# Options on specific money market instruments

Money market options are options that are written on specific money market instruments, such as commercial paper, NCDs, deposits, etc. Not many countries have specific asset money market options, because of the existence of the active markets in other money market derivatives (swaps, swaptions, repos, caps and floors, FRAs, and interest rate futures).

Some countries, however, have options on notional money market instruments. A UK example is presented in Table 8.54

Let us focus in on the June call option at a strike (exercise) price of 9350, and a premium of 0.09. What do these numbers mean? The holder of the option has the right to make a deposit of GBP 500 000 on the expiry date in June (the date is specified) at an interest rate of 6.5% (100 - 93.50) for 3 months. Each tick movement on the contract, which is equivalent to one basis point, is worth the value of the contract (GBP 500 000) multiplied by 1 basis point (0.01% or 0.0001) and a quarter of a year (0.25), i.e.:

GBP 500 000 x 0.0001 x 0.25 = GBP 12.50.

 Dec Mar Dec Mar Jun 0.11 0.08 0.09 0.06 0.33 0.66 9375 0.01 0.02 0.04 0.21 0.52 0.86 9400 0.00 0.01 0.02 0.45 0.76 1.09

Table 8: Example of option on money market instrument

The cost of the call option (i.e. the premium) is therefore 9 x GBP 12.50 = GBP 112.50.

If by the expiry date the contract strike price rises to 9450 (interest rates have fallen to 5.5%) the holder is entitled to a gain of 100 basis points, and the profit is 100 x GBP 12.50 = GBP 1 250.00 less the premium of GBP 112.50 = GBP 1 137.50.

On the other hand, if interest rates have risen (to 7% pa) so that the contract is trading at 9300, the contract will not be exercised and the holder will forego the premium of GBP 112.50.

# Caps and floors

## Description

Caps and floors (a combination of which is termed a collar) are akin to options. In fact they are so similar to options that they could be termed cap options and floor options. Because of their option-like attributes, they are placed in this section on options.

A cap purchased makes it possible for a company with a borrowing requirement to hedge itself against rising interest rates. The cap contract establishes a ceiling, but the company retains the right to benefit from falling interest rates. On the other hand, a floor contract allows a company with an investment requirement (surplus funds) to shield itself against declining interest rates by determining a specified floor upfront, while it retains the right to profit from rising interest rates.

On the exercise date of the cap or floor contract, the specified strike rate is evaluated against the standard reference rate (i.e. usually the equivalent-term JIBAR rate). The interest differential is then applied to the notional principal amount that is specified in the contract, and the difference is paid by the seller/ writer to the buyer/holder. The buyer of a floor or cap pays a premium for the contract, as in the case of an option or insurance policy.

## Caps

It is perhaps best to elucidate a cap with the assistance of an example: borrowing company buys a 73-month - T6-month cap (see Figure 15).

A company needs to borrow LCC 20 million in 3 months' time for a period of 3 months, and is concerned that interest rates are about to rise sharply. The present 3-month market rate (JIBAR55 rate = market rate) is 10.3% pa. The company is quoted a T3-month - T6-month (T3m-T6m) cap by the dealing bank at 10.5%, i.e. the 3-month JIBAR borrowing rate for the company is fixed 3-months ahead. The company accepts the quote and pays the premium of LCC 25 000 to the dealing bank. The number of days of the period for which the rate is fixed is 91.

Figure 15: example of T3-month - T6-month cap

If the JIBAR rate (= market rate on commercial paper, the borrower's borrowing habitat) in 3-months' time (i.e. settlement date), is 9.3%, the company will allow the cap to lapse (i.e. will not exercise the cap) and instead will borrow in the market at this rate by issuing 91-day commercial paper. The total cost to the company will be the 9.3% interest plus the premium paid for the cap:

Cost to company = (C x ir x t) + P

where

C = consideration (amount borrowed)

ir = interest rate (expressed as a unit of 1)

t = term, expressed as number of days / 365

Cost to company = (C x ir x t) + P

= LCC 20 000 000 x 0.093 x 91 / 365) + LCC 25 000 = LCC 463 726.03 + LCC 25 000 = LCC 488 726.03.

It will be apparent that the interest rate actually paid by the company (ignoring the fact that the premium is paid upfront) is:

Total interest rate paid = LCC 488 726.03 / LCC 20 000 000 x 365 / 91

= 0.0244363 x 4.010989

= 0.09801

= 9.80% pa.

If the JIBAR rate on the settlement date is say 11.2% pa, settlement will take place with the dealing bank according to the following formula:

SA = NA x [(rr - csr) x t]

where

SA = settlement amount

NA = notional amount

rr = reference rate

csr = cap strike rate

t = term, expressed as number of days / 365

SA = LCC 20 000 000 x [(0.112 - 0.105) x 91 / 365]

= LCC 20 000 000 x (0.007 x 91 / 365)

= LCC 34 904.11.

The financial benefit to the company is equal to the settlement amount minus the premium:

Financial benefit = SA - P

= LCC 34 904.11 - LCC 25 000 = LCC 9 901.11.

The company thus borrows at the market rate of 11.2%, but this rate is reduced by the amount paid by the bank to the company less the premium paid to the bank:

Cost to company = (C x ir x t) - (SA - P)

= (LCC 20 000 000 x 0.112 x 91 / 365) - (LCC 9 901.11) = LCC 558 465.75 - LCC 9 901.11

= LCC 548 564.64

Total interest rate paid = (LCC 548 564.64 / LCC 20 000 000) x (365 / 91) = 0.0274282 x 4.010989 = 0.110001

= 11.00% pa.

This of course ignores the fact that the premium is paid upfront.

## Floors

It is useful to elucidate floors with the use of a specific example: investing company buys a T3-month -T6-month floor (see Figure 16).

Figure 16: example of T3-month - T6-month floor

An investor expects to receive LCC 20 million in 3 months' time, and these funds will be free for 3 months before it is required for a project. The investor expects rates to fall and would like to lock in a 3-month rate now for the 3-month period (assume 91 days) in three months' time. He approaches a dealing bank and receives a quote for a T3m-T6m floor at 11.0% on a day when the 3-month market (JIBAR) rate is 11.4%. He verifies this rate with other dealing banks, and decides to deal. The premium payable is LCC 19 000.

Three months later (on the settlement date) the JIBAR 3-month rate is 10.4% pa. The investor was correct in his view and the bank not, and the bank coughs up the following (fsr = floor strike rate):

SA = NA x [(fsr - rr) x t]

= LCC 20 000 000 x [(0.11 - 0.104) x 91 / 365]

= LCC 20 000 000 x (0.006 x 91 / 365)

= LCC 20 000 000 x 0.00149589 = LCC 29 917.81.

The financial benefit to the company is:

Financial benefit

= SA - P

= LCC 29 917.81 - LCC 19 000 = LCC 10 917.81.

The company thus invests at the 3-month cash (spot) market rate of 10.4% pa on the settlement date, and its earnings are boosted by the settlement amount less the premium paid to the bank:

Earning on investment

= (C x ir x t) + (SA - P)

= [LCC 20 000 000 x (0.104 x 91 / 365)] + LCC 10 917.81 = (LCC 20 000 000 x 0.025929) = LCC 10 917.81 = LCC 518 575.34 + LCC 10 917.81 = LCC 529 493.15.

Thus, the actual rate (ignoring the fact that the premium is paid upfront) earned by the company is:

Total interest rate earned

= (LCC 529 493.15 / LCC 20 000 000) x (365 / 91) = 0.0264747 x 4.010989 = 0.1061897 = 10.62% pa.

It will be evident that if the spot market rate is say 11.5%, the treasurer of the investing company will let the floor contract lapse (i.e. not exercise). He will invest at 11.5% for the 3-month period, but this return is eroded by the premium paid for the floor. The following are the relevant numbers:

Earnings on investment

= (C x ir x t) - P

= (LCC 20 000 000 x 0.115 x 91 / 365) - LCC 19 000 = LCC 573 424.66 - LCC 19 000

= LCC 554 424.66.

It will be apparent that the interest rate actually earned by the company (ignoring the fact that the premium is paid upfront) is:

Total interest rate earned

= (LCC 554 424.66 / LCC 20 000 000) x (365 / 91) = 0.0277212 x 4.010989 = 0.1118943 = 11.12% pa.

Thus, the investor would have been worse off if he had exercised the floor.