Interest Rate Options

Interest rate guarantees

An interest rate guarantee (IRG) is an over the counter option on a forward rate agreement (FRA) period. A call on the forward rate is termed a BORROWER'S IRG and a put on the forward rate is termed a LENDER'S IRG. As an example, let us take the following option :  Borrower's £ IRG, European style, Strike 6%Underlying is a 3 month FRA out of the 15th September 199X
Expiry date of option 15th September 199X
Trade date of option 15th June 199X
Cash settlement on exercise
Nominal option size £100 million
Premium 0.2% at 0.3% of nominal

At the trade date, the forward rate period is the 3's 6's FRA. As the option approaches expiry the forward rate period moves progressively nearer . It is important to note that the option is on a fixed period starting at a specific date, not an option to exercise into a 3's 6's FRA as of the exercise date. The option gives the holder the right to borrow a nominal amount of £100 million at a rate of 6% for this period, though of course as with FRAs themselves, cash settlement applies and no actual transfer of principal occurs. The option premium is quoted by a market maker as 0.2% at 0.3% of the nominal size (£100 million), therefore the premium amount is £200,000 bid £300,000 offered. The holder notifies the writer of his intention to exercise on the expiry date. The cash settlement amount due to the holder of the option if exercise occurs is calculated with reference to an agreed rate such as libor in exactly the same way as for an FRA position at the settlement date. The writer of such an option would therefore be paying a settlement amount based on the difference between the market level of the specified floating rate and the strike rate on the day of exercise.

Caps and floors
A cap is a series of borrower's IRGs. A floor is a series of lender's IRGs. Both caps and floors are therefore types of serial option, in that they are comprised of more than one option and the options are structured into consecutive periods. The individual IRGs within caps and floors each have the same strike rate.
The value of a cap or floor is the same as the summed value of the constituent IRGs that make up that cap or floor. Therefore the option valuation model will calculate the values of the individual IRGs in order to arrive at a value for the cap or floor premium. It is therefore necessary to provide the option model with some method of calculating the appropriate FRA rates for each IRG period, or to provide the FRA rates direct into the model. Frequently this is achieved by inputting cash market deposit rates and swap rates, or a combination of cash market, deposit and swap rates.
These rates must be taken from the market and are continually updated by traders as the market moves. The model will then have to generate a yield curve from the data supplied, usually of the zero-coupon type, and it is from this curve that the relevant forward rates are taken. Here is an example of a cap :
2 year £ Cap
Strike 6% with 3 month rollovers
Trade date 15th September 199X
Nominal size £100 million
Premium 1.00% at 1.10% of nominal
Cash settlement

This cap gives the holder the right to pay 6% on a nominal size of £100 million on each of eight borrower's IRGs, the first of which begins on the trade date and the last of which ends on the 14th September 199X. The premium quoted by the market maker is 1.00% at 1.10% of nominal size, in other words the cap is £1 million bid and £1.1 million offered. Usually, traders will agree to eliminate the first IRG in such caps and floors since there is little point in trading an option on a rate that is already known in the market (the 3 month deposit in the case of the first period here). Such a process is sometimes referred to as trading the cap or floor 'without the first fix'. Upon each IRG expiry date, the cap holder exercises against the agreed reference rate such as libor, and the settlement is calculated in exactly the same way as for the IRGs described above.
Some traders prefer to look at caps and floors as derivatives of swaps. This becomes clear when one sees that a synthetic long swap position can be achieved by the purchase of a cap and the sale of a floor at the same strike and with otherwise identical terms. Also a synthetic short swap position can achieved by the sale of a cap and the purchase of a floor at the same strike and with otherwise identical terms. If a synthetic long or short position in an asset can be created by two options, then the behaviour of those option premiums must in some way be related to the underlying asset that has been synthesised (here a swap rate).
Traders therefore often decide to hedge caps and floors with swap trades. At other times, the future, the FRA or even the cash deposit market may be used to provide hedge cover. The hedge for a long cap position would be an appropriate short position in a swap (i.e. a receiver's position) and vice versa for the short cap position. Since there are several options within a cap or floor, the amount traded for a single 'all in one' hedge must necessarily be an average of the amounts that would be traded as a hedge for each individual IRG (see the discussion of delta in "Option Theory").

Swap options
Most swap options are traded on fixed for floating interest rate swaps. Swap options on the other major types of swap are possible but the volume of such trading in the market is less substantial. The following information applies to fixed for floating interest rate swap options.
A payer's swap option gives the holder the right to pay the fixed in a fixed for floating interest rate swap. A receiver's swap option gives the holder the right to receive the fixed in a fixed for floating interest rate swap. The other details of the underlying swap are confirmed at the time of trading the related option and will include all the features normally quoted for that swap in the underlying market, such as currency, swap period, nature of floating rate, frequency of fixed rate payments, nominal size and so on. If the swap option is exercisable into the underlying swap, then that swap commences from the value date which would be used if the exercise date were a normal swap trade date. This would be a 'physically settled' swap option.
Alternatively, the swap option may be 'cash settled', in which case a suitably agreed independent reference source for the underlying swap rate is agreed between the counter parties at the time of trading the option. This source is consulted in the event of exercise.
The difference between the cash-flows that would occur in a physical swap transacted at the reference rate and one transacted at the strike rate is discounted at the settlement rate and paid up-front in settlement of the option.

Since swaps are quoted as rates, swap options are options on rates and the volatility values spoken of in this market are therefore yield (or rate) volatilities. Market traders sometimes look to hedge swap options with government bonds in order to take advantage of forecast changes in the spread between the bond market and swap market.

Cash bond options
Cash bond options are often traded over the counter. Most of the volume of trading in this market is on government bonds, though corporate bond options can also be traded.
A call on a bond gives the holder the right to buy the bond whilst a put on a bond gives the holder the right to sell the bond. Cash bond options are usually traded for physical settlement, though where an independent quotation source can be agreed, cash settlement can occur.
The cash settlement is then the difference between the strike price and the independently quoted price as agreed at the time of exercise.
Bond prices, and therefore cash bond option strike prices, are quoted in terms of the clean price of the bond. If the option is exercised, accrued interest is paid from the bond buyer to the bond seller as in a normal bond trade.
Since bonds are quoted in terms of price and each price has an associated yield to maturity, the volatility of a bond option can be quoted as a price volatility or a yield volatility. Important differences in bond option valuation can result from the incorrect use of these two types of volatility. The problem arises because of differences in duration between bonds. Hence, whilst yield volatility at a particular point of the bond yield curve is usually more or less uniform, bonds of different coupons at that point on the yield curve will display different price volatilities for any one given yield volatility.
It is therefore preferable to compare cash bond options in terms of yield volatility rather than price volatility. Some traders aim to arbitrage the difference between the implied volatilities of two different option products based on the same sector of the yield curve, for example options on ten year swaps and options on ten year bonds (see the discussion of yield volatility in "Option Theory").
Cash bond options may be hedged with cash bonds themselves, with bond future contracts, and sometimes with swaps. As with swap option hedging, an analysis of the behavior of the spread between the underlying cash bond and the instrument used to hedge the option must be undertaken. Such an analysis will help a trader to understand the extra risk incurred when the hedge is not the same instrument as the underlying on which the option is based.