The document discusses various interest rate derivatives products including forward rate agreements (FRAs), interest rate swaps, and options. It provides details on FRAs, including how they work, examples of FRA deals and calculations, and potential benchmarks. It also covers interest rate swaps, including how they are analogous to FRAs, common uses of swaps, and criteria for floating rate benchmarks. The document concludes with an overview of overnight index swaps and constant maturity swaps.

1. Interest Rate Derivatives

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.

30. Other Swap Structures
• Amortizing swaps
• Accreting swaps
• Leveraged swaps
• Basis swaps
• In-arrears swap
• Inverse floaters
• Differential swap
• Forward start swap
• Range Accrual swaps

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

58. Thank You