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Chapter 14

Chapter 14. Interest Rate Options: Fundamentals. Spot Option: Definition. An option is a security that gives the holder the right (but not the obligation) to buy an asset at a specific price (exercise price: X) on or possibly before a specific date (expiration date: T).

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Chapter 14

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  1. Chapter 14 Interest Rate Options: Fundamentals

  2. Spot Option: Definition • An option is a security that gives the holder the right (but not the obligation) to buy an asset at a specific price (exercise price: X) on or possibly before a specific date (expiration date: T). • A Call option is an option that gives the holder the right to buy a specific asset or security. • A Put option is an option that gives the holder the right to sell a specific asset or security.

  3. Terms • Option Holder: Buyer of the option; has the right to exercise; long position. • Option Writer: Seller of the option; has the responsibility to fulfill the terms of the option if the holder exercises; short position. • Option Premium: Price of the option: • C = call premium • P = put premium

  4. Terms • American Option: Option that can be exercised at any time on or before the expiration date. • European Option: Option that can be exercised only on the expiration date.

  5. Symbols • Symbols: • T = Expiration or when the option is exercised. • 0 = current period • t = any time between current and expiration • Example: • CT = Call price at expiration • C0 = Current call price

  6. Terms • Spot Option: Options contracts on stocks, debt securities, foreign currencies, and indices are sometimes referred to as spot options or options on actuals. • This reference is to distinguish them from options on futures contracts (also called options on futures, futures options, and commodity options).

  7. Futures Options • A futures option gives the holder the right to take a position in a futures contract. • Call option on a futures contract gives the holder the right to take a long position in the underlying futures contract. • Put option on a futures option gives the holder the right to take a short position in the underlying futures contract.

  8. Futures Options • Like all option positions, the futures option buyer pays an option premium for the right to exercise, and the writer, in turn, receives a premium when he sells the option and is subject to initial and maintenance margin requirements on the option position.

  9. Futures Call Option • A call option on a futures contract gives the holder the right to take a long position in the underlying futures contract when she exercises, and requires the writer to take the corresponding short position in the futures. • Upon exercise, the holder of a futures call option in effect takes a long position in the futures contract at the current futures price and the writer takes the short position and pays the holder via the clearinghouse the difference between the current futures price and the exercise price.

  10. Futures Put Option • A put option on a futures option entitles the holder to take a short futures position and the writer the long position. • Upon exercise, the put holder in effect takes a short futures position at the current futures price and the writer takes the long position and pays the holder via the clearinghouse the difference between the exercise price and the current futures price.

  11. Exercising Futures Call Options • In practice, when the holder of a futures call option exercises, the futures clearinghouse will establish for the exercising option holder a long futures position at the futures price equal to the exercise price and a short futures position for the assigned writer. • Once this is done, margins on both positions will be required and the position will be marked to market at the current settlement price on the futures. • When the positions are marked to market, the exercising call holder’s margin account on his long position will be equal to the difference between the futures price and the exercise price, ft-X, while the assigned writer will have to deposit funds or near monies worth ft-X to satisfy her maintenance margin on her short futures position.

  12. Exercising Futures Call Options • Thus, when a futures call is exercised, the holder takes a long position at ft with a margin account worth ft-X; if he were to immediately close the futures he would receive cash worth ft-X from the clearinghouse. • The assigned writer, in turn, is assigned a short position at ft and must deposit ft-X to meet her margin.

  13. Exercising Futures Put Options • If the futures option is a put, the same procedure applies except that holder takes a short position at ft (when the exercised position is marked to market), with a margin account worth X-ft, and the writer is assigned a long position at ft and must deposit X-ft to meet her margin.

  14. Differences Between Futures Options and Spot Options • Spot options and futures options are equivalent if • The options and the futures contracts expire at the same time • The carrying‑costs model holds • The options are European.

  15. Differences Between Futures Options and Spot Options • There are, though, several factors that serve to differentiate the two contracts: • Since many futures contracts are relatively more liquid than their corresponding spot security, it is usually easier to form hedging or arbitrage strategies with futures options than with spot options. • Futures options often are easier to exercise than their corresponding spot. For example, to exercise an option on a T-bond futures, one simply assumes the futures position, while exercising a spot T‑bond option requires an actual purchase or delivery. • Most futures options are traded on the same exchange as their underlying futures contract, while most spot options are traded on exchanges different from their underlying securities. This, in turn, makes it easier for futures options traders to implement arbitrage and hedging strategies than spot options traders.

  16. Markets for Interest Rate Options • Many different types of interest rate options are available on the • Organized futures and options exchanges, and • OTC market

  17. Markets for Interest Rate Options • Exchange-traded interest rate options include both futures options and spot options. • On the U.S. exchanges, the most heavily traded options are the CME’s and CBOT’s futures options on T-bonds, T-notes, T-bills, and Eurodollar contracts. • The CBOE, AMEX, and PHLX have offered options on actual Treasury securities and Eurodollar deposits. These spot options, however, proved to be less popular than futures options and have been delisted. • A number of non-U.S. exchanges, though, do list options on actual debt securities, typically government securities.

  18. Markets for Interest Rate Options • There is a large OTC market in debt and interest-sensitive securities and products in the U.S. and a growing OTC market outside the U.S.. • Currently, security regulations in the U.S. prohibit off-exchange trading in options on futures. • All U.S. OTC options are therefore options on actuals.

  19. Markets for Interest Rate Options • The OTC markets in and outside the U.S. consists primarily of dealers who make markets in the underlying spot security, investment banking firms, and commercial banks. • OTC options are primarily used by financial institutions and non-financial corporations to hedge their interest rate positions.

  20. Markets for Interest Rate Options • The option contracts offered in the OTC market include: • Spot options on Treasury securities • LIBOR-related securities • Special types of interest rate products, such as: • Interest rate calls and puts • Caps • Floors • Collars

  21. Types: CBOT’s Futures Options The CBOT offers trading on interest rate futures options on T-bonds, T-notes with maturities of 10 years, 5 years, and 2 years, the Municipal Bond Index, and the Mortgage-Backed bond contract.

  22. Types: CBOT’s Futures Options Futures Options on T-Bonds and Notes • The call and put contracts on the T-bond and T-note futures are set with exercise prices that are one point apart (104, 105, 106, etc.; ½ point intervals for other T-notes) and with expiration months following the March, June, September, and December cycle, with one expiration month being the one in front of the month with the current quarter. • The premiums on the options are quoted as a percentage of the face value of the underlying bond or note.

  23. Types: CBOT’s Futures Options Futures Options on T-Bonds and Notes • A buyer of an April 104 T-bond futures call trading at 2 –11 (or 2 11/64 = 2.171875) would pay $2,171.87 for the option to take a long position in the April T-bond futures at an exercise price of $104,000.

  24. Types: CBOT’s Futures Options Futures Options on T-Bonds and Notes • If long-term rates were to subsequently drop, causing the April T-bond futures price to increase to ft = 108, then the holder, upon exercising, would have a long position in the April T-bond futures contract and a margin account worth $4,000. • If she closed her contract at 108, she would have a profit of $1,828.13:

  25. Types: CBOT’s Futures Options Futures Options on T-Bonds and Notes • By contrast, if long-term rates were to stay the same or increase, then the call would be worthless and the holder would simply allow it to expire, losing the $2,171.87 premium.

  26. Types: CME’s Futures Options Futures Options on Eurodollars and T-Bills • The CME offers trading on futures options on T-bills, Eurodollar deposits, and 30-day LIBOR contracts. • The maturities of the options correspond to the maturities on the underlying futures contracts. • The exercise quotes are based on the system used for quoting the futures contracts.

  27. Types: CME’s Futures Options Futures Options on Eurodollars and T-Bills • The exercise prices on the Eurodollar and T-bill futures contracts are quoted in terms of an index equal to 100 minus the annual discount yield: 100 – RD. The formula for X:

  28. Types: CME’s Futures Options Futures Options on Eurodollars and T-Bills • The option premiums are quoted in terms of an index point system. • For T-bill and Eurodollars, the dollar value of an option quote is based on a $25 value for each basis point underlying a $1M T-bill or Eurodollar. • The actual quotes are in percents; thus a 1.25 quote would imply a price of $25 times 12.5 basis points: ($25)(12.5) = $312.50 Or simply: ($250)(1.25) = $312.50

  29. Types: CME’s Futures Options Note: • For the closest maturing month, the options are quoted to the nearest quarter of a basis point. • For other months, they are quoted to the nearest half of a basis point.

  30. Types: CME’s Futures Options • Example: The actual price on a March Eurodollar call with an exercise price of 94.5 quoted at 5.92 is $1,481.25. The price is obtained by rounding the 5.92 quoted price to 5.925, converting the quote to basis points (multiply by 10), and multiplying by $25: • A 10.30 quote on a 94.5 April call indicates a call price of $2,575: (5.925)(100)($25) = $1,481.25 Or (5.925)($250) = $1,481.25 (10.30)(10)($25) = $2,575 Or (10.30)($250) = $2,575

  31. Types: CME’s Futures Options An investor buying the 94.5 March call would therefore pay $1,481.25 for the right to take a long position in the CME’s $1M March Eurodollar futures contract at an exercise price of $986,250:

  32. Types: CME’s Futures Options If short-term rates were to subsequently drop, causing the March Eurodollar futures price to increase to an index price of 95.5 (RD = 4.5 and ft = [[100 – 4.5(90/360)]/100]($1,000,000) = $988,750), the holder, upon exercising, would have a long position in the CME March Eurodollar futures contract and a futures margin account worth $2,500. If she closed the position at 95.5, she would realize a profit of $1,018.75:

  33. Types: CME’s Futures Options • If short-term rates were at RD = 5.5% and stayed there or increased, then the call would be worthless and the holder would simply allow it to expire, losing her $1,018.75 premium.

  34. Types: OTC Options • OTC options can be structured on almost any interest-sensitive position an investor or borrower may wish to hedge. • U.S. Treasuries, LIBOR-related instruments, and Mortgage-backed securities are often the most common underlying security. • When spot options are structured on securities, terms such as the specific underlying security, its maturity and size, the option’s expiration, and the delivery are all negotiated.

  35. Types: OTC Options • For an OTC option on a Treasury, the underlying security is often a recently auctioned Treasury (on-the-run bond), although some selected existing securities (off-the-run securities) are used. • The bid-ask spreads on OTC Treasury options tend to be larger than exchange-trade ones. • The option maturities on OTC contracts can range from one day to several years, with many of the options being European.

  36. Types: OTC Options • In the case of OTC spot T‑bond or T-note options, OTC dealers either offer or will negotiate contracts giving the holder to right to purchase or sell a specific T‑bond or T-note. • Example: A dealer might offer a T‑bond call option to a fixed income manager giving him the right to buy a specific T‑bond maturing in year 2016 and paying a 6% coupon with a face value of $100,000.

  37. Types: OTC Options • Note: Because the option contract specifies a particular underlying bond, the maturity of the bond, as well as its value, will be changing during the option's expiration period. • Example: a one‑year call option on the 15‑year bond, if held to expiration, would be a call option to buy a 14‑year bond.

  38. Types: OTC Options • Note: A spot T‑bill option contract offered by a dealer on the OTC market usually calls for the delivery of a T‑bill meeting the specified criteria (e.g., principal = $1 million; maturity = 91 days). • With this clause, a T‑bill option is referred to as a fixed deliverable bond, and unlike specific‑security T‑bond options, T‑bill options can have expiration dates that exceed the T‑bill's maturity.

  39. Types: OTC Options • A second feature of a spot T‑bond or T-note options offered or contracted on the OTC market is that the underlying bond or note can pay coupon interest during the option period. • As a result, if the option holder exercises on a non‑coupon paying date, the accrued interest on the underlying bond must be accounted for. For a T‑bond or T-Note option, this is done by including the accrued interest as part of the exercise price.

  40. Types: OTC Options • Like futures options, the exercise price on a spot T‑bond or T-note option is quoted as an index equal to a proportion of a bond with a face value of $100 (e.g., 95). • If the underlying bond or note has a face value of $100,000, then the exercise price would be:

  41. Types: OTC Options • The prices on spot T‑bond and T-note options are typically quoted like futures T-bond options in terms of points and 32nds of a point. Thus, the price of a call option on a $100,000 T-Bond quoted at 1 5/32 is $1,156.25 = (1.15623/100)($100,000)

  42. Types: OTC Options Interest Rate Call and Interest Rate Put • In addition to option contracts on specific securities, the OTC market also offers a number of interest-rate option products. • These products are usually offered by commercial or investment banks to their clients. • Two products of note are interest rate calls and interest rate puts.

  43. Types: OTC Options Interest Rate Call • An interest rate call, also called a caplet, gives the buyer a payoff on a specified payoff date if a designated interest rate, such as the LIBOR, rises above a certain exercise rate, Rx. • On the payoff date: • If the designated rate is less than Rx, the interest rate call expires worthless. • If the rate exceeds Rx, the call pays off the difference between the actual rate and Rx, times a notional principal, NP, times the fraction of the year specified in the contract.

  44. Types: OTC Options Interest Rate Call • Example: Given an interest rate call with a designated rate of LIBOR, Rx = 6%, NP = $1M, time period of 180 days, and day-count convention of actual/360, the buyer would receive a $5,000 payoff on the payoff date if the LIBOR were 7%: (.07-.06)(180/360)($1M) = $5,000

  45. Types: OTC Options Interest Rate Call • Interest rate call options are often written by commercial banks in conjunction with futures loans they plan to provide to their customers. • The exercise rate on the option usually is set near the current spot rate, with that rate often being tied to the LIBOR.

  46. Types: OTC Options Interest Rate Call • Example: A company planning to finance a future $10M inventory 60 days from the present by borrowing from a bank at a rate equal to the LIBOR + 100 BP at the start of the loan could buy from the bank an interest rate call option with an exercise rate equal to say 8%, expiration of 60 days, and notional principal of $10M. • At expiation, 60 days later, the company would be entitled to a payoff if rates are higher than 8%. Thus, if rates on the loan increase, the company would receive a payoff that would offset the higher interest on the loan.

  47. Types: OTC Options Interest Rate Put • An interest rate put, also called a floorlet, gives the buyer a payoff on a specified payoff date if a designated interest rate is below the exercise rate, Rx. • On the payoff date: • If the designated rate is more than Rx, the interest rate put expires worthless. • If the rate is less than Rx, the put pays off the difference between Rx and the actual rate times a notional principal, NP, times the fraction of the year specified in the contract.

  48. Types: OTC Options Interest Rate Put • Example: Given an interest rate put with a designated rate of LIBOR, Rx = 6%, NP = $1M, time period of 180 days, and day-count convention of actual/360, the buyer would receive a $5,000 payoff on the payoff date if the LIBOR were 5%: (.06-.05)(180/360)($1M) = $5,000

  49. Types: OTC Options Interest Rate Put • A financial or non-financial corporation that is planning to make an investment at some future date could hedge that investment against interest rate decreases by purchasing an interest rate put from a commercial bank, investment banking firm, or dealer.

  50. Types: OTC Options Interest Rate Put • Example: suppose that instead of needing to borrow $10M, the previous company was expecting a net cash inflow of $10M in 60 days from its operations and was planning to invest the funds in a 90-day bank CD paying the LIBOR. • To hedge against any interest rate decreases, the company could purchase an interest rate put (corresponding to the bank's CD it plans to buy) from the bank with the put having an exercise rate of say 7%, expiration of 60 days, and notional principal of $10M. • The interest rate put would provide a payoff for the company if the LIBOR were less than 7%, giving the company a hedge against interest rate decreases.

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