Interest Rate Derivatives
Products• Forward Rate Agreements (FRAs)• Interest Rate Swaps• Interest Rate Options   o Embedded bond options   o Put/cal...
Requirements for Development of    Market in Interest Rate Derivatives• A well-developed yield curve• A liquid market• Exi...
Forward Rate Agreement (FRA)• A financial contract between two parties to  exchange interest payments based on a ‘notional...
QuotingA typical FRA quote would look like           6 X 9 months: 7.20 - 7.30% p.a.This has to be interpreted as• The ban...
Example of a FRA deal• A corporate has an expected requirement for  funds after 3 months but is concerned that  interest r...
Terms of the FRA deal• Bank & corporate enter into a 3 X 6 FRA.  Corporate pays FRA rate of 6.75%. Bank pays  benchmark ra...
Cash flows for the FRA deal• Assume, 3 month CP rate for the Corporate on fixing  date (say 27/10/2002) = 7%• Cash flow Ca...
Possible benchmarks for FRAs• 3-month, 6-month OIS rates• 3-month, 6-month CP or T-bill• OIS rates could be the best bench...
Uses of FRAs• For corporates seeking to hedge their future loan  exposures against rising rates.• For inter-bank participa...
Interest Rate Swaps (IRS)• An agreement to exchange a series of fixed cash  flows with a series of floating cash flows• Th...
Analogy between FRA and IRS• IRS is similar to a FRA except that  o   in a typical FRA the benchmark rate is reset only   ...
Uses of swaps• Asset-liability management• Convert floating rate exposure to fixed exposure  and vice-versa• Take a specul...
Criteria for floating rate benchmarks• Available for the lifetime of the swap• Market determined rate• Relevant to the cou...
Overnight Index Swap• The floating rate is an overnight rate such as  NSE MIBOR or MITOR, which is reset daily• The intere...
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 @ 6.5...
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   ...
Calculating Cash flowsTotal accrual on a floating leg = Rs 108098Total accrual on fixed leg = 100000000*6.50% *7/365      ...
Settlement • Net interest payment= 124657 - 108098= Rs 16659 • This amount will be paid by party A to party B at   maturity
Reversing an Outstanding OIS                Position• Unwinding/reversing an existing OIS position is  entails deriving th...
Option 1: Booking a Reverse Swap• Bank A can book a reverse swap with a  counterparty for the residual tenor of 4 days  wh...
Option 2 : Cancelling the outstanding                OIS• Canceling an OIS will have two components  o   Component 1 : The...
Cancelling the OIS: CalculationsOriginal OISPrincipal INR 100 croresTenor of the swap 7 daysStart Date 27th July 1999End d...
Cancelling the OIS: CalculationsComponent 1Overnight rate Notional Principal Accrued interestDay 1 7.83% 1,000,000,000 214...
Cancelling the OIS: CalculationsComponent 2Cancellation OIS rate = 8.25%Difference in fixed rates payable by bank A on mat...
Constant Maturity Swaps (CMS)• Atleast one of the legs of the swap is linked to a  floating rate which has a constant teno...
Types of CMS Structures• One side pays fixed and the other pays a CMS  rate.• Both sides are floating, one is a CMS rate a...
Advantages of CMS over Plain Vanilla               IRS• It enables to indulge in curve play- taking  advantage of expectat...
Advantages of CMS over Plain Vanilla               IRS• Investors can use CMS/CMT swap to target  specific instrument matu...
Other Swap Structures•   Amortizing swaps•   Accreting swaps•   Leveraged swaps•   Basis swaps•   In-arrears swap•   Inver...
Amortizing Swaps• Principal amount decreases at pre-specified  points of time over the life of the swap• Motivation  o   s...
Accreting Swaps• Accreting  o   principal amount increases at pre-specified points of      time over the life of the swap•...
Basis Swaps• A Basis swap is  o   contractual agreement  o   exchange a series of cash flows  o   over a period of time.  ...
Leveraged Swap• The counterparty on the floating leg makes  payments which are a multiple of a floating  benchmark• Exampl...
Significance of Leveraged Swaps for         Indian Corporates• For corporates interested in positive carry deals  o   Leve...
In-arrears Swap• Normally, in a swap, there is a time lag between  the observed value of the floating rate and the  paymen...
Inverse Floater Swaps• Seek to take advantage of, or protect against, a  steep yield curve• Pay/receive floating rate inde...
Differential Swaps• Have been used in recent years by investors and  corporates who are attempting to take on a view  on f...
Forward Start Swap• Let us say that a company knows that six months  from today, it will borrow via a floating rate loan• ...
Range Accrual Swaps• The interest on one side accrues only when the  floating rate benchmark is within a certain range• Th...
Embedded Bond Options• A callable bond allows the issuer to buy back the  bond at a specified price at certain times in th...
Embedded Bond Options• A puttable bond allows the holder early  redemption at a specified price at certain times in  the f...
Examples of Embedded Bond               Options• Early redemption features in fixed rate deposits• Prepayment features in ...
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...
European Put/Call Options on            Interest Rates• Here, the option underlying is some benchmark  interest rate.• He ...
Interest Rate Caps• They provide insurance against rising interest  rates on a floating rate loan exceeding a certain  lev...
Interest Rate Cap- Example • Consider a floating rate loan with a principal   amount of Rs 10 crore • The floating rate is...
Interest Rate Floors• They guarantees a minimum interest rate level on  a floating rate investment• Just like a cap, they ...
Interest Rate Collars• They put a cap on the maximum rate as well as a  floor on the minimum rate that will be charged• Th...
European Swaptions• They are options on interest rate swaps• They give the holder the right to enter into a  interest rate...
European Swaption - Example• Consider a corporate that knows that in 6  months, it will enter into a 5-yr floating rate lo...
Advantages of swaptions• They guarantee to corporates that the fixed rate  of interest that they will pay on the loan at s...
Interest Rate Futures• It is a futures contract on an asset whose price is  dependent on the level of interest rates.• Mai...
Treasury bond futures • The underlying is a government bond with more   than 15 years to maturity • Depending on the parti...
Treasury bill futures • The underlying asset is a 90-day Treasury bill • The party with the short position delivers $1   m...
EuroDollar futures • It is structurally the same as a Treasury bill   futures contract • The formula for calculating the E...
Difference between Treasury Bill   Futures and Eurodollar Futures• For a Treasury bill, the contract price converges  at m...
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Interest rate derivatives

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Interest Rate Derivatives

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Interest rate derivatives

  1. 1. Interest Rate Derivatives
  2. 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. 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. 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. 5. QuotingA 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 18. Calculating Cash flowsTotal accrual on a floating leg = Rs 108098Total accrual on fixed leg = 100000000*6.50% *7/365 = Rs 124657
  19. 19. Settlement • Net interest payment= 124657 - 108098= Rs 16659 • This amount will be paid by party A to party B at maturity
  20. 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. 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. 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. 23. Cancelling the OIS: CalculationsOriginal OISPrincipal INR 100 croresTenor of the swap 7 daysStart Date 27th July 1999End date 3rd Aug 1999Swap rate Bank A pays fixed rate to bank B at 8.50 %Bank A receives overnight MIBOR from Bank BCancellationBank A approaches Bank B to cancel the outstanding OISon 30th July, 1999Bank B quotes a rate of 8.25% to cancel the outstandingswap
  24. 24. Cancelling the OIS: CalculationsComponent 1Overnight rate Notional Principal Accrued interestDay 1 7.83% 1,000,000,000 214,521Day 2 7.76% 1,000,214,521 212,648Day 3 7.32% 1,000,427,169 200,634Interest accrued on floating leg 627,803payable by Bank B on unwind dateInterest 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. 25. Cancelling the OIS: CalculationsComponent 2Cancellation 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= 27,397Cancellation value on maturity date payable by bank A to bankB= Component 1 + Component 2= 97,656Value if settled on cancellation date= 97,656 / (1+8.25%*4/365)= INR 97,568
  26. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 beginningof the quarter
  48. 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. 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. 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. 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. 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. 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. 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. 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 priceZ = 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. 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 of10000[100 – 0.25(100-93.96)]= $984900
  57. 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. 58. Thank You

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