International Financial Management

P G Apte

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 Cross-Currency 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

Party A (Firm) Party B (Bank)

Funding objective $ Fixed Rate $ Floating Rate

Fixed Rate Cost 6% 4.5%

Floating Rate Cost 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 Prime-25bp Prime-25bp Prime+75bp 6.5% Fixed To Floating to Fixed Rate Lenders Rate Lenders

SWAP BANK

XYZ CORP.

ABC BANK

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. Beta Bank Requirement: Fixed rate USD Fixed rate CHF

Funding Funding Cost of $Funding: 12.5% 11% Cost of CHFFunding: 6.5% 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 6.5% CHF 6.5% CHF CHF USD USD CHF 6.5% TO CHF LENDERS 11% TO USD LENDERS INITIAL EXCHANGE OF PRINCIPALS FINAL RE-EXCHANGE OF PRINCIPALS

SWAP BANK

ALPHA COMPANY

BETA BANK

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 fixed-to-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    

Fixed $ Flt. DEM Fixed DEM   Fixed $ Fixed $   Fixed DEM Flt.DEM  Flt. DEM to Fixed $ to Lenders Bondholders    

   Fixed DEM to Lenders

 

THE BANK  PMWSYNDICATE

BANKS

FINANCIALINSTITUTION

XYZ    

                                  

 

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

TABLE 1 Exchange CHF Flows CHF DEM flows DEM Date (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  

Fixed Rate Market       

Prime Floating Rate Market  

Flt $ Flt $  

  LIBOR Prime 

LIBOR Floating Rate Market

 Japanese Bank

MANUFACTURINGFIRM

US BANK

 

 

 

  

Flt $ Fixed $ LIBOR

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

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

Interest Rate Swaps in the Indian Market

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

T=0

T=92

Pays 9.25%

Receives Compounded Overnight Rate, Rf Net cash flows to fixed rate payer = (Rf - 9.25%) x 92/365 x 10,00,00,000

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

T=0T=92

Pays 9.25%

Receives Rf

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

• 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 ExamplePrincipal : 100 crores Term : 7 Days Fixed rate received : 8.50%

Overnight index for 7 daysDay 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)

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%*7/365Interest accrued on floating leg = 1515068 = 1000000000*7.90%*7/365Net 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 Mismatch2. Buy 1 year asset High Funds locked No

mismatch3. Enter into an OIS High High No mismatch(Pay float, receive fix)and continue to lend in overnight markets

Before After

Receives o/n rates

Pays o/n rate in OIS

Receives fixed in OIS

Bank A

Pays fixed 9.5% on deposit

Lends in o/n markets

Pays fixed 9.5% on deposit

Bank A

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

Receives fixed on bonds

Pays fixed in OIS

Receives o/n in OIS

PDPays o/n for funding positions

Receives fixed on bonds

PD

Entire position exposed to call rates

Pays o/n for funding positions

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 3-year 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+rtD1tD1)(1+D1D2D1D2) = (1+rtD2tD2)

The forward rate D1D2 is given by

(1+rtD1tD1)(1+D1D2D1D2) = (1+rtD2tD2)

Denote by Fi the discount factor applicable at time t to date Di. We have

Fi = 1/[1+rtDitDi]

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

)F - FP( = CF 51j

5=j

2=j

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 ExamplePrincipal:100 crores Term : 28 Days Fixed rate received : 8.50%Unwind after 7 daysOvernight index for 7 daysDay 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%*7/365Interest accrued on floating leg = 1515068 = 1000000000*7.90%*7/365Net interest accrued for first 7 days = 115069 = 1630137 - 1515068Profit / Loss locked into for 21 day = 143836 = 1000000000*(8.50%-8.25%)*21/365Unwind value on maturity date = 258905 = 143836 + 115069Value 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 mid-market 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.