2. Products
• Forward Rate Agreements (FRAs)
• Interest Rate Swaps
• Interest Rate Options
o Embedded bond options
o Put/call options on bonds and interest rates
o Interest rate Caps, Floors and Collars
o Range Accruals
o Swaptions
• Interest Rate Futures
3. Requirements for Development of
Market in Interest Rate Derivatives
• A well-developed yield curve
• A liquid market
• Existence of sufficient volatility
• An unambiguous way of determining term
structure of volatility.
• Mechanisms for hedging the product.
4. Forward Rate Agreement (FRA)
• A financial contract between two parties to
exchange interest payments based on a ‘notional
principal’ for a specified future period
• On the settlement date, the contracted rate is
compared to an agreed benchmark/reference rate
as reset on the fixing date
• Terminology
o 3 x 6- An agreement to exchange interest payments
for a 3-month period, starting 3 months from now.
o Buy FRA – pay fixed and receive benchmark rate
o Sell FRA – receive fixed and pay benchmark rate
• Settlement takes place at the start date of the
FRA
5. Quoting
A typical FRA quote would look like
6 X 9 months: 7.20 - 7.30% p.a.
This has to be interpreted as
• The bank will accept a 3 month deposit starting six
months from now, maturing 9 months from now, at an
interest rate of 7.20% (bid rate)
• The bank will lend for a period of 3 months starting six
months from now, maturing 9 months from now, at an
interest rate of 7.30% (offer rate)
6. Example of a FRA deal
• A corporate has an expected requirement for
funds after 3 months but is concerned that
interest rates will head higher from current
levels.
• The corporate can enter into a FRA to hedge or
fix his borrowing cost today for the loan to be
raised after 3 months.
• The rate agreed in the FRA has to be compared
to the benchmark rate to determine the
settlement
• Therefore, the corporate buys a 3 X 6 FRA from a
Bank at say 6.75% with the benchmark rate being
the 3 month CP issuance rate.
7. Terms of the FRA deal
• Bank & corporate enter into a 3 X 6 FRA.
Corporate pays FRA rate of 6.75%. Bank pays
benchmark rate based on 3 month CP issuance
rate of the above corporate 3 months later.
• Notional principal Rs 10 crore
• FRA trade date 27th July 2002
• FRA start/settlement date 27th October 2002
• FRA maturity date 27th January 2003
• Theoretically, the fixed rate of 6.75% is obtained
by pricing of the forward rate, from the current
rates.
8. Cash flows for the FRA deal
• Assume, 3 month CP rate for the Corporate on fixing
date (say 27/10/2002) = 7%
• Cash flow Calculations
o (a) Interest payable by Corporate
= 10 Cr * 6.75% *90/365
= Rs 16643836
o (b) Interest payable by Bank
= 10 Cr * 7% * 90/365
= Rs 17260274
o (c) Net payable by Bank on maturity date = Rs 616438
o (d) Discounted amounted payable
= Rs 61,644/(1+7%*92/365) = Rs 605750
Amount payable by the Bank on settlement date
=Rs 605750
9. Possible benchmarks for FRAs
• 3-month, 6-month OIS rates
• 3-month, 6-month CP or T-bill
• OIS rates could be the best benchmarks as it is
then possible to hedge the FRA position by
takings positions in OIS
10. Uses of FRAs
• For corporates seeking to hedge their future loan
exposures against rising rates.
• For inter-bank participants, for speculative
purposes
o Buy FRA if the view is that the realized forward rate
will be higher than the agreed fixed rate
o Sell FRA if the view is that the realized forward rate
will be lower than the agreed fixed rate
11. Interest Rate Swaps (IRS)
• An agreement to exchange a series of fixed cash
flows with a series of floating cash flows
• The floating cash flows are based on the
observed value of the floating rate on the
previous reset date
• The fixed rate in the swap is referred to as the
swap rate
• There is no exchange of principal in an IRS
• Available benchmarks in the Indian market are
o overnight NSE MIBOR and MITOR
o 6-month rupee implied rate (MIFOR)
o INBMK rates (GSec yields)
12. Analogy between FRA and IRS
• IRS is similar to a FRA except that
o in a typical FRA the benchmark rate is reset only
once whereas in a swap, there are more than one
resets.
o in a typical IRS the settlement happens at maturity
whereas in a FRA the net settlement amount is
discounted to the FRA start date
• An IRS can be considered as a series of FRAs
13. Uses of swaps
• Asset-liability management
• Convert floating rate exposure to fixed exposure
and vice-versa
• Take a speculative view on interest rates and
spreads between interest rates
• Change the nature of an investment without
incurring the costs of selling one portfolio and
buying another
• Reduce cost of capital
• Access new sources of funding
• Credit risk is also low since there is no exchange
of principal and only net interest payments are
exchanged.
14. Criteria for floating rate benchmarks
• Available for the lifetime of the swap
• Market determined rate
• Relevant to the counterparties
• The rate should be unambiguously known to all
market participants
• Should be liquid and deep
15. Overnight Index Swap
• The floating rate is an overnight rate such as
NSE MIBOR or MITOR, which is reset daily
• The interest on the floating leg is calculated on a
daily compounded basis
• Overnight index swaps can be categorized into
o <= 1 yr maturity
o > 1 yr maturity
• In the <=1 yr category, exchange of cash flows
takes place only at maturity, there are no
intermediate cash flows
• In the > 1 yr category, cash flows are exchanged
every 6 months
16. Overnight Index swap - an example
• Bank A enters into a 7 day OIS with Bank B,
where Bank A pays a 7 day fixed rate @ 6.50%
and receives overnight NSE MIBOR. The notional
amount is Rs 10 cr.
17. Calculating Cash Flows
• Let us say NSE MIBOR rates are as follows
o Day 1 6.61%
o Day 2 6.40%
o Day 3 6.82%
o Day 4 6.75%
o Day 5 6.70%
o Day 6 6.74%
o Day 7 6.68%
• The principal amount of Rs 10 cr on the floating
leg gets compounded on a daily basis.
18. Calculating Cash flows
Total accrual on a floating leg = Rs 108098
Total accrual on fixed leg = 100000000*6.50% *7/365
= Rs 124657
19. Settlement
• Net interest payment
= 124657 - 108098
= Rs 16659
• This amount will be paid by party A to party B at
maturity
20. Reversing an Outstanding OIS
Position
• Unwinding/reversing an existing OIS position is
entails deriving the mark-to-market position of
the swap
• As per the example : Bank A enters into a 7 day
OIS with Bank B, whereby it pays fixed and
receives floating. After 3 days Bank A wants to
get out of the position. What can Bank A do ?
o Option 1: book a reverse swap - receive fixed and
pay floating for 4 days
o Option 2: cancel the outstanding OIS with Bank B
21. Option 1: Booking a Reverse Swap
• Bank A can book a reverse swap with a
counterparty for the residual tenor of 4 days
where it receives a fixed rate and pays Overnight
MIBOR
• The reverse swap would have to be booked on a
revised principal which is the original principal
plus the interest accrued on the floating leg
• This method replicates cancellation of the
outstanding swap
• However, this method is credit and capital
inefficient
22. Option 2 : Cancelling the outstanding
OIS
• Canceling an OIS will have two components
o Component 1 : The first component will be the
difference between the interest accrued on the OIS
fixed leg and on the floating leg from the start date
to the current date
o Component 2 : The second component will be the
difference between the original fixed rate and the
reversal rate
23. Cancelling the OIS: Calculations
Original OIS
Principal INR 100 crores
Tenor of the swap 7 days
Start Date 27th July 1999
End date 3rd Aug 1999
Swap rate Bank A pays fixed rate to bank B at 8.50 %
Bank A receives overnight MIBOR from Bank B
Cancellation
Bank A approaches Bank B to cancel the outstanding OIS
on 30th July, 1999
Bank B quotes a rate of 8.25% to cancel the outstanding
swap
24. Cancelling the OIS: Calculations
Component 1
Overnight rate Notional Principal Accrued interest
Day 1 7.83% 1,000,000,000 214,521
Day 2 7.76% 1,000,214,521 212,648
Day 3 7.32% 1,000,427,169 200,634
Interest accrued on floating leg 627,803
payable by Bank B on unwind date
Interest accrued on floating leg payable by Bank B on maturity
= Future Value of INR 627,803 on maturity date
= 627,803*(1+627,803*8.25%*4/365)
= 628,371
25. Cancelling the OIS: Calculations
Component 2
Cancellation OIS rate = 8.25%
Difference in fixed rates payable by bank A on maturity date
= 1,000,000,000*(8.50%-8.25%)*4/365
= 27,397
Cancellation value on maturity date payable by bank A to bank
B
= Component 1 + Component 2
= 97,656
Value if settled on cancellation date
= 97,656 / (1+8.25%*4/365)
= INR 97,568
26. Constant Maturity Swaps (CMS)
• Atleast one of the legs of the swap is linked to a
floating rate which has a constant tenor
• The most common is the constant maturity
Treasury (CMT) swap, where the floating rate is
the INBMK GSec yield
• Examples of a CMT swap
o an agreement to receive 7.5% fixed and pay the 5-yr
INBMK GSec rate every six months.In this case, the
benchmark security will keep changing on each
reset date such that it is close to the maturity of 5
yrs
o An agreement to exchange 6-month MIFOR rate with
the 5-yr OIS swap rate every 6 months, for the next 5
yrs
27. Types of CMS Structures
• One side pays fixed and the other pays a CMS
rate.
• Both sides are floating, one is a CMS rate and the
other a floating rate such as 6-month MIFOR
• Both sides pay a CMS rate
28. Advantages of CMS over Plain Vanilla
IRS
• It enables to indulge in curve play- taking
advantage of expectations of movements in the
spreads between two rates
o If one believes that the spread between the 10-year
swap rate and the 6-month LIBOR rate is going to
decrease in the future, one can enter into a CMS in
which one will receive the 6-month LIBOR and will
pay the 10-year swap rate.
• It enables one to execute views on the shape of
the yield curve.
o A belief that the 5-10 segment of the yield curve is
steep can be exploited by paying the 5-yr GSec rate
in one CMS and receiving the 10-yr GSec rate in
another CMS.
29. Advantages of CMS over Plain Vanilla
IRS
• Investors can use CMS/CMT swap to target
specific instrument maturities.
• The structure of the swaps is such that you can
effectively lock into a rate on a constantly rolled
over instrument of specific term. This is in
contrast to the investor who holds say a fixed
asset instrument.
o For e.g. the investor wants to hold a bond of 10
years maturity. If he buys the bond, after one year,
its maturity becomes 9 years and so the investor’s
purpose is not served. But by entering into a CMS,
the investor can maintain constant asset duration.
31. Amortizing Swaps
• Principal amount decreases at pre-specified
points of time over the life of the swap
• Motivation
o swap an exact series of flows derived from some
form of liability financing
o Hedge for an amortising asset if the investor wants
to take only the credit risk and not interest rate risk
32. Accreting Swaps
• Accreting
o principal amount increases at pre-specified points of
time over the life of the swap
• Motivation
o swap an exact series of flows derived from some
form of asset inflows
o Hedge for an accreting asset if the investor wants to
take only the credit risk and not interest rate risk
33. Basis Swaps
• A Basis swap is
o contractual agreement
o exchange a series of cash flows
o over a period of time.
o each swap leg is referenced to a floating rate index
• A Basis Swap is most commonly used when
o liabilities are tied to one floating index and
o financial assets are tied to another floating index
o This mismatch can be hedged via a basis swap
34. Leveraged Swap
• The counterparty on the floating leg makes
payments which are a multiple of a floating
benchmark
• Examples
o USD IRS where A receives USD 10% sa and pays
2.75 x 6-month USD LIBOR, every six months
o MIFOR swap where A pays 10% fixed INR sa and
receives 1.5 x 6-month MIFOR sa.
35. Significance of Leveraged Swaps for
Indian Corporates
• For corporates interested in positive carry deals
o Leveraged swap increases the positive carry for the
first setting, though the negative carry towards the
end of the swap will increase
• For corporates interested in view taking
o The leverage factor helps to multiply the quantum of
bet with the same notional principal. It magnifies the
quantum of both profits and losses
• For corporates interested in hedging
o In case the corporate has offered a deposit structure
with leverage involved in it
36. In-arrears Swap
• Normally, in a swap, there is a time lag between
the observed value of the floating rate and the
payment on the floating leg.
o The payment on the floating leg is based on the
value of the floating benchmark at the last reset
date.
• In an in-arrears swap, the payment on the
floating leg is based on the value of the floating
rate on the payment date itself
37. Inverse Floater Swaps
• Seek to take advantage of, or protect against, a
steep yield curve
• Pay/receive floating rate index versus
receive/pay fixed rate less floating rate index
(inverse side)
• Inverse side’s flows move inversely with floating
rate index
• Used to ‘leverage’ a specific view on the floating
rate index (I.e., compound the effect of the
movement)
38. Differential Swaps
• Have been used in recent years by investors and
corporates who are attempting to take on a view
on foreign markets, without being exposed to
currency risk
• Typical structure - Bank receives 6 month USD
LIBOR in exchange for paying 6 month MIFOR,
all in rupees
• No currency risk for the bank
39. Forward Start Swap
• Let us say that a company knows that six months
from today, it will borrow via a floating rate loan
• The company wishes to to swap the floating
liability for a fixed liability by entering into a
swap where it will receive floating and pay fixed
• The company can enter into a six-month forward
start swap today.
40. Range Accrual Swaps
• The interest on one side accrues only when the
floating rate benchmark is within a certain range
• The range may be fixed for the life of the swap or
may be variable
• Example
o Interest of 6% on fixed leg is to be exchanged every
quarter with 3-month LIBOR, for a period of 3 years
o Interest of 8% will accrue only on the days when
3-month LIBOR is between 0 and 6% for the first year
3-month LIBOR is between 0 and 6.5% for the first
year
3-month LIBOR is between 0 and 7% for the first year
41. Embedded Bond Options
• A callable bond allows the issuer to buy back the
bond at a specified price at certain times in the
future
• The holder of the bond has sold a call option to
the issuer
• The call option premium gets reflected in the
yield quoted on the bond
• Bonds get call options offer higher yields
42. Embedded Bond Options
• A puttable bond allows the holder early
redemption at a specified price at certain times in
the future.
• The holder of the bond has purchased a put
option from the issuer
• The option premium gets reflected in the yield
quoted on the bond
• Bonds with put options provide lower yields
43. Examples of Embedded Bond
Options
• Early redemption features in fixed rate deposits
• Prepayment features in fixed rate loans
• Situation where a bank quotes a particular 5-yr
rate to a borrower and says that the rate is valid
for the next two months
o The borrower has effectively purchased a put option
in this case with a maturity of two months
44. European Put/Call Options on Bonds
• A call option refers to the right to buy a bond for
a certain price at a certain date
• A put option refers to the right to sell a bond for
a certain price at a certain date
• The strike price could be defined to be either the
clean price or dirty price
• In most exchange-traded bond options, the strike
price is a quoted price or clean price
45. European Put/Call Options on
Interest Rates
• Here, the option underlying is some benchmark
interest rate.
• He strike rate is also specified in terms of the
level of the benchmark interest rate
• Let
• R = value of benchmark rate at maturity of option
• X = strike level
• P= notional principal
• Call option value = P x max (R-X, 0)
• Put option value = P x max (X –R,0)
46. Interest Rate Caps
• They provide insurance against rising interest
rates on a floating rate loan exceeding a certain
level
• The above level is referred to as the cap rate
• It is written by the lender of interest rate funds
• If the same bank or financial institution is
providing both the loan and the cap, the cap
premium gets reflected in a higher rate charged
on the loan. The cap is of embedded type
• They can be regarded as a series of call options
on interest rates, with the option payoffs
occurring in arrears or as a series of put options
on bonds
47. Interest Rate Cap- Example
• Consider a floating rate loan with a principal
amount of Rs 10 crore
• The floating rate is 3-month LIBOR and it is reset
every 3 months
• The rate has been capped at 10%.
• So, at the end of each quarter, payment made by
the financial institution to the borrower
= 0.25 x 10 x max (R - 0.1 , 0)
where R is the 3-month LIBOR rate at the beginning
of the quarter
48. Interest Rate Floors
• They guarantees a minimum interest rate level on
a floating rate investment
• Just like a cap, they can be either in naked form
or can be embedded in a loan or swap
• They are written by the borrower of interest rate
funds
• They can be regarded as a a series of put options
on interest rates or a series of call options on
discount bonds
49. Interest Rate Collars
• They put a cap on the maximum rate as well as a
floor on the minimum rate that will be charged
• They can be considered as a combination of a
long position in a cap and a short position in a
floor.
• They can be structured in such a way that the
price of the cap equals the price of the floor, so
that the net cost of the collar is zero
50. European Swaptions
• They are options on interest rate swaps
• They give the holder the right to enter into a
interest rate swap at some time in the future
o If the right is to receive fixed in the swap, it is
referred to as receiver swaption
o If the right is to pay fixed in the swap, it is referred to
as payer swaption
• They can be regarded as options to exchange a
fixed rate bond for the principal of the swap
o A payer swaption is a put option on the fixed rate
bond with strike price equal to the principal
o A receiver swaption is a call option on the fixed rate
bond with strike price equal to the principal
51. European Swaption - Example
• Consider a corporate that knows that in 6
months, it will enter into a 5-yr floating rate loan
with 6-monthly resets
• Company wishes to convert the floating rate loan
into a fixed rate loan
• The company enters into a swaption, wherein it
agrees to pay a fixed rate of X% in the swap.
• If the swap rate at the end of 6 months turns out
to be more than X%, the company will exercise
the swaption.
• If the swap rate at the end of 6 months turns out
to be less than X%, the company will not exercise
the swaption but will access the swap market
directly.
52. Advantages of swaptions
• They guarantee to corporates that the fixed rate
of interest that they will pay on the loan at some
future time will not exceed a certain level
• They are an alternative to forward-start swaps
• Whereas forward start swaps obligate the
company to enter into a swap, this is not the
case with swaptions
• With swaptions, the company can acquire
protection from unfavourable interest rate moves
as well as obtain the benefit of favourable
interest rate moves
53. Interest Rate Futures
• It is a futures contract on an asset whose price is
dependent on the level of interest rates.
• Main types of instruments
o Treasury bond futures
o Treasury bill futures
o Eurodollar futures.
54. Treasury bond futures
• The underlying is a government bond with more
than 15 years to maturity
• Depending on the particular bond that is
delivered, there is a mechanism for adjusting the
price received by the party with the short
position, defined by a Conversion Factor
• Cash received by party with short position
= quoted futures price x conversion factor
+ accrued interest since last coupon date
• Party with the short position can choose the
bond that is cheapest to deliver
55. Treasury bill futures
• The underlying asset is a 90-day Treasury bill
• The party with the short position delivers $1
million of Treasury bills
• If Z is the quoted futures price and Y is the cash
futures price
Z = 100 – 4(100 – Y)
Y = 100 – 0.25(100 – Z)
Contract Price = 10000[100 – 0.25(100 – Z)
• The amount paid or received by each side equals
the change in the contract price
56. EuroDollar futures
• It is structurally the same as a Treasury bill
futures contract
• The formula for calculating the Eurodollar futures
price is the same as that for the Treasury bill
futures
• For example, a Eurodollar price quote of 93.96
corresponds to a contract price of
10000[100 – 0.25(100-93.96)]
= $984900
57. Difference between Treasury Bill
Futures and Eurodollar Futures
• For a Treasury bill, the contract price converges
at maturity to the price of a 90-day $ 1 million
face value Treasury bill
• For a Eurodollars future, the final contract price
will be equal to 10000(100 – 0.25R), where R is
the quoted Eurodollars rate at that time
• The Eurodollars future contract is a future
contract on an interest rate
• The Treasury bill future contract is a future
contract on the price of a Treasury bill or a
discount rate
