Introduction
• Financial Swaps are an asset-liability management
technique which permits a borrower (investor) to
access one market and then exchange the liability
(asset) for another type of liability (asset)
• Swaps by themselves are not a funding instrument;
they are a device to obtain the desired form of
financing indirectly which otherwise might be
inaccessible or too expensive
• Swaps exploit some capital market imperfection or
special tax legislation or differences in financial
norms to provide savings in borrowing costs or
enhanced return on assets
• Swaps may also be used purely for hedging purposes
Major Types of Swap Structures
• All swaps involve exchange of a series of
periodic payments between two parties, usually
through an intermediary which is normally a large
international financial institution which runs a
“swap book”
• The two major types are Interest Rate Swaps
(also known as Coupon Swaps) and Currency
Swaps. The two are combined to give a CrossCurrency Interest Rate Swap
• Other less common structures are equity swaps,
commodity swaps, yield curve swaps etc.
– Liability swaps exchange one kind of liability for
another
– Asset swaps exchange incomes from two
different types of assets
Major Types of Swap Structures
• Interest Rate Swaps
– A standard fixed-to-floating interest rate swap, known in
the market jargon as a plain vanilla coupon swap
(also referred to as "exchange of borrowings") is an
agreement between two parties in which each contracts
to make payments to the other on particular dates in
the future till a specified termination date
– One party, known as the fixed rate payer, makes
fixed payments all of which are determined at the
outset
– The other party known as the floating rate payer
will make payments the size of which depends upon the
future evolution of a specified interest rate index
– Both payments calculated as interest on a specified
“notional” principal.
Major Types of Swap Structures
–The Key Features of an Interest Rate
Swap
The Notional Principal; The Fixed Rate; Floating
Rate Trade Date, Effective Date, Reset Dates and
Payment Dates (each floating rate payment has
three dates associated with it as shown in Figure
below
D(S), the setting date is the date on which the
floating rate applicable for the next payment is set
D(1) is the date from which the next floating
payment starts to accrue and D(2) is the date on
which the payment is due
Major Types of Swap Structures
– Fixed and Floating Payments
Fixed Payment = P  Rfx  Ffx
Floating Payment = P  Rfl  Ffl
• P is the notional principal, Rfx is the fixed
rate, Rfl is the floating rate set on the reset
date, Ffx is known as the "Fixed rate day
count fraction" and Ffl is the "Floating rate
day count fraction"
– In an interest rate swap, there is no
exchange of underlying principal; only
the streams of interest payments are
exchanged between the two parties
A Three Year Fixed-to-Floating Interest Rate Swap
Notional principal P = $50 million
Trade Date : August 30, 2008.
Effective Date : September 1, 2008.
Fixed Rate : 9.5% p.a. payable semiannually, Actual/360
Floating Rate : 6 Month LIBOR.
Fixed and Floating Payment Dates : Every March 1 and
September 1 starting March 1, 2009 till September 1, 2011.
Floating Rate Reset Dates : 2 business days prior to the
previous floating payment date, 11 am London time
Floating Rate Quote Source: REUTERS. Floating rate set
in advance paid in arrears.
The fixed payments are as follows :
__________________________________________________
Payment Date
Day Count Fraction
Amount
__________________________________________________
1/3/2009
181/360
$2388194.40
1/9/2009
184/360
$2427777.80
1/3/2010
181/360
$2388194.40
1/9/2010
184/360
$2427777.80
1/3/2011
181/360
$2388194.40
1/9/2011
184/360
$2427777.80
Suppose the floating rates evolve as follows :
Reset Date
LIBOR (% p.a.)
30/8/2008
9.80
28/2/2009
9.20
30/8/2009
9.50
27/2/2010
8.90
30/8/2010
9.70
27/2/2011
10.20
This will give rise to the following floating payments :
Payment Date
Amount ($)
1/3/2009
2477222.20
1/9/2009
2351111.10
1/3/2010
2388194.40
1/9/2010
2274444.40
1/3/2011
2438472.20
1/9/2011
2606666.70
Normally, the payments would be netted out with only the net
payment being transferred from the deficit to the surplus party.
An Example: Interest Rate Swap
SIGNET and MICROSOFT. (Borrow 10 Million for 5 years).
Company
Fixed
Floating
Microsoft
1.5%
6 month Libor + 0.30%
Signet
2.7%
6 month Libor + 1.00%
Microsoft wants to borrow floating while Signet fixed. Note
Microsoft is more credit worthy and credit spread is higher in
fixed rate markets.
The following swap is negotiated directly between companies.
(in reality a Matchmaker is there which generally warehouses).
Microsoft agrees to pay Signet Libor. Signet agrees to pay
Microsoft fixed at 1.45% both on notional principal of $10m
Interest Rate related Cash flows for Microsoft are:
1. Pays 1.5% to lenders.
2. Pays Libor to Signet
3. Receives 1.45% from Signet
4. Total Cost: Libor + 0.05 (0.25% less if it went directly to
floating-rate markets)
Interest Rate related Cash flows for Signet are:
1. Pays Libor + 1% to lenders.
2. Pays 1.45 % to Microsoft.
3. Receives Libor from Microsoft.
4. Total Cost: 2.45% (0.25% less if it went directly to fixed-rate
markets).
A Typical Plain Vanilla Coupon Swap
Funding objective
Fixed Rate Cost
Floating Rate Cost
Party A (Firm)
Party B (Bank)
$ Fixed Rate
$ Floating Rate
6%
4.5%
Prime+75bp
Prime
This is an instance of quality spread differential. Bank has
absolute advantage in both fixed and floating rate markets
but less so in floating rate market. Each party should access
the market in which it has a “comparative advantage”. They
should then exchange their liabilities.
A TYPICAL USD IRS
A FIXED-TO-FLOATING INTEREST RATE SWAP
6.75% Fixed
6.5% fixed
SWAP BANK
Prime-25bp
XYZ CORP.
Prime+75bp
To Floating
Rate Lenders
Prime-25bp
ABC BANK
6.5% Fixed
to Fixed
Rate Lenders
Major Types of Swap Structures
– A number of variants of the standard structure
are found in practice
• Varying notional principal – Amortizing,
Accreting and Roller-Coaster Swaps
• A Zero-Coupon Swap has only one fixed
payment at maturity
• A Basis Swap involves an exchange of two
floating payments, each tied to a different
market index
• In an Extendable Swap, one of the parties
has the option to extend the swap beyond
the scheduled termination date
• Index maturity not equal to reset frequency
• Set and paid in arrears swaps
Major Types of Swap Structures
• In a Forward Start Swap, the effective date is
several months even years after the trade date
so that a borrower with a future funding need
can take advantage of prevailing favourable
swap rates to lock in the terms of a swap to be
entered into at a later date
An Indexed Principal Swap is a variant in which
the principal is not fixed for the life of the swap
but tied to the level of interest rates - as rates
decline, the notional principal rises according to
some formula
• In a Callable Swap the fixed rate payer has the
option to terminate the agreement prior to
scheduled maturity while in a Putable Swap
the fixed rate receiver has such an option
Major Types of Swap Structures
• Currency Swaps
– In a currency swap, the two payment streams
being exchanged are denominated in two
different currencies
– Fixed-to-Fixed Currency Swap
– A Fixed-to-Floating Currency Swap also
known as cross-currency coupon swap will
have one payment calculated at a floating
interest rate while the other is at a fixed
interest rate
A Typical Currency Swap
Alpha Corp.
Requirement: Fixed rate USD
Funding
Cost of $
Funding:
12.5%
Cost of CHF
Funding:
6.5%
Beta Bank
Fixed rate CHF
Funding
11%
6%
Once again, bank B has absolute advantage in both markets
but firm A has a comparative advantage in CHF market.
Could be due to market saturation – Bank has tapped CHF
market too often. Again each should access market in which
it has a comparative advantage and then exchange liabilities
A CURRENCY SWAP
12.3% USD
12%USD
SWAP BANK
6.5% CHF
6.5% CHF
CHF
ALPHA
COMPANY
BETA BANK
USD
USD
CHF
6.5% TO CHF LENDERS
11% TO USD LENDERS
INITIAL EXCHANGE OF PRINCIPALS
FINAL RE-EXCHANGE OF PRINCIPALS
Currency Swaps : An Example of Currency Swap
Currency Swap : in its simplest form, involves exchanging
principal and fixed-rate interest payments on a loan in one
currency for principal and fixed-rate interest payments on an
approximately equivalent loan in another currency. To
explain the mechanics of a swap, consider the following
simple example, where two companies are offered the
following Borrowing Schedule :
Company
Dollar
Pound
DELL
3%
4.5%
SHELL
5%
5.5%
Pound rates are higher than dollar.
Dell is more credit worthy (lower rates compared to Shell).
Shell pays 2% more in U.S. market and 1% in U.K. market. (if a
swap occurs the maximum overall gain can be 1.0%).
Dell has comparative advantage in the U.S. (better known to U.S.
investors) and Shell in U.K. Suppose Dell wants to borrow pounds
and Shell dollars. This creates a perfect scenario for the Swap
Contract . So Dell borrows in Dollars and Shell in Pounds . Then
they use a currency swap (via an intermediary) to transform DELL's
loan into a Pound loan and Shell's loan into a dollar loan.
Here is one possible sequence of a Swap. Let the principal amounts
be 15 million $ and 10 Million Pounds. Let the spot exchange rate
be 1.50 Dollars = 1 Pound. Let the contract be for 5 years.
1. Dell borrows Dollars and Shell Pounds.
2. Transform the 3% dollar cost into a 4% Pound loan costs (for
example).This makes Dell better off by 0.5% (cost would have
been 4.5% otherwise). Intermediary passes on 3.75% to Shell.
3. Transform a 5.5% pound cost for Shell into a 4.65% dollar
loan cost. 2.9% fixed dollar paid to intermediary, 1.75% sterling
added to pounds received from intermediary.
4. Financial intermediary gains 0.25% on pound cash flows (4
versus 3.75) and losses 0.1% on dollar ( 2.9% versus 3%).
5. Total Gain is 1.0%: Dell (0.5%), Intermediary (0.15%) and
Shell (0.35%)
6. Initially $15 M and 10 M pounds are exchanged (between
Dell and Shell).
7. For the next 5 years, Dell receives $0.45 Million
(3% of 15 M) from Fin.Intermediary and pays
£0.4m (4% of £10 m Pound). The same for Shell.
It receives £0.375 (3.75% of £10m) and pays
$0.435m ( 2.9% of $15m) for the next 5 years.
8. At the end of the swap, Dell pays a principal of
10 M pounds and receives a principal of 15 M
Dollars.
Cross-Currency Interest Rate Swaps
Involves the swap of floating-rate debt denominated in one
currency for fixed-rate debt denominated in another currency.
Renault wanted to issue fixed rate Yen debt (i.e., borrow) but faced
regulatory barriers. A swap arranged by Bankers trust :
Yamaichi purchased dollar floating rate notes and passed the dollar
payments from the notes to Renault via Banker's trust. Renault used
the dollar payments to service its own floating rate dollar debt. In
return, Renault made Yen fixed -rate interest and principal payments
to Yamaichi (via Banker's Trust). By this scheme, Renault turned its
floating-rate dollar payment obligations into fixed rate Yen
obligations. Yamaichi had acquired dollar assets but had
subsequently hedged its exchange risk, as it now received yen
payments from Renault.
Cross-Currency Interest Rate Swaps
Some Swap Quotation Details and Terminology
1. All in Cost (AIC): The price of swap is quoted as the rate the
fixed rate payer will pay to the floating -rate payer. Quoted on a
semi-annual basis either as an absolute value or as a basis point
spread over Treasuries.
2. The fixed rate payer is said to be long or to have bought the swap.
The floating rate payer is said to be short or to have sold the swap.
3. Swaps are also quoted with a bid-ask spread in terms of yield. A
quote of 74 bid 79 offered signifies that fixed payers (the long side)
are willing to pay 74 basis points over the treasury.
4. Interest Rate Swap market and Currency Swap Market.
Motivations Underlying Swaps
• Why would a firm want to exchange one
kind of liability or asset for another?
• Capital market imperfection or factors like
differences in investor attitudes,
informational asymmetries, differing
financial norms, peculiarities of national
regulatory and tax structures and so forth
explain why investors and borrowers use
swaps.
• Swaps enable users to exploit these
imperfections to reduce funding costs or
increase return while obtaining a preferred
structure in terms of currency, interest
rate basis etc.
Motivations Underlying Swaps
• Swaps help borrowers and investors
overcome the difficulties posed by market
access and/or provide opportunities for
arbitraging some market imperfection
– Quality Spread Differential
• Absolute advantage
• Comparative advantage
– Market Saturation
– Differing Financial Norms
– Hedging Price Risks
– Other Considerations
Evolution of Swap Markets
• Origins of the swap markets can be traced
back to 1970s when many countries
imposed exchange regulations and
restrictions on cross-border capital flows
• Early precursors of swaps are seen in the
so-called back-to-back and parallel loans
• As exchange controls were liberalised in
the eighties, currency swaps with the
same functional structure replaced
parallel and back-to-back loans
Evolution of Swap Markets
• Further impetus to the growth of swaps
was given by the realization that swaps
enable the participants to lower financing
costs by arbitraging a number of capital
market imperfections, regulatory and tax
differences
• In the early years, banks only acted as
brokers to match the two counterparties
with complementary requirements and
market access
Evolution of Swap Markets
• With the increase in the use of swaps as
an active asset/liability management tool,
banks became market makers i.e. the bank
would "take a swap on its own books" by
itself becoming a counterparty
• When a bank takes the swap onto its
books, it subjects itself to a variety of
risks. It assumes the credit risk of the
counterparty, exchange rate risk, interest
rate risk, basis risk and so forth
APPLICATIONS OF SWAPS : SOME ILLUSTRATIONS
 Locking in a Low Fixed Rate
XYZ Co. raised 7-year fixed rate funding three years ago via
a bond issue at a cost of 12% p.a. It then swapped into
floating rate funding in which it received fixed at 11.75%
annual and paid 6-month LIBOR. Thus it achieved floating
rate funding at LIBOR+25bp. The rates have now eased and
the firm wishes to lock-in its funding cost. The swap market
is now quoting a swap offer rate of 8.60% against 6-month
LIBOR for 4-year swaps. XYZ enters into a 4-year swap in
which it pays fixed at 8.60% annual and receives 6-month
LIBOR. It has locked-in a fixed funding cost of 8.85% p.a.
A Multi-Party Swap
In late 1985 XYZ Gmbh., a medium sized German
engineering firm decided to raise a 5-year US dollar funding
of $100 million to initiate some operations in the US. The firm
was unknown outside Germany and initial exploration
revealed that it will have to pay at least 10% on a fixed rate
medium term dollar borrowing. It could acquire a floating
DEM loan at a margin of 75 bp over 6 month LIBOR. It
approached a large German bank (referred to as "the Bank"
in what follows) for advice.
The Bank located four smaller German banks who were
willing to acquire fixed dollar assets but could fund
themselves only in the EuroDEM market on a floating rate
basis. They were willing to lend dollars to XYZ on the
following terms :
A Multi-Party Swap…
Amount
: $100 million
Interest rate : 9.5% p.a. payable annually.
Up-front fee : 1% of the principal.
Repayment
: Bullet in January 1991.
The effective cost for XYZ works out to 9.76%, 24 bp below
what it would pay in a direct approach to the market.
The syndicate of banks wished to convert their DEM
liability into a dollar liability to match this dollar asset.
The Bank did cross-currency fixed to floating swap with the
four banks in the syndicate as follows :
A Multi-Party Swap…
 Each bank in the syndicate sold DEM 40 million to the bank in
return for $24.75 million.
 Each bank agreed to pay fixed dollar payments annually
beginning January 1987 to the Bank calculated as 9% interest on
$25 million.
 Each bank received 6 month LIBOR on DEM 40 million in
January and July beginning July 1986, the last payment being in
January 1991.
 Each bank agreed to exchange $25 million against DEM 40
million with the Bank in January 1991.
The Bank acquired $99 million in the spot market at the rate of
DEM 1.59/USD The Bank now has a series of fixed dollar
inflows against floating DEM outflows.
A Multi-Party Swap
PMW, a large German automobile firm had an outstanding fixed
rate liability of $100 million, at a coupon of 8.5% annual, bullet
repayment in January 1991. The liability was contracted in January
1981 when the exchange rate was DEM 2.50/USD. PMW wished
to lock in the capital gain on this by exchanging it for a fixed rate
DEM liability. The Bank did a currency swap with PMW as
follows :
 Beginning January 1987, the Bank will pay PMW each year till
January 1991, fixed dollars at the rate of 8.50% on $100 million.
 Beginning January 1987, PMW will pay the Bank fixed DEM at
8% on DEM 160 million annually till January 1991.
 In January 1991, the Bank will pay PMW $100 million in
exchange for DEM 160 million.
A Multi-Party Swap …
Now the Bank has laid off its fixed dollar inflow from the
syndicate banks. It now has a fixed DEM inflow and a
floating DEM outflow.
A well known German financial institution specialising in
floating rate housing loans was planning to enter the capital
market with an issue of fixed rate DEM bonds. It wished to
convert this liability into a floating rate liability. The all-in
cost of the DEM bond issue was 7.88% p.a.
The Bank and the financial institution entered into a fixedto-floating interest rate swap in which the Bank paid fixed
DEM to the financial institution and received floating DEM.
The Bank now has a fully balanced swap book. No market
risk. Credit risk of six counterparties.
A MULTIPARTY SWAP
XYZ
Fixed $
Flt. DEM
SYNDICATE
BANKS
Fixed $
Fixed DEM
THE BANK
Fixed DEM
Flt. DEM to
Lenders
Fixed $
PMW
Flt.DEM
FINANCIAL
INSTITUTION
Fixed DEM to Lenders
Fixed $ to
Bondholders
The World Bank-IBM Currency Swap
In the summer of 1981, the World Bank wished to raise
CHF and DEM funding for its lending programme. Instead
of tapping these markets directly via fixed rate bond issues,
it achieved the same objective by means of a currency swap
with IBM.
In exploring the swap avenue, the Bank had three
primary guidelines :
(1) The cost of borrowing via a swap must be no higher
than that via direct borrowing
(2) The counter-party must be of top credit-worthiness and
(3) No currency exposure must be created.
At the time, IBM had several outstanding bond issues in
CHF and DEM on which a potential capital gain had been
made because of the strengthening of the dollar against these
two currencies and increase in interest rates in both the CHF
and DEM markets. IBM wished to realise the gain by
converting its liabilities to dollars. There is another issue here
which makes swaps attractive. IBM could have realised the
capital gain by borrowing dollars to retire its DEM and CHF
liabilities. However without a call option written into the
bond covenant this might not have been possible. Also, if it
did follow this course it would pay a capital gains tax. The
swap allowed it to lock in the gain without realising it thus
deferring the tax liability.
The steps in designing the swap were as follows :
1. On August 11 1981, the Bank launched a bond issue in the
US market with a face value of $210 million, maturity 4.6
years. Net of commissions and expenses at 2.15%, it realised
$205,485,000. The bond issue was settled on August 25 which
also became the effective date for the swap. How this amount
was arrived at is explained below.
2. IBM's CHF and DEM liabilities called for annual interest
payments of CHF 12.375 million and DEM 30 million starting
March 30 1982, with bullet repayments of principal of CHF
200 million and DEM 300 million respectively on March 30
1986. An all-in cost of 8% for CHF and 11% for DEM was
acceptable to the Bank. The CHF and DEM cash flows
associated with the IBM bonds were discounted at these rates
to find their present value as of August 25 1981.
The only minor complication here is that the discount factors
had to incorporate the first fractional year period - August 25
1981 to March 30 1982 or 215 days. Thus the discount factor
for the first cash flow occurring on March 30 1982, at 8%
discount rate is
1/(1.08)215/360 = 1/(1.08)0.597222 = 0.95507746
For the subsequent cash flows occurring on March 30 1983,
1984 etc. the exponents in the discount factors would be
1.597222, 2.597222 etc. Similarly for the DEM cash flows with
a discount rate of 11%.
The table below sets out the cash flows on the DEM and CHF
liabilities of IBM
Exchange
Date
TABLE 1
CHF Flows
CHF DEM flows DEM
(Mill)
Discount (Mill)
Discount
Factor
Factor
___________________________________________________
30/3/82
12.375
0.95507746 30.00
0.93957644
30/3/83
12.375
0.88433099 30.00
0.84646526
30/3/84
12.375
0.81882499 30.00
0.76258132
30/3/85
12.375
0.75818128 30.00 0.68702010
30/3/86
212.375
0.70201045 330.00
0.61892811
The present values of these flows (as of August 25, 1981) are
CHF 191,367,478 and DEM 301,315,273 respectively. On
August 11 1981, World Bank bought forward these amounts
of CHF and DEM against the dollar, for delivery on August
25. The rates it obtained were CHF/USD 2.18 and DEM/USD
2.56. At these rates, the above CHF and DEM amounts
translate into $87,783,247 and $117,701,753 respectively for a
total of $205,485,000. To realise this net amount, the face
value of the dollar issue had to be $210 million, issued at par.
Dollar funding cost acceptable to IBM was 16%. This rate is
applied to the principal amount of $ 210 million to compute
dollar outflows on World Bank’s liability.
TABLE 2
Date
Dollar Cash Flow
30/3/1982
20,066,667
30/3/1983
33,600,000
30/3/1984
33,600,000
30/3/1985
33,600,000
30/3/1986
243,600,000
World Bank and IBM agreed to exchange the CHF and
DEM flows in Table 1 against the dollar flows in Table 2.
Gain to World Bank was a lower cost of funding than via
direct borrowing. IBM locked in its capital gain without
realising it.
Basis Swap + A Plain Vanilla Swap
A large US manufacturing firm preferred fixed dollar funding. It
had prime-based floating rate funding. It was willing to pay 175 bp
over 5 year treasuries and receive floating prime. However it was
found to be very difficult to locate a counterparty who would do a
fixed-to-prime dollar swap. An intermediary structured a three
party swap in which :
1. A group of Japanese banks paid LIBOR in return for fixed
dollar at 100 bp over 5 year treasuries. A Plain vanilla coupon
swap.
2. A US based bank with LIBOR based funding and prime based
assets was willing to receive floating dollars at LIBOR and pay
floating dollars at prime minus 75 bp. This is a basis swap.
Outcome: The firm paid fixed and received prime-based floating.
Basis Swap + Vanilla Swap
Japanese Bank
Flt $
Fixed Rate Market
Fixed $
LIBOR
MANUFACTURING
FIRM
Flt $
LIBOR
US BANK
Prime Floating
Rate Market
Flt $
Prime
LIBOR Floating
Rate Market
 Transforming Callable Debt into Straight Debt
A firm issues a 7-year bond, callable at par after three years. The
issue is priced to yield 6.20% which is 20 bp above what the firm
would have paid for a straight i.e. non-callable bond. The firm
then sells a seven year swap callable after 3 years in which it
receives fixed at 6.40% and pays 6 month LIBOR. The
counterparty to this swap has paid a 40 bp premium for the option
to terminate the swap prematurely. The firm now has floating rate
debt at LIBOR-20bp. It then combines this with a plain vanilla
coupon swap in which it pays 6% fixed and receives 6 month
LIBOR. Net cost 5.80% fixed.
3 years later: Rates have risen, bond not called, callable swap not
called, the structure continues. Cost 5.80% for seven years.
Rates have fallen : Bond called, firm refunds at LIBOR, callable
swap called, plain vanilla swap continues. Firm has 6% fixed cost
for 4 years.
Further Innovations
• Several innovative products during the
last five or so years
• Originated as a response to specific needs
of investors and borrowers to achieve
customized risk profiles or to enable them
to speculate on interest rates or exchange
rates when their views regarding future
movements in these prices differed from
the market
Further Innovations
• A Callable Coupon Swap is a coupon
swap in which the fixed rate payer has the
option to terminate the swap at a specified
point in time before maturity and a
Puttable Swap can be terminated by the
fixed rate receiver
– Application of callable swap
– Transforming Callable Debt into Straight Debt
• Swaptions, as the name indicates are
options to enter into a swap at a specified
future date, the terms of the swap being
fixed at the time the swaption is
transacted
Further Innovations
• A Cross Currency Swaption (also
known as Circus Option) is an option
to enter into a cross-currency swap
with any combination of fixed and
floating rates
• Switch LIBOR Swaps, also known as
Currency Protected Swaps(CUPS)
and Differential Swaps (DIFFS) is a is
a cross-currency basis swap without
currency conversion
Further Innovations
• A Yield Curve Swap is, like a basis swap, a
floating-to-floating interest rate swap in
which one party pays at a rate indexed to
a short rate such as 3 or 6 month LIBOR
while the counterparty makes floating
payments indexed to a longer maturity
rate such as 10-year treasury yield
• In a Fixed-to-Floating Commodity Swap
one party makes a series of fixed
payments and receives floating payments
tied to a commodity price index or the
price of a particular commodity
Further Innovations
• In an Equity Swap, one party pays the
total return on an equity index such as
S&P 500 and receives payments tied to a
money market rate
Interest Rate Swaps in the Indian Market
Criteria for selecting a floating rate benchmark
• Available for the lifetime of the swap
• Market determined rate
• Relevant to the counterparties
• Transparent and easily calculated
• Benchmark rate should be liquid and deep
• Possible floating rate benchmarks in Indian markets
–
–
–
–
–
Term money rates
Treasury bill yields
Bank Rate
Bank deposit / lending rates
Overnight rates
Overnight Index is likely to be the most
relevant and acceptable floating rate
benchmark
• Overnight markets are deep and liquid
• Significant exposure and dependence on
overnight markets
• Lack of a deep and vibrant term money market
• Determination of overnight index would be
relatively simple
A Typical Overnight Indexed Swap deal
• Bank A wants to pay fixed rates and receive floating rates
• Bank B wants to pay floating rates and receive fixed rates
The two Banks enter into an OIS
• A notional principal is agreed upon
• Start dates and maturity dates are fixed (the term of the swap
could range from 1 week to a year depending on the
requirements of the two banks)
• The fixed rate (to be paid by Bank A to Bank B) is agreed
upon
• The floating rate calculations are made to replicate the
accrual on the notional principal as if the notional is actually
lent in O/N market for the term of the swap
• The two cash flows (fixed and floating) are netted and
settled at maturity
A Typical Overnight Indexed Swap deal
An example
• Counterparty pays 3m OIS at 9.25% for Rs 10 crore,
receives overnight rate
• In this case the details are as follows
– Notional principal is Rs 10 crores
– Term of the swap is 3 months, beginning March1, 1999 and
ending on June 1, 1999 (number of days is 92 )
– Rate for the fixed leg is 9.25%
– Rate for the floating leg is determined on maturity
• The cash flows will look as shown below
Pays 9.25%
T=92
T=0
Receives Compounded Overnight Rate, Rf
Net cash flows to fixed rate payer = (Rf - 9.25%) x 92/365 x 10,00,00,000
OIS Replicates the Behavior of a Cash Instrument
• Bank receives 3m deposit at 9.25% for Rs 10
crore, and lends in O/N market
Pays 9.25%
T=0
T=92
Receives Rf
• Cash flows replicate a bank paying 3m OIS at 9.25% for
Rs 10 crore and receiving overnight rate
• An OIS therefore, works like a corresponding cash
instrument
Computing OIS cashflows : An Example
Principal : 100 crores
Term : 7 Days
Overnight index for 7 days
Day 1 R 1
7.83%
Day 2 R 2
7.76%
Day 3 R 3
7.32%
Day 4 R 4
8.02% (weekend)
Day 5 R 5
8.11%
Day 6 R 6
8.22%
Fixed rate received : 8.50%
F 1 = 1.000215 = (1+R1*1/365)
F 2 = 1.000213 = (1+R2*1/365)
F 3 = 1.000201 = (1+R3*1/365)
F 4 = 1.000439 = (1+R4*2/365)
F 5 = 1.000222 = (1+R5*1/365)
F 6 = 1.000225 = (1+R6*1/365)
Overnight index compounded average for 7 days (Rf) = 7.90%
= ((F1*F2*F3*F4*F5*F6)-1)*365/7
Interest accrued on fixed l= 1630137 = 1000000000*8.50%*7/365
Interest accrued on floating leg = 1515068 = 1000000000*7.90%*7/365
Net interest payment by fixed rate payer = 115069
Example 1 : Asset Liability
Management
•
A typical nationalised Bank A : cash surplus, long term
liabilities, lack of assets, lends overnight and therefore
– runs asset liability mismatches, and gets lower
returns on funds
•
This bank receives 1 year deposit at 9.5% , options
available are
Returns
Liquidity
ALM
1. Lend it in overnight market
Low
High
Mismatch
2. Buy 1 year asset
High
Funds locked
No
mismatch
3. Enter into an OIS
High
High
No mismatch
(Pay float,Before
receive fix)and continue to lend in overnight markets
After
Pays fixed 9.5% on deposit
Bank A
Lends in o/n markets
Pays o/n rate in OIS
Pays fixed 9.5% on
deposit
Bank A
Receives o/n rates
Receives
fixed in OIS
Example 2 : Hedging Interest Rate Exposure
• Primary dealer typically fund securities positions in
overnight markets
– run asset liability mismatches
– are exposed to volatility in overnight rates
• Absence of term money market limits funding
options of a PD
• OIS offers the opportunity to hedge interest rate risk
and reduce asset liability mismatches
– PD pays fixed and receives floating
– still borrows in call and retains flexibility in
position management
Entire position exposed to call rates
Pays fixed in OIS
Pays o/n for
funding
positions
PD
Receives
fixed on
bonds
Pays o/n for
funding
positions
PD
Receives fixed on
bonds
Receives o/n in
OIS
Example 3 : Cash Management Tool for
Corporates
• Cash surplus entities like mutual funds, financial
institutions and some corporates allocate some
cash in liquid assets like overnight deposits for
maintaining liquidity
• Through an OIS, these entities can still lend
overnight and keep their liquidity but lock into a
term rate thus enhancing the returns on funds
deployed.
• Similarly corporates who need cash issue CPs at
fixed rates, but have a view that interest rates are
coming down
• These corporates, through an OIS can convert their
fixed rate liabilities to liabilities linked to overnight
rates to benefit from any drop in rates.
Example 4 : Position Taking / View
Execution
• Carry Trades
– Overnight rates expected to remain
stable
– Position replicated in OIS by receiving
fixed and paying floating
• Stable Steep Yield Curve
– Ideal position is to borrow overnight
and invest in longer term
– Position replicated in OIS by receiving
fix and paying overnight
• Stable Inverted Yield Curve
– Ideal position is to borrow long term
and lend overnight
– Position replicated in OIS by paying
fixed and receiving overnight
Minimal Capital Adequacy Requirements
• Capital adequacy has to be maintained on the swap’s balance sheet
exposure
• Balance sheet exposure is sum of mark to market gains and
potential exposure over the remaining life of the swap
• Mark to market gains
– amount the bank would need to pay to replace the stream of
payments in case the counterparty defaults
• Potential exposure on account of future fluctuations in interest rate
– can be determined by applying credit conversion factors to the
notional
– credit conversion factors will be based on volatility of the
underlying floating rate and residual maturity of the swap
– Basle committee norms could be used as a reference for credit
conversion factors
COMPARISON SWAP METHOD OF VALUATION
To value the given swap, we construct a notional "comparison swap"
with the following characteristics :
(1) It must value to zero i.e. it must be at a fixed rate that a swap dealer
would be prepared to trade given the prevailing rates for standard swaps.
(2) It should have an identical floating leg as the swap being valued
except having no margin over the floating index and a "stub" first
period.
Consider a 5-year GBP coupon swap which has 3 years and 9 months to
go.
The LIBOR for the current 6-month period, which was set 3 months ago,
is 10.5%.
The swap market quotes fixed rates vs. LIBOR for swap maturities of 1,2
3..10 years
The given swap has the following payment streams (stated as %
of underlying notional principal :
Months from Now
Fixed
Floating
3
5.5%
-5.25%
9
5.5%
?
15
5.5%
?
21
5.5%
?
27
5.5%
?
33
5.5%
?
39
5.5%
?
45
5.5%
?
What stream of payments a swap dealer would be willing to exchange in a
swap starting now and terminating 3 years and 9 months from now given
the current state of the swap market?
(1) Interpolate between the 3-year and 4-year swap rates. Assume that the 3year rate is 9.75% semiannual payments and the 4-year is 10% semiannual
payments. the interpolated rate is given by :
9.75 + (9/12)[10.00-9.75] = 9.9375% s.a.
(2) Further, since the first fixed payment is going to be 3 months from now,
we must "decompound" this rate i.e. use a quarterly equivalent of this
semiannual rate. Use the formula
Rm = m{[1+(Rn/n)]n/m –1}
With m = 4, n = 2, Rn = 9.9375%
(3) Rm works out to 9.8170%. Thus the first fixed payment on the
comparison swap must be (1/4)(9.8170) = 2.45425%. Thus the payments
stream on the comparison swap would be (again as % of face value) :
Months from Now
Fixed
Floating
3
2.45425
-2.625
9
4.96875
?
15
4.96875
?
21
4.96875
?
27
4.96875
?
33
4.96875
?
39
4.96875
?
45
4.96875
?
The value of the given swap can be found by subtracting the cashflows of
the comparison swap from those of the given swap and finding the present
value of the residual cash flows. In this process, the unknown floating
payments cancel out.
Months from Now
Residual Cash Flow (% of Principal)
3
0.42075
9
0.53125
15
0.53125
21
0.53125
27
0.53125
33
0.53125
39
0.53125
45
0.53125
Find the PV of this stream, first as of 3 months from now using the
interpolated rate of 9.9375% s.a. and discount this back to today at
today's 3-month LIBOR which is 10.5%. This works out to 3.41% of the
underlying principal.
INTRODUCTION TO ZERO-COUPON PRICING
The problem of pricing consists in finding a sequence of fixed payments
C at , 2,... which has the same present value as the sequence of floating
payments. If we know the floating payments at each of these dates, we
can discount them back to the start date by an appropriate discount
factor and then find C. The difficulty is we do not know the size of
floating payments.
Suppose we are at time t. A floating payment is due at time D2. The
floating rate will be set at D1, t < D1 < D2. The payment will equal
P  rD1D2  D1D2.
where P is the notional principal, rD1D2 is the applicable rate to be set at
D1 and D1D2 is the day-count fraction between D1 and D2 We do not
know rD1D2 but we do know the forward rate implied by the two
observed rates rtD1 and rtD2. The forward rate D1D2 is given by
(1+rtD1tD1)(1+D1D2D1D2) = (1+rtD2tD2)
The forward rate D1D2 is given by
(1+rtD1tD1)(1+D1D2D1D2) = (1+rtD2tD2)
Denote by Fi the discount factor applicable at time t to date Di. We have
Fi = 1/[1+rtDitDi]
Then
D1D2 = (1/D1D2)[(F1/F2)-1]
With rD1D2 unknown, the best we can do is to use D1D2 in its place.
Therefore the floating payment due at D2 is
P  D1D2  D1D2 = P[(F1/F2)-1]
and its present value at time t is
F2P[(F1/F2)-1] = P(F1 - F2)
This is simply the PV of an inflow of P at D1 and an outflow of P at D2.
Thus a floating payment can be simply looked at as a combination of an
inflow and an outflow of the underlying principal amount.
Now consider a two year fixed to LIBOR swap with effective date D1 and
four floating payments every six months starting D2. This is equivalent to an
inflow of P at D1 and an outflow of P at D5 two years later. Figure A.16.2
illustrates. The present value of this sequence is then
P(F1 - F5)
To price the swap, find the size C of an annuity such that
j= 5
CF
j
= P( F1 - F5 )
j= 2
To implement the procedure, we must get the discount
factors F1, F2 ...etc. These can be obtained from a yield
curve estimated from data on treasury bond prices. A
credit risk premium would have to be added. This
premium itself may have a term structure. Alternatively
they can be obtained from data on money market yields
and par swap quotes.
Valuation Issues for Interest Rate Swaps
One can view interest rate swaps as:
Long position in bond with a short position in another bond or as
a portfolio of forward contracts.
The value of the swap (for the institution paying floating and
receiving fixed), denoted V, is (assume that the financial
institution receives fixed payments of C dollars at times s and
make floating payments at the same times):
V ( t ) = b ( t ) – b*(t)
b( t ): value of fixed-rate bond underlying swap.
b*( t ): value of floating-rate bond underlying swap.
The discount rates used in the valuation reflect the riskiness of
the cash flows. Note that: [r(n) is the discount rate at date n]:
b =  C  e-r(s) s + Q  e-r(T) T
where Q is the notional principal underlying the interest rate
swap, C is the fixed payment and the summation goes from s=1
to s=T the termination date of the swap
b* = C*  e-r(t1) t1 + Q  e-r(t1) t1
where the floating rate bond, b* must have, after the payment at
time t1 value equal to the notional principal , Q , and C* is the
floating rate payment due at time t1 .
Interest Rate Swaps
Example: Financial institution pays 6-month LIBOR and receives
8% per annum (with semiannual compounding) on a notional
principal of $100 Million. The swap has a remaining life of 1.25
years. The relevant discount rates are 10%, 10.5%, and 11% for 3
months, 9 months, and 15 months. The 6 month LIBOR rate at the
last payment date was 10.2% (and the reset frequency is 3
months).
Note For s= 3/12 = 0.25; r = 0.10 For s = 9/12 = 0.75; r=0.105
For s = 1.25; r = 0.11
t1 = 3 months = 0.25
r ( t1 = 1) = 0.10 [reset frequency discount rate]
C = ½  0.08 100 = 4 Million [coupon for fixed]
C* = ½  0.102 100 = 5.1 Million [coupon for floating].
Interest Rate Swaps
Example: Financial institution pays 6-month LIBOR and receives
8% per annum (with semiannual compounding) on a notional
principal of $100 Million. The swap has a remaining life of 1.25
years. The relevant discount rates are 10%, 10.5%, and 11% for 3
months, 9 months, and 15 months. The 6 month LIBOR rate at the
last payment date was 10.2% (and the reset frequency is 3
months).
Note For s= 3/12 = 0.25; r = 0.10 For s = 9/12 = 0.75; r=0.105
For s = 1.25; r = 0.11
t1 = 3 months = 0.25
r ( t1 = 1) = 0.10 [reset frequency discount rate]
C = ½  0.08 100 = 4 Million [coupon for fixed]
C* = ½  0.102 100 = 5.1 Million [coupon for floating].
Interest Rate Swaps .. Example of Valuation of
a Swap
Then
b = 4 (e-0.25  0.1 + e-0.75  0.105) + 104 (e-1.25  0.1) = 98.24
million
b* = 5.1 (e-0.25  0.10) + 100 e-0.25  0.10 = 102.51
The value of the swap to the fixed rate receiver is
98.24 – 102.51 = -4.27 million.
The value to the fixed rate payer is obviously +
4.27million
Unwinding of OIS : An Example
Principal:100 crores Term : 28 Days Fixed rate received : 8.50%
Unwind after
7 days
Overnight index for 7 days
Day 1 R 1 7.83%
F 1 = 1.000215 = (1+R1*1/365)
Day 2 R 2 7.76%
F 2 = 1.000213 = (1+R2*1/365)
Day 3 R 3 7.32%
F 3 = 1.000201 = (1+R3*1/365)
Day 4 R 4 8.02% (weekend) F 4 = 1.000439 = (1+R4*2/365)
Day 5 R 5 8.11%
F 5 = 1.000222 = (1+R5*1/365)
Day 6 R 6 8.22%
F 6 = 1.000225 = (1+R6*1/365)
21 day OIS rate
8.25%
Overnight index compounded average for 7 days (Rf) = 7.90% =
((F1*F2*F3*F4*F5*F6)-1)*365/7
Interest accrued on fixed leg = 1630137 = 1000000000*8.50%*7/365
Interest accrued on floating leg = 1515068 = 1000000000*7.90%*7/365
Net interest accrued for first 7 days = 115069 = 1630137 - 1515068
Profit / Loss locked into for 21 day = 143836 = 1000000000*(8.50%-8.25%)*21/365
Unwind value on maturity date = 258905 = 143836 + 115069
Value if settled on unwind date = 257682 = 258905/(1+8.25%*21/365)
Valuation Formula for Currency Swaps
Let V be the value of the swap to the party paying U.S. dollar
interest rates.
Then V ( t ) = S ( t ) b*( t; T ) – b(t, T)
S(t): exchange rate, USD per unit of FC
b*( t; T ): is the value of foreign currency denominated bond
underlying the swap.
b ( t; T ): value of the U.S. dollar underlying the swap.
Example : Let the term structure be flat in the U.S. and Japan and
is respectively 9% and 4%. A financial institution has entered into
a currency swap where it receives 5% in yen and pays 8% in
dollars once every year. The principals are 10 M Dol. And 1,200
M yen. The swap will last for another 3 years and the current
exchange rate is 110 yen = 1$.
In this case:
b ( t; T ) = 0.8e-0.09 + 0.8e-0.18 + (10.8)e-0.27 = 9.64m
USD
And
b*(t, T) = 60e-0.04 + 60e-0.08 + 1260e-0.12 = 1230.55m
JPY
The value of the swap is:
V ( t ) = (1/110)(1230.55) – 9.64 = 1.55m USD
If the financial institution had been paying yen and
receiving USD, the value of the swap would have
been –1.55m USD
CREDIT DERIVATIVES
CREDIT DEFAULT SWAP (CDS)
An example may help to illustrate how a typical deal is
structured. Suppose that two parties enter into a five-year
credit default swap on March 1, 2010. Assume that the
notional principal is $50 million and the buyer agrees to
pay 80 basis points annually for protection against default
by the reference entity. If the reference entity does not
default (that is, there is no credit event), the buyer receives
no payoff and pays $400,000 on March 1 of each of the
years 2011, 2012, 2013, 2014, and 2015. If there is a credit
event a substantial payoff is likely. Suppose that the buyer
notifies the seller of a credit event on September 1, 2013
(half way through the fourth year).
CDS …
If the contract specifies physical settlement, the buyer has the
right to sell $50 million par value of the reference obligation for
$50 million. If the contract requires cash settlement, the
calculation agent would poll dealers to determine the midmarket value of the reference obligation a predesignated number
of days after the credit event. If the value of the reference
obligation proved to be $25 per $100 of par value, the cash
payoff would be $37.5 million.
In the case of either physical or cash settlement, the buyer would
be required to pay to the seller the amount of the annual
payment accrued between March 1, 2003 and September 1, 2003
(approximately $200000), but no further payments would be
required.
There are a number of variations on the standard credit default
swap.
• In a binary credit default swap, the payoff in the event of a
default is a specific dollar amount.
• In a basket credit default swap, a group of reference entities
are specified and there is a payoff when the first of these
reference entities defaults.
• In a contingent credit default swap, the payoff requires both a
credit event and an additional trigger. The additional trigger
might be a credit event with respect to another reference entity
or a specified movement in some market variable.
• In a dynamic credit default swap, the notional amount
determining the payoff is linked to the mark-to-market value of
a portfolio of swaps.
CREDIT DEFAULT SWAP
TOTAL RETURN SWAP
A swap agreement in which one party makes payments based
on a set rate, either fixed or variable, while the other party
makes payments based on the return of an underlying asset,
which includes both the income it generates and any capital
gains. In total return swaps, the underlying asset, referred to
as the reference asset, is usually an equity index, loans, or
bonds. This is owned by the party receiving the set rate
payment.
Total return swaps allow the party receiving the total return
to gain exposure and benefit from a reference asset without
actually having to own it. These swaps are popular with hedge
funds because they get the benefit of a large exposure with a
minimal cash outlay.
In a total return swap, the party receiving the total return will
receive any income generated by the asset as well as benefit if the
price of the asset appreciates over the life of the swap. In return,
the total return receiver must pay the owner of the asset the set
rate over the life of the swap. If the price of the assets falls over
the swap's life, the total return receiver will be required to pay
the asset owner the amount by which the asset has fallen in price.
For example, two parties may enter into a one-year total return
swap where Party A receives LIBOR + fixed margin (2%) and
Party B receives the total return of the S&P 500 on a principal
amount of $1 million. If LIBOR is 3.5% and the S&P 500
appreciates by 15%, Party A will pay Party B 15% and will
receive 5.5%. The payment will be netted at the end of the swap
with Party B receiving a payment of $95,000 ($1 million x 15% 5.5%).
TOTAL RETURN SWAP
Total-rate-of-return swaps (TRORSS) transfer the returns and
risks on an underlying reference asset from one party to another.
TRORSS involve a “total return buyer,” who pays a periodic fee
to a “total return seller” and receives the total economic
performance of the underlying reference asset in return.
“Total return” includes all interest payments on the reference
asset plus an amount based on the change in the asset’s market
value. If the price goes up, the total-return buyer gets an amount
equal to the appreciation of the value, and if the price declines,
the buyer pays an amount equal to the depreciation in value. If a
credit event occurs prior to maturity, the TRORS usually
terminates, and a price settlement is made immediately
CDOs vary in structure and underlying assets, but the basic
principle is the same. A CDO is a type of Asset-backed
security. To create a CDO, a corporate entity is constructed
to hold assets as collateral and to sell packages of cash flows
to investors. A CDO is constructed as follows:
A special purpose entity (SPE) acquires a portfolio of
underlying assets. Common underlying assets held include
mortgage-backed securities, commercial real estate bonds
and corporate loans.
The SPE issues bonds (CDOs) in different tranches and the
proceeds are used to purchase the portfolio of underlying
assets. The senior CDOs are paid from the cash flows from
the underlying assets before the junior securities and equity
securities. Losses are first borne by the equity securities, next
by the junior securities, and finally by the senior securities.