INTEREST RATE OPTIONSSukumar NandiIndian Institute of Management Lucknow : INTEREST RATE OPTIONSSukumar NandiIndian Institute of Management Lucknow
Interest Rate Options : Interest Rate Options Interest rate options exist as options on the most commonly traded Interest rate futures contracts. The inter-bank market, on the other hand, provides interest rate options in the form of caps, floors and collars.
7.1 Options on Interest Rate Futures
In addition to employing interest rate futures contracts, it is possible to hedge against interest rate risks with exchange traded interest rate options. An option on interest rate futures entitles but does not obligate, the buyer to receive (call option) or to pay (put option) an agreed basis interest rate (also called strike rate) on a designated date.
Slide 3: The same basis rules apply to the use of options on interest rate futures as to interest rate futures themselves:
An investor will consider buying call options on interest rate futures if he expects interest rates to fall and, as a result, futures prices to rise. Conversely it would be advantageous for a borrower expecting higher interest rates and falling futures prices to buy put options on interest rate futures.
The option buyer pays the option writer (or seller) a premium, the amount of which, like that of any market price, is determined by supply and demand. Analogously to foreign currency options, the main factors determining the price are:
– The difference between the strike rate and the current market rate
– The maturity of the option contract
– The volatility of a certain reference interest rate, i.e. its fluctuation during time.
Slide 4: Market participants can choose between different strike prices with their corresponding option premiums. The strike rates are found by deducting the relevant interest rate from 100. Since different strike prices are quoted, the market participant can choose between in-the-money, at-the-money and out-of-the-money options.
The term in-the-money means in the case of a call option that the price of the underlying contract is higher than the strike price of the option; whereas in the case of a put option, the price of the underlying contract is lower than the strike price of the option.
When a call or put option is at-the-money, it means that the strike price is equal to the price of the underlying contract.
Slide 5: An out-of-the-money call option is one where the price of the underlying contract is lower than the strike price; whereas in the case of an out-of-the-money put option, the price of the underlying contract is higher than the strike price.
In the following table the premiums quoted in the market for different strike prices related to 3-month Eurodollar deposits (maturities of December and March) are shows for a day on which the December contract was quoted at 91.59 and the March contract at 91.16.
Strike Call Option Premiums Put Option PremiumsPrices Dec March Dec March
91.00 0.73 0.62 0.15 0.4691.25 0.54 0.49 0.21 0.5791.50 0.38 0.36 0.29 0.6991.75 0.25 0.28 0.41 0.8492.00 0.16 0.20 0.56 1.01
Slide 6: The table in previous slide makes it possible to calculate the various break-even interest rates for call and put options.
The break even interest rate for the purchase of the call option can be found by adding the strike price and the premium. At a strike price of 91.50, for example, the breakeven interest rate for a December contract is shown below:
100 – (91.50 + 0.38) = 8.12% p.a.
The breakeven interest rate for the purchase of a put option, in contrast, is found by subtracting the premium from the strike price:
100 – (91.50 – 0.29) = 8.79% p.a.
Maturities of option contracts run, for the most part, parallel to the interest rate futures contracts, with the most heavily traded running periods covering the 2 nearest trading months of the futures contracts.
Slide 7: In view of the fact that options on interest rate futures are actively traded, positions can be closed out at any time. The options are automatically closed out on the last trading day. The buyer of a call or put option is then credited with the positive difference between the strike price and the prevailing price of the underlying futures contract or the difference is debited to the writer (seller), respectively, if the difference between the strike price and the prevailing price should be negative, the option expires without value.
A positive difference results, for instance, in the case of a call option if the price of the futures contract is 92.00 and the strike price is 91.50. The same call option would expire without value if the price were 91.00 on the other hand.
Ways of using options on interest rate futures are described in the following paragraphs.
Slide 8: At the beginning of March a company must take up a short -term loan for 3 months in the amount of US$ 10 million in connection with a major investment project. The Treasurer wishes to establish a firm foundation for his calculations in January, especially as it is anticipated that interest rates could rise in the coming months.
The Treasurer therefore buys on LIFFE 10 put options on 3-month Eurodollar futures contracts at a strike price of 91.50 and a March expiration date against payment of a premium amounting to 35 basis points, or 0.35.
10 PUT x 35 basis points x US$ 25 = US$ 8,750
(see Session V for calculating the value of one basis point)
The breakeven interest rate of his borrowing, excluding the commission, is thus :
100 – (91.50 – 0.35) = 91.15 or 8.85 % p.a.
Slide 9: On the last trading day, there are two possible scenarios :
The interest rate have rise, as expected. On the last trading day (two business days prior to the third Wednesday in March). the price of the Eurodollar futures contract is 90.25, i.e. 3-month LIBOR is at 9¾ % p.a. The difference of 125 basis points (91.50 – 90.25) is credited to the company. The net income from his put options transactions can be calculated as follows :
10 PUT x 125 basis points x US$ 25 US$ 31,250– paid premium US$ 8,750– commission (10 x US$ 12.50 for the purchase) US$ 125
Net income from the put options US$ 22,375
Slide 10: The total costs for the loan taken up in March are calculated as follows :
Interest on US$ 10,000,000 – for 3 months(90 days) at 9¾% p.a. US$ 243,750– income from put options US$ 22,375
Total borrowing cost US$ 221,375
or 8.86 % p.a.
2. Interest rate have fallen. On the last trading day (two business days prior to the third Wednesday in March) the price of Eurodollar futures contracts is 92.25, which means that 3-month LIBOR is at 7¾% p.a. The option expires without value
Slide 11: The total costs for the loan taken up in March are :
Interest on US$ 10,000,000 for 3 months(90 days) at 7¾ % p.a. US$ 193,750+ paid premium US$ 8,750+ commission (10 x US$ 12.50 for purchase) US$ 125
total borrowing costs US$ 202,625
or 8.11 % p.a
Slide 12: Caps, Floors and Collars
The warm reception given to the tailor-made currency and precious metal options formed one of the reasons why the interbank market supplemented call and put options on interest rate futures by the following alternatives :
1. Cap : Hedge against higher interest rates by fixing a maximum interest rate
2. Floor : Hedge against falling interest rates by fixing a minimum interest rate
3. Collar : Combination of a cap and a floor in order to fix a certain interest rate range
The above interest rate hedging instruments feature standardized contract specifications. These can be defined in summary form as follows :
Strike rate : Guarantee maximum/minimum interest ratein % p.a.
Slide 13: Reference rate : Agreed interest basis (such as 3 or 6-month LIBOR)
Capital amount : Amount and currency of the contract. Used only in calculations as there is no capital payment
Premium : Price as a % of capital amount
Settlement amount : Interest difference between the strike interest rate and the market interest rate on the fixing day with regards to capital amount and term
Fixing day : 2 business days prior to the value date
Settlement rate : The reference rate (e.g. 3 or 6 month LIBOR) valid at 11:00 a.m. London time on the fixing day
Value date : Value dates agreed in advance on which the settlements amounts, if any, are paid.
Slide 14: Calculation of the Settlement Amount : Calculation of the settlement amount from the interest differential employs the following formula :
(S – G) x D x C B x 100
S = Settlement rateG = Strike (guaranteed) rateD = Number of days in reference period (Such as 91 in case of 3-month LIBOR)
C = Capital amountB = Basis of 360 or 365 days, depending on the interest practice applied
These contract specifications are explained in greater detail in the presentation of the individual instruments in the following text in order to highlight their significance in each special case.
Slide 15: Cap
Caps are interest rate options traded in the interbank market which place an upper limit on the interest costs of debt instruments with variable or floating interest rates by designating a maximum interest rate for a specified future period. If the market interest rate rises above the agreed maximum interest rate, the seller of the cap will pay the difference to the buyer.
The seller receives a premium for his guarantee which, in accordance with the option theory, is determined by the agreed maximum rate and the market rates. The premium is paid to the seller at the outset, which means that the premium becomes payable by the buyer at the time the cap is granted. The seller of an at-the-money cap will demand a higher premium than the seller of an out-of-the-money cap owing to the greater difference that exists between the designated maximum rate and the prevailing market rate.
Slide 16: The seller of a cap can improve the yield on an investment with variable interest rates by the amount of the premium he has collected as long as the interest rates do not move above the maximum interest rates plus premium. If interest rates rise above the maximum rate plus annualized premium, the option seller will suffer an opportunity loss as he must pay the amount of the interest differential to the cap buyer. The cap buyer, on his part, limits his interest costs to the maximum interest rate plus annualized premium as he profits from interest rates which are lower than the maximum rate.
Caps can be employed in a flexible manner as a hedging instrument according to the requirements and the expectations of future interest rate trends of a borrower or investor. The most common maturities cover a period from 2 to 5 years. Caps can also be bought for the specific use in those quarters where large seasonal needs for credit may be experienced
Slide 17: We shall now present the cap as an instrument which can hedge interest rate changes and improve yields
A Company has obtained a 3-year roll-over credit for US$ 10 million on the basis of 6-month LIBOR from a bank one year ago. The Treasurer is of the opinion that interest rates are likely to rise in the coming months. He wants to hedge against an interest rate rise of ¼ % above the prevailing interest level of 7 ¾ % p.a.
He buys a cap for US$ 10 million expiring in 2 years with a 6-month-LIBOR reference rate, strike rate 8% p.a., against payment of a 1.20% premium. The first settlement will take place in 6-months, the second in 12 and the third in 18 months (the current interest period does not have to be hedged, of course, since the prevailing market rate is known).
Slide 18: Hedging costs (premium)
US$ 10,000,000 x1.20 = US$ 120,000 100
The maximum interest rate included hedging costs for the last 3 half-year periods of the loan (without refinancing cost of the premium) therefore come to :
1.20% x 2 8% + 3 = 8.80% p.a.
The development of the interest rate over the residual term of the loan is as follows :
1. In 6 months (first settlement) 6-month LIBOR is at 10% p.a. The company is credited with the following amount
(10 – 8) x 180 x US$ 10,000,000 = US$ 100,000 360 x 100
Slide 19: The company receives the above amount with a value date of 2 business days, even though it has to pay the interest of 10% p.a. on its loan in 6 months. This party offsets the refinancing costs for the premium paid when the cap was bought, which are not included in these calculations
2. In 12 months (2nd settlement) 6-month LIBOR is at 9% p.a. The company receives the following amount credited to its account with a value date of 2 business days hence:
(9 – 8) x 180 x US$ 10,000,000 = US$ 50,000 360 x 100
3. in 18 months (3rd settlement) 6-month LIBOR is at 7.75% p.a. The company does not receive a settlement payment and pays the annual rate of 7.75% p.a. for the next 6 months.
Slide 20: By buying the cap, the company was able to benefit from the lower interest rate during the 3rd period and had to pay only 8% p.a. interest during the first 2 periods. This produced the following result if the premiums are included : 1st 2nd 3rd Settlement Settlement Settlement Averageint. costs 8.00% 8.00% 7.75% 7.92%p.a.+ premium 0.80% 0.80% 0.80% 0.80%p.a.
Total costs 8.80% 8.80% 8.55% 8.72%p.a.
Without the purchase of the cap the result would have looked like this : 1st 2nd 3rd Settlement Settlement Settlement Averageint. costs 10.00% 9.00% 7.75% 8.92%p.a.Cost
difference +1.20% +0.20% –0.80% 8.72%p.a.
Under these circumstances, it has paid for the company to buy a cap
Slide 21: The Treasurer of a different company feels that US dollar interest rates will remain stable at the current level of 7½% p.a. or ease slightly in the next few years. He would like to improve the yield on his money market investments.
He therefore decides to sell a cap on US$ 10 million, reference rate 6-month LIBOR, strike rate 8% p.a., expiring in 2 years, against the receipt of a premium of 0.60%.
Income from the sale of the cap (premium) :
US$ 10,000,000 x 0.60 = US$ 60,000 100
The interest rate development during the life of the cap is as follows :
1. In 6 months (1st settlement) 6-month LIBOR is at 7.75% p.a. The cap seller does not have to make a settlement payment since LIBOR is lower than the strike rate.
Slide 22: 2. In 12 months (2nd settlement) 6-month LIBOR is at 8% p.a., which is exactly equal to the strike rate. Again, the cap seller does not have to make a settlement payment.
3. In 18 months (3rd settlement) 6-month LIBOR is at 8.50 p.a. The cap seller must make the following settlement payment :
(8.50 – 8.00) x 180 x US$ 10,000,000 = US$ 25,000 360 x 100
Assuming that the Treasurer has simultaneously placed his money market deposit of US$ 10 million on each settlement day at LIBID, the following yield result :
1st 2nd 3rd Settlement Settlement Settlement AverageDeposit 7.625% 7.875% 8.375% 7.958%p.a.+ premium 0.40% 0.40% 0.40% 0.40%– payments – – 0.50% 0.167%p.a.
Yield 8.025% 8.275% 8.275% 8.191%
Slide 23: If the Treasurer had invested his funds exclusively on the money market on a 6-month basis, he would have obtained an average interest rate return of 7.958% p.a. Although his assessment of the interest rate trend was not correct and he had therefore written the cap under the wrong assumptions, the average yield on his investment was improved to 8.191% p.a.
Floor
A floor agreement means that the floor seller guarantees that the floor buyer will receives a minimum interest rate (e.g. 7% p.a.) for a specified period of time. The buyer pays a premium for this guarantee. Should the reference interest rate be below the minimum interest rate on the settlement days, the seller will pay the interest rate difference to the buyer.
Slide 24: An investor has placed US$ 10 million in bonds with floating interest rates.
He hedges his investment by buying a floor on US$ 10 million, with a reference rate of 6-month LIBOR, a strike rate of 7% p.a. and a maturity of 2 years against payment of a premium of 0.60% for 2 years.
Hedging costs (premium)
US$ 10,000,000 x 0.60 = US$ 60,000 100
Minimum interest rate (incl. hedging costs) for the coming 3 semi-annual periods (excl. refinancing costs for the premium) :
7% – 0.60 x 2 = 6.60% p.a. 3
Slide 25: The interest rate develops as follows during the remaining life of the investment :
1. In 6 months (1st settlement) 6-month LIBOR is at 6% p.a. The investor receives the following settlement payment with a value date of 2 business days :
(7 – 6) x 180 x US$ 10,000,000 = US$ 50,000 360 x 100
2. In 12 months (2nd settlement) 6-month LIBOR is at 6.50% p.a. The investor receives the following settlement payment with value date of 2 business days :
(7 – 6.5) x 180 x US$ 10,000,000 = US$ 25,000 360 x 100
3. In 18 months (3rd settlement) 6-month LIBOR is at 7.50% p.a. The investor does not receive a settlement payment. His investment in bonds with variable interest rates pays interest at 7.50% p.a.
Slide 26: By buying the floor the investor was assured of a minimum interest rate of 7% p.a. for the first 2 interest periods, whereas he was paid the higher market rate of 7.50% p.a. for the 3rd period. If we disregard the financial costs of the premium paid, he obtained the following result : 1st 2nd 3rd Settlement Settlement Settlement Averageint. income 7.00% 7.00% 7.50% 7.17%p.a.– premium 0.40% 0.40% 0.40% 0.40%p.a.
Total income 6.60% 6.60% 7.10% 6.77%p.a.
If the investor had not bought the floor, his yield would have been as follows : 1st 2nd 3rd Settlement Settlement Settlement Averageint. Income 6.00% 6.50% 7.50% 6.67%p.a.
In this case, the hedging operation did not have much effect on the income since the interest rate fluctuations were not wide enough
Slide 27: Collar
The collar is a combination of a cap and a floor. The buyer of the collar buys a cap with a specified strike rate and sells at the same time a floor with a lower strike rate. By doing so he reduces the fluctuation range of the interest rate to the difference between the maximum and the minimum interest rates. By selling the floor he lowers the costs incurred by buying the cap. Obviously these two opposite transactions eliminate the possibility of benefitting from interest rates falling below the minimum rate.
A company must borrow US$ 20 million for 5 years in order to finance an investment. The interest rate is readjusted semi-annually at 6-month LIBOR. The Treasurer does not exclude the possibility of rising interest rates and would therefore like to lock in a maximum interest rate of 10.75% p.a.
Slide 28: 6-month LIBOR is at 8% p.a. and a cap for 5 years with a strike rate of 10.50% p.a. costs 3.90%. Since the company would be satisfied with a minimum interest rate of 7.75% p.a., the Treasurer decides to lower the premium of the aforementioned cap by selling a floor with a strike rate of 7.50% p.a. He obtains 3% for this floor and thereby reduces the net costs of his collar to 0.90%.
The bought collar of US$ 20 million, reference rate 6-month LIBOR, and a maturity of 5 years, consists of the following :
Cap purchase Strike rate 10.50% p.a., premium 3.90%Floor sale Strike rate 7.50% p.a., premium 3.00%
Slide 29: This collar results in the following maximum and minimum interest rates (including net premium) :
Maximum interest rate :
Cap 10.50% + 0.90 x 2 = 10.70% p.a. 9
Minimum interest rate :
Floor 10.50% + 0.90 x 2 = 10.70% p.a. 9
The following table shows the effective financing costs with differing 6-month LIBOR rates under the assumption that LIBOR remains the same during all 9 periods.
Slide 30: Libor at the Settlement days 5% 8% 11% 14%
Settlement payments:+ debiting company 2.50% – – –
– creding company – – 0.50% 3.50%
+ premium 0.20% 0.20% 0.20% 0.20%
Total costsin % p.a. 7.70% 8.20% 10.70% 10.70%
The desired result concerning maximum and minimum interest rates was reached with a low premium. The collar proved to be an optimal and flexible hedging instrument.