $155B     $331B




Swaps                       Zvi Wiener             slide 25
                    Mark to market
        • daily repricing
        • collateral
        • adjustments
        • reduces credit exposure




Swaps                       Zvi Wiener   slide 26
          Reasons to use swaps by firms
        • Lower cost of funds
        • Home market effects
        • Comparative advantage of highly rated firms




Swaps                      Zvi Wiener              slide 27
Swaps   Zvi Wiener   slide 28
Swaps   Zvi Wiener   slide 29
Swaps   Zvi Wiener   slide 30
        Global Derivatives Markets 1999
   Exchange traded $13.5T                    OTC Instruments $88T
  IR contracts       11,669                 IR contracts         60,091
  Futures            7,914                  FRAs                 6,775
  Options            3,756                  Swaps                43,936
  FX contracts       59                     Options              9,380
  Futures            37                     FX contracts         14,344
  Options            22                     Forwards             9,593
  Stock-index contr. 1,793                  Swaps                2,444
  Futures            334                    Options              2,307
  Options            1,459                  Equity-linked contr. 1,809
  World GDP in 99 = 30,000                  Forw. and swaps      283
  All stocks and bonds = 70,000             Options              1,527
  Liquidation value = 2,800                 Commodity contr. 548
                                            Others               11,408
Swaps                          Zvi Wiener
                             Source BIS                           slide 31
                  FRM-GARP 00:47
        Which one of the following deals has the
        largest credit exposure for a $1,000,000 deal
        size. Assume that the counterparty in each
        deal is a AAA-rated bank and there is no
        settlement risk.
        A. Pay fixed in an interest rate swap for 1 year
        B. Sell USD against DEM in a 1 year forward
        contract.
        C. Sell a 1-year DEM Cap
        D. Purchase a 1-year Certificate of Deposit

Swaps                        Zvi Wiener               slide 32
                  FRM-GARP 00:47
        Which one of the following deals has the
        largest credit exposure for a $1,000,000 deal
        size. Assume that the counterparty in each
        deal is a AAA-rated bank and there is no
        settlement risk.
        A. Pay fixed in an interest rate swap for 1 year
        B. Sell USD against DEM in a 1 year forward
        contract.
        C. Sell a 1-year DEM Cap
        D. Purchase a 1-year Certificate of Deposit

Swaps                        Zvi Wiener               slide 33