Swaps Lecture 2

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SwapsLecture 2
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Types of Rates

• Treasury rates
• LIBOR rates
• Euribor rates

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Zero Rates

• A zero rate (or spot rate), for maturity T,
  is the rate of interest earned on an investment
  that provides a payoff only at time T

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Example

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Bond Pricing

• To calculate the cash price of a bond we discount
  each cash flow at the appropriate zero rate
• In our example, the theoretical price of a
  two-year bond providing a 6 coupon semiannually
  is

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Bond Yield

• The bond yield is the discount rate that makes
  the present value of the cash flows on the bond
  equal to the market price of the bond
• Suppose that the market price of the bond in our
  example equals its theoretical price of 98.39
• The bond yield is given by solving
• to get y0.0676 or 6.76.

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Forward Rates

• The forward rate is the future zero rate
  implied by todays term structure of interest
  rates

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Calculation of Forward Rates

Zero Rate for
Forward Rate
an
n
-year Investment
for
n
th Year
Year (
n
)
( per annum)
( per annum)
1
10.0
2
10.5
11.0
3
10.8
11.4
4
11.0
11.6
5
11.1
11.5
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Formula for Forward Rates

• Suppose that the zero rates for time periods T1
  and T2 are R1 and R2 with both rates continuously
  compounded.
• The forward rate for the period between times T1
  and T2 is

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Duration

• Duration of a bond that provides cash flow c i
  at time t i is
• where B is its price y is its yield
  (continuously compounded)
• This leads to

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Duration Matching

• This involves hedging against interest rate risk
  by matching the durations of assets and
  liabilities
• It provides protection against small parallel
  shifts in the zero curve

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Nature of Swaps

• A swap is an agreement to exchange cash flows at
  specified future times according to certain
  specified rules

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An Example of a Plain Vanilla Interest Rate
Swap

• An agreement by Company B to receive 6-month
  LIBOR pay a fixed rate of 5 per annum every 6
  months for 3 years on a notional principal of
  100 million
• Next slide illustrates cash flows

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Cash Flows to Company B
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Typical Uses of anInterest Rate Swap

• Converting a liability from
• fixed rate to floating rate
• floating rate to fixed rate

• Converting an investment from
• fixed rate to floating rate
• floating rate to fixed rate

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A and B Transform a Liability
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5.2
A
B
LIBOR0.8
LIBOR
A from 5.2 fixed to floating ---gt pays
Libor0.2 B from floating Libor0.8 to fixed
---gt pays 50.8
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A and B Transform an Asset

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4.7
A
B
LIBOR-0.25
LIBOR
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The Comparative Advantage Argument

• Company A wants to borrow floating
• Company B wants to borrow fixed

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The Swap

9.95
10
A
B
LIBOR1
LIBOR
A from 10 fixed to floating ---gt pays
Libor0.05 B from floating Libor1 to fixed
---gt pays 9.951
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Valuation of an Interest Rate Swap

• Interest rate swaps can be valued as the
  difference between the value of a fixed-rate
  bond the value of a floating-rate bond

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Valuation in Terms of Bonds

• The fixed rate bond is valued in the usual way
• The floating rate bond is valued by noting that
  it is worth par immediately after the next
  payment date

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Swapping a BTP
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Credit Risk

• A swap is worth zero to a company initially
• At a future time its value is liable to be either
  positive or negative
• The company has credit risk exposure only when
  its value is positive

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Examples of Other Types of Swaps

• Amortizing step-up swaps
• Extendible puttable swaps
• Index amortizing swaps
• Equity swaps
• Commodity swaps
• Differential swaps