Written in the late nineties by James Orlin Grabbe. This is the last part of the series.
A gold forward rate agreement (FRA) is a contract whose payout depends on whether the market interest rate diverges from an agreed “contract rate”. It is called a “forward rate” agreement, because the interest rate applies to a gold deposit or loan starting at some time period in the future. That is, the interest rate in question is the gold lease rate (also called gold libor). Recall that we used the gold “lease” rate as a generic term to refer to both the bid rate for taking in gold deposits and the offer rate for making gold loans. Recall also that the interest in this case is typically paid or received as so many ounces of gold. Similarly, a gold FRA will be typically settled with one party paying the other in gold.
A typical FRA contract in this regard might be a gold deposit that begins three months from today, and lasts for three months (ending six months from today). This would be called a 3 vs. 6 FRA. The terminology “3 vs. 6″ implies the contract starts in 3 months and ends in 6 months.
What is agreed to is a contractual interest rate: the FRA rate. If the actual realized market rate turns out to differ from the FRA rate (as it almost inevitably will), then one makes or receives payment depending on the terms of the contract.
There are five principal parts to an FRA contract: the contract rate, the notional amount of gold in a contract, the fixing date when the market interest rate is compared to the contract rate, the start date of the deposit (or loan), and the maturity date of the deposit (loan).
One can buy or sell this contract. The settlement amount S paid to the buyer of the FRA from the seller is calculated as follows:
S = notional amount x (market rate – contract rate) x (days in period)/360.
If the market rate is below the contract rate, so that the sign on the amount S is negative, then the FRA buyer pays the FRA seller the absolute value of S.
The calculation above assumes that payment is made at the end of the FRA period (on the maturity date). But if (as is normally the case) payment is made on the start date instead, the settlement amount S given above is discounted by the market rate at which the contract was settled:
S/[1 + market rate x (days in period)/360].
Let’s do an example.
Example: Consider a depositor who will have one ton (32,000 ounces) of gold available in 3 months, but will not be utilizing the gold for another 3 months after that. He wants to lock in the interest rate he will receive on his gold deposit now. He asks for a quote of the 3 vs. 6 months FRA, and receives the quotation:
3 vs. 6 FRA 1.50-1.80 %
This quotation means he can “sell” the FRA at a contract rate of 1.50 percent (.015), or “buy” the FRA at a contract rate of 1.80 percent.
So, in this case, he sells the FRA with a contract rate of 1.50, and a notional amount of 32,000 ounces of gold.
Three months from today, on the fixing date, he will determine the best market rate available, and this will be compared to the contract rate to determine the FRA settlement amount. (The fixing date will typically be two business days prior to the conceptual start date of the deposit or loan.) Suppose the best deposit rate at that time is 1.00 percent (.01). Suppose also that the three- month deposit period from start date to maturity date is 92 days. The settlement amount S is then calculated as:
S = 32,000 x (.01-.015) x (92/360) = – 40.889 oz.
The sign here is negative, which means the FRA buyer pays the FRA seller (our hypothetical depositor) 40.889 oz. of gold on the maturity date (if payment is made then). If payment is made on the start date, it is discounted by the time period of the deposit:
40.889/[1+.01 x (92/360)] = 40.785 oz.
So in this event the FRA buyer pays the FRA seller 40.785 oz. of gold on the start date.
Now if the depositor deposits his ton of gold at the market rate of 1.00 percent for three months, he will end up with an equivalent interest rate of 1.50 percent, the FRA rate, because the difference has been paid out on the FRA contract.
The same would have been true if the depositor had lost, rather than gained, from the FRA contract. For in that case the market rate paid on deposits would be higher than 1.50 percent, but the depositor would lose the difference on the FRA contract.
Similar examples could be done for gold borrowers. Gold borrowers typically borrow at the gold lease (gold libor) rate plus a margin: say
market rate + .75%
and make periodic gold interest payments at intervals of 6 months. By using FRAs for 6 month intervals (such as 6 vs. 12, 12 vs. 18, 18 vs. 24, etc.), the next few interest payments on this loan can be locked in as
FRA rate + .75%
if that seems desirable.
Gold Interest Rate Swaps
It is important not to get the word “swap” as used here confused with “swap” in the gold forward market. There the term referred to the relationship between spot and forward prices. Here, in “interest rate swap,” we are referring to a trade of a fixed interest rate for a floating interest rate.
The swap “buyer” in an interest rate swap agrees to pay a fixed interest rate to another party, and in return receives at periodic intervals an interest rate that fluctuates (floats) with the market. That is, the buyer pays a fixed gold rate and receives the market- determined gold lease rate (or some equivalent).
The other side of the interest rate swap contract is the seller who receives fixed and pays floating.
If, for example, the floating rate is the 3-month gold lease rate, then every 3 months there will be a net interest payment whenever the market lease rate diverges from the fixed rate. If the market rate is above the fixed rate, then the swap buyer (who pays fixed) will receive an interest payment representing the positive net difference of floating minus fixed. If the market rate is below the fixed rate, then the swap seller (who receives fixed) will receive an interest payment representing the positive net difference of fixed minus floating.
In essence, then, a gold interest rate swap is just a series of gold FRAs. If the floating rate in the market is above the fixed rate, the swap buyer (who pays fixed) is in the same positon as the buyer of an FRA. If we equate the “fixed rate” with the “contract rate” in an FRA, then the FRA buyer receives a positive cash flow if the market rate is above the fixed rate.
So buying a gold interest rate swap represents the purchase of a series of gold FRAs at a single contract rate (fixed rate), while selling a gold interest rate swap represents the sale of a series of gold FRAs at a single contract rate (fixed rate).
Why would someone want to do this? Let’s consider an example.
Example: Consolidated Gold Nuggets has an existing loan of 1 million ozs. of gold with two years remaining to maturity. It pays floating interest at the 3-month gold lease rate plus a margin of 1.75 percent. However, gold lease rates have fallen, and the treasurer wishes to lock in a low fixed rate. Renegotiating the loan will involve contractual penalties. The treasurer shops the market and determines she can buy a two- year gold interest rate swap, paying 2 percent fixed against the floating 3-month gold lease rate flat. She does the swap.
Her swap payments are
2% – 3-month gold lease.
Her loan payments are
3-month gold lease + 1.75%.
The net interest payment is the sum of these:
2% + 1.75% = 3.75% .
So by doing the gold interest rate swap, she has turned the floating rate loan into a fixed rate loan of 3.75 percent.
Gold Interest Rate Guarantees
Gold IRGs are a form of insurance. Typically they take the form of a floating rate, with a guaranteed maximum or minimum. The gold borrower might prefer to borrow floating, and hence have the ability to profit from falling interest rates, but nevertheless want a guarantee that the floating rate paid will not rise above some maximum or ceiling level.
In a similar vein, a gold lender might prefer to lend at floating rates, in order to profit from rising interest rates, but desire a guarantee that the rate received will not fall below some minimum or floor level.
These types of guarantee contracts are analytically equivalent to interest rate options. Hence we will defer their discussion until we have discussed options in general in the context of options on the gold price.
Hedging is the process of substituting a certain, or known, outcome for an uncertain one. A gold producer, for example, does not know what the spot price of gold will be a year from now. But he can hedge future gold sales by selling gold forward at the known one-year forward price. This will enable him to determine his cash flow in advance– at least that part of it that depends on the fluctuating price of spot gold. It will simplify financial planning.
The actual spot price of gold a year from now may be higher than the preagreed forward rate, or it may be lower. Thus, by hedging and substituting a known price for an unknown one, the gold producer could just as easily suffer an opportunity loss as an opportunity gain.
Many in the gold market are looking not for a fixed forward price, but rather for a boundary guarantee. A future seller of gold might want a guarantee that the sales price will not fall beyond a minimum level below which he could not tolerably live, but otherwise prefer to remain unhedged in hopes the market price will rise. Similarly, a future gold buyer might look for a guarantee that the purchase price will not rise above a tolerable maximum level, but otherwise prefer to remain unhedged in hopes the market price will fall.
What can be said of the gold price can be said of gold interest rates. A future borrower of gold might look for insurance that the borrowing rate will not be too high, while a future lender of gold might look for insurance that the lending rate will not fall below a level yielding an acceptable return.
The gold market creates and sells such guarantee or insurance contracts. In the financial literature (and in the market), these same contracts are also called options. Naturally the market does not provide such insurance contracts for free. Like anything else, they are available for a price. The price or amount paid for an option (or guarantee or insurance) is called the premium. Options trade over-the-counter and at organized securities and futures exchanges.
Just as there are natural buyers of insurance, such as gold mining companies, there are natural writers of insurance. Central banks with large holdings of gold have written thousands of options over the past decade. Along with gold lending, this activity provides an income to the banks even when the gold price does not move much.
Options have the mystique of being a very arcane subject. But there is nothing terribly difficult about them, really. All that you need to know about options can be gotten by thinking through the consequences of the terms of the options contracts themselves. The option mystique comes from the use of a not-commonly-understood branch of mathematics called stochastic calculus in order to price them mathematically, and to produce numerical computer programs to generate prices and associated statistics for trading and risk-management purposes. But those same traders and risk-managers who use the output of the programs rarely know anything about stochastic calculus. It’s simply not necessary for understanding options.
Options are usually classified according to whether they are options to buy (calls) or options to sell (puts), and according to whether they can be used only on a specific date (European) or at any time prior to a specific date (American). The terms “European” and “American” refer to types of options and have nothing to do with the geographical location of trading or the manner in which prices are quoted. We will divide gold options into two further categories: options on spot gold, and options on gold futures.
Options on Spot Gold
An American gold call is a contract between a buyer and a writer whereby the call buyer pays a price (the “premium”) to the writer in order to acquire the right, but not the obligation, to purchase a given amount (“size”) of gold from the writer at a purchase price (the “exercise” or “strike” price) stated in terms of a (usually) fiat currency, on or before a stated date (the “expiration” or “maturity” date). For example, a call option on gold might give one the right to purchase two tons of gold of .995 fineness at $310/oz. on or at any time before the third Wednesday in December 1999.
An American gold put is similar, except that it gives the right to sell a given amount of gold. For example, such a put option might give one the right to sell 40,000 ozs. of gold of .9999 fineness for $285/oz. on or before June 13, 2000.
A European option differs from an American option in that it may be exercised (used) only on the expiration date. If the call option in the penultimate paragraph were European, then it could be exercised only on, but not prior to, the third Wednesday in December 1999. If the put option in the preceding paragraph were European, it could be exercised only on June 13, 2000.
There are two sides to every option contract. There is the buyer of the option, who purchases the right either to buy (call) or sell (put) the asset contained in the option contract, and there is the writer of the option, who sells the right either to buy or sell the asset contained in the option contract. The buyer of an option on spot pays the price (or premium) of the option up front, and subsequently has the right to exercise or not to exercise the option contract. For example, the buyer might pay $20,000 to purchase a put that allows the buyer to sell 25,000 ozs. of gold at a strike price of $280/oz. The other side of the put contract is the writer who sells this right. The writer receives the $20,000 premium the buyer pays. Then if the buyer decides to exercise the right to sell 25,000 ozs. of gold, the writer has to purchase the gold at $280/oz. from the buyer of the put option. The buyer might be, for example, a Nevada gold-mining company and the writer a U.S. bank. If the bank writes the put to the company, and then the company exercises its right to sell gold at the strike price of $280/oz., the bank has to accept the 25,000 ozs. of gold and pay the company $7,000,000 in return.
Options on Gold Futures
Options on gold futures contracts, such as those traded at the COMEX Division of the New York Mercantile Exchange, are somewhat different from options on spot gold. A call on gold futures is a contract between a buyer and a writer whereby the call buyer pays a price (the premium) to the writer in order to acquire the right, but not the obligation, to go long an exchange-traded gold futures contract at an opening price (the strike price) stated in terms of a fiat currency. If the buyer of a call on futures exercises his or her right to go long a futures contract, the writer of the option must go short the futures contract. A put on gold futures similarly gives the right to establish a short position in an gold futures contract at a price given by the exercise price of the option. If the buyer of a put on futures exercises his or her right to go short a futures contract, the writer of the option must go long the futures contract.
(For credit purposes, the futures clearinghouse becomes the effective counterparty in all futures option trades. The clearhouse in effect becomes the writer to every option buyer, and the buyer to every option writer. But this does not change any of the contractual obligations associated with an option. In particular, the clearinghouse does not itself exercise long option positions. If the holder of a long option (put or call) exercises the option, the clearinghouse picks someone who is short the same option contract to meet the contractual obligation.)
All currently traded options on gold futures contracts are American in type, and can be exercised on any business day prior to expiration. For example, if you have an American call on December gold futures with a strike price of $280/oz. and the current futures price is $283.50/oz., exercising the option will give you a long position of one December gold futures contract at an opening futures price of $280/oz. Since the current futures price is $283.50/oz., the value of this futures position is
$283.50/oz. – $280/oz. = $3.50/oz.
This profit can be realized immediately by closing out the futures position (going short to offset), or by withdrawing the cash from the account (if futures margin requirements are otherwise already met).
At this point a short summary of the basic option definitions might be useful:
1. There are two sides to each option contract–the buyer who obtains the option right to exercise, and the writer who issues this right.
2. From the buyer’s perspective, a call is an option to buy or go long, while a put is an option to sell or go short.
3. From the writer’s perspective, a call is an obligation to sell or go short (if the call buyer exercises), while a put is an obligation to buy or go long (if the put buyer exercises).
4. An option on spot gold involves an up-front cash payment of the premium from the buyer to the writer, and in addition a subsequent exchange of gold for a fiat currency if the buyer exercises the option.
5. An option on futures involves an up-front cash payment of the premium from the buyer to the writer, and in addition a subsequent futures position in which the buyer and writer are on opposite sides if the buyer exercises the option.
6. Any of these options can be American or European. The option is European if it can only be exercised on the final day, the expiration day. An American option can also be exercised on any business day prior to expiration.
Gold Options as Insurance
Let’s look at the use of gold options for hedging from the point of view of an option buyer. For the moment, we will simply treat options as contracts that are available to the buyer or the writer at a market-determined price, without concerning ourselves with the separate question of what the fair value (fair to both the buyer and writer) of a gold option is.
For the purpose of hedging, gold options can be viewed as price insurance. Consider how insurance works in general. Suppose you buy fire insurance on a $100,000 house. You insure the house for its full value of $100,000, and the insurance is good for one year. If, by the end of the year, your house has not been damaged by fire, the insurance will have proved worthless. You throw away the unused insurance policy. Your total cost has been the cost of the insurance premium. On the other hand, suppose that fire does $40,000 worth of damage to your house. In this case, you have a $40,000 loss. But the insurance policy pays off the difference between the amount of the insurance ($100,000) and the current value of the insured asset ($60,000), making up exactly the amount of your loss ($40,000). Thus your total loss is zero, except again for the insurance premium, which you pay in any case.
An option works in the same way. Suppose you buy a put option on the value of a house. In particular, suppose the strike price of the put is $100,000. That is, it gives you the right to sell the house for $100,000. You buy an American put (so that it can be used at any time), and it expires in one year. If the market value of the house stays at $100,000 or greater for the year, there would be no advantage in exercising the put. Thus the put would expire worthless. You would throw it away rather than use it to your disadvantage.
But if, because of fire or for some other reason, the value of the house dropped to $60,000, you could exercise the put and sell the house for $100,000. The put has then served as insurance. It paid off the difference between the strike price ($100,000) and the current value of the house ($60,000), thus making up the entire loss in value ($40,000). In any case, whether or not the house lost value, you pay the cost of the put. The price paid for an option is (conveniently) referred to in the options market as the premium and is analogous to an insurance premium. Overall, then, the put serves as an insurance policy. (Or, as some prefer to say, insurance itself is just a put option.)
Let’s extend the analogy to deductible insurance. Suppose that, instead of insuring your house for $100,000, you insured it for $80,000. In this case if your house is damaged by fire, you will have to bear the loss of the first $20,000. On the other hand, the insurance premium on $80,000 will be less than the premium on $100,000, so that you may be willing to trade off the greater risk of loss in the case of fire with the lower fixed cost of the insurance premium. In the same way, if you purchased a put option on the house with a strike price of $80,000 instead of a strike price of $100,000, the premium (purchase price) of the put would be lower. But the insurance level of the put will be lower, because it will only pay to exercise the put if the value of the house falls below $80,000. Thus, buying a put option with a strike price that is lower than the current market value of the asset involved is like buying deductible insurance. Whether you like deductible insurance depends on your attitude to trading off lower insurance premiums with the risk of greater loss in the event disaster strikes.
Both options on spot gold and options on gold futures can be considered types of insurance against adverse gold price movements. Options on spot gold represent insurance bought or written on the spot price, while options on gold futures represent insurance bought or written on the futures price (which, as we saw in earlier parts of this series, is equivalent to the forward price).
Floors and Ceilings
An individual with gold to sell can use put options on spot gold to establish a floor price on the fiat currency value of gold. For example, a put option on 1 oz. of gold with an exercise price of $300/oz. will ensure that, in the event the value of gold falls below $300/oz., the 1 oz. of gold can be sold for $300/oz. anyway. If the put option costs $3/oz., this floor price can be roughly approximated as
$300/oz. – $3/oz. = $297/oz.,
or the strike price minus the premium. That is, if the option is used, you will be able to sell the 1 oz. of gold for the $300/oz. strike price, but in the meantime you have paid a premium of $3/oz.. Deducting the cost of the premium leaves $297/oz. as the floor price established by the purchase of the put. (This ignores fees and interest rate adjustments.)
Similarly, an individual who has to buy gold at some point in the future can use call options on spot gold to establish a ceiling price on the fiat currency amount that will have to be paid to purchase the gold. For example, a call option on 1 oz. with an exercise price of $305/oz. will ensure that, in the event the value of gold rises above $305/oz., the 1 oz. can be bought for $305/oz. anyway. If the call option costs $1/oz., this ceiling price can be approximated as
$305/oz. + $1/oz. = $306/oz.,
or the strike price plus the premium. To summarize these two important points involving gold puts and calls:
1. Gold put options can be used as insurance to establish a floor on the fiat currency value of gold. This floor price is approximately
Floor price = Exercise price of put – Put premium.
2. Gold call options can be used as insurance to establish a ceiling on the fiat currency cost of gold. This ceiling price is approximately
Ceiling price = Exercise price of call + Call premium.
These calculations are only approximate for essentially two reasons. First, the exercise price and the premium of the option on spot gold cannot be added directly without an interest rate adjustment. The premium will be paid now, up front, but the exercise price (if the option is eventually exercised) will be paid later. The time difference involved in the two payment amounts implies that one of the two should be adjusted by an interest rate factor. Second, especially in the case of exchange-traded options, there may be brokerage or other expenses associated with the purchase of an option, and there may be an additional fee if the option is exercised.
Gold options are dealt over-the-counter in the form of a two-way price: a bid price at which the option will be purchased, and an asked price at which the option will be sold. At the time an option is dealt, the following must be specified in addition to the premium or cost of the option:
whether the option is a put or call
the strike (exercise) price of the option
the date the option expires
the principal amount of the option (number of oz. of gold)
whether the option is American or European.
There are four dates associated with each option. The first of these is the contract date, which is the date the option is traded or dealt. Since the option premium and strike price are agreed at this time, the option is actually in existence as of this date. The next is the premium settlement date, which is the date the option premium is actually paid. This is typically two working days after the contract date–following the two-day settlement convention in the foreign exchange market. The next date is option expiration, which is the final date on which the option may be exercised–the day the insurance runs out. The fourth date is the option settlement date, which again is typically two working days after the option expiration date. If an option is exercised on the expiration date, then gold and cash will exchange hands two working days later on the option settlement date. In the event the option is American, and thus can be exercised prior to the expiration date, option settlement will be two business days after the option is exercised.
Options are typically traded over-the-counter on a month basis. Thus, an “April” option will mean an option whose settlement date is the last trading day in April. The expiration day of the option will be two business days prior to the last trading day. Such options are traded for every calendar month. (Frequently a company will want a price quotation on a strip of options; for example, a strip of 24 puts, one put for each month in the next two years.)
Let’s look at a simple example.
A gold refiner wants a 290 November European put on 24,000 ozs. of gold. The marketmaker gives a quote of 2.20- 2.60. This quotation is in U.S. dollars per ounce. The first price, $2.20/oz., is the premium that the refiner will receive if he sells the put, while $2.60/oz. is the price he will pay if he purchases the put. The strike price of the option is $290/oz. The refiner buys the put for $2.60.
In two business days, the refiner will pay the marketmaker the option premium. The premium amount is
24,000 oz. x $2.60/oz. = $62,400.
Since the option is European, nothing more will happen until option expiration in November, which is two business days prior to the last trading day.
Note, however, that the refiner has assured that the selling price for gold will not be less than
$290/oz. – $2.60/oz. = $287.40/oz.
The number $287.40/oz. is the refiner’s floor price. The refiner is assured he will not receive less than this, but he could receive more. The price the refiner will actually receive will depend on the spot gold price on the November expiration date. To illustrate this, we can consider two scenarios for the spot price of gold.
Spot gold on the November expiration date is $296/oz. The refiner would not use the put option (which has a $290 strike price) but would sell gold spot at the higher market rate of $296/oz. (Settlement will take place two days later.)
The total amount received per oz. of gold, once we subtract the cost of insurance, is
$296 – $2.60 = $293.40.
The $2.60/oz. that was the original cost of the put turned out in this case to be an unnecessary expense.
Now, to be strictly correct, a further adjustment to the calculation should be made. Namely, the $296 and $2.60 represent cash flows at two different times. Thus, if x is the amount of interest paid per dollar over the time period to end November, the proper calculation is
$296 – $2.60(1 + x).
The spot rate on the November payment date is $284/oz. The refiner can either exercise his option or sell it back to the marketmaker for its market value of $6/oz. Assuming the refiner exercises the option, he sells 24,000 oz. of gold for
($290/oz.)(24,000 oz.) = $6,960,000.
Subtracting the premium paid earlier, the net amount is
$6,960,000 – $62,400 = $6,897,600 .
This, of course, works out to be $287.40/oz., the floor price established by the option. (Here we have ignored the interest opportunity cost on the $62,400 premium.)
Writing Gold Options
The writer of a gold option on spot or futures is in a different position from the buyer of one of these options. The buyer pays the premium up front and afterward can choose to exercise the option or not. The buyer is not a source of credit risk once the premium has been paid. The writer is a source of credit risk, however, because the writer has promised either to sell or to buy gold if the buyer exercises his option. The writer could default on the promise to sell gold if the writer did not have sufficient gold available, or could default on the promise to buy gold if the writer did not have sufficient cash available.
If the option is written by a bank, this risk of default may be small, depending on which bank in which country. But if the option is written by a company, the bank may require the company to post margin or other security as a hedge against default risk. For exchange-traded options, as noted previously, the relevant clearinghouse guarantees fulfillment of both sides of the option contract. The clearinghouse covers its own risk, however, by requiring the writer of an option to post margin. At the COMEX, for example, the clearinghouse will allow a writer to meet margin requirements by having the actual gold or U.S. dollars on deposit, by obtaining an irrevocable letter of credit from a suitable bank, or by posting margin in the form of Treasury securities.
From the point of view of a company or individual, writing options is a form of risk-exposure management of importance equal to that of buying options. It may make perfectly good sense for a company to sell gold insurance in the form of writing gold calls or puts. The choice of strike price on a written option reflects a straightforward trade- off. Gold call options with a lower strike price will be more valuable than those with a higher strike price. Hence the premiums the option writer will receive are correspondingly larger. However, the probability that the written calls will be exercised by the buyer is also higher for calls with a lower strike price than for those with a higher strike. Hence the larger premiums received reflect greater risk taking on the part of the insurance seller (the option writer).
James Orlin Grabbe