
Option Premiums
It is difficult to completely separate the futures markets from the options markets. Not only do futures and options share a pedigree, they trade on related exchanges and share a great deal of vocabulary. It is also important to note that options on futures contracts comprise an important component of these overlapping fields. To know how to value futures, one needs to know how to value options.
Valuation
"Premium" is one of those words with different meanings in different contexts. In terms of option pricing, a premium is the price the buyer pays to an option writer for granting an option contract.
Although the option premium is set entirely by supply and demand forces in a public market, conceptually it is comprised of two elements: "intrinsic value," the option's value if immediately exercised and "time value," the option's potential to gain intrinsic value before it expires.
Time value, then, is the delta between what the option is worth today and what it was sold for. An option's time value equals the option premium minus the option's intrinsic value.
One reason this is important to players in the futures market is that there is often a gap between an option's strike price â€“ its intrinsic value â€“ and the futures price for the same underlying assets. That futures price is essentially a proxy for the option's time value.
Premium Quotations
The premium quote on a Chicago Mercantile Exchange (CME) Euro FX September 1.325 call option is quoted at .54 cents/euro. In other words, the buyer of this option has the right, but not the obligation, to go long CME Euro FX futures at 1.325 any time before expiration. The buyer of this call will pay $675.00 (.54 cents/euro x125,000 euro = $675.00) to the seller for this right.
Quotes for Treasury and municipal obligation contracts are slightly different. These interest rate options provide investors with an opportunity to take positions based upon their expectations of the direction of interest rates. A call buyer believes interest rates will go up, while a put buyer anticipates that rates will go down. Underlying securities have tenors ranging from 90 days to 30 years, so investors can place their bets with regards to the timing of their anticipated interest rate fluctuations.
Treasury obligation contracts are traded on the CME. Their premium quotes are stated in decimals, with one point equaling $100. The minimum tick for options trading below 3.00 ($300) is 0.05 ($5). For all other series, the minimum tick is 0.10 ($10). These contracts are "Europeanstyle," which means that they can be exercised only on the last business day before the expiration date. This is in contrast to "Americanstyle" options, which can be exercised on any date before expiration. Most options traded in the United States that are not related to interest rates are Americanstyle.
These options are also cashsettled, so there is no need to deliver Treasury instruments upon exercise.
When Treasury rates change, corresponding underlying values for the options on interest rates also change. For example, if the yieldtomaturity on the 30year Tbond increases from 6.25 to 6.36%, the option quote would move from 62.50 to 63.60. For every one percentage point rise or fall in interest rates, underlying values would rise or fall 10 points.
Tbills have face values of $1 million and a time to maturity of 90 days; the clock starts at the expiration date of the futures contract. Price quotes for Tbill futures use the International Monetary Market (IMM) Index, which is computed by subtracting the discount yield from 100. Thus, if a Tbill has a discount yield of 7.45%, its IMM index value is 92.55.
Formula 4.1
IMM Index = 100.00 â€“ discount yield
Quoting, however, is not pricing. The IMM index is simply a convention to ensure that ask prices are above bid prices in the interest rate markets, just like they are in all other markets.
There is more involved in computing the price of a Tbill future than subtracting out the discount yield. First, one must compute the price of the underlying Tbill.
Formula 4.2
Tbill price = $1,000,000  discount yield x $1,000,000 x days to maturity 360
From Formula 4.2, we can work an example to compute the price of a Tbill with a 6.00% discount and 90 days to maturity. (Most Tbills dedicated to the futures market will have 90 days to maturity.) The numerator would come to $5,400,000 (.06 x $1,000,000 x 90). Divided by 360, that comes to $15,000. Subtracted from $1,000,000, that equals $985,000.
If the futures yield rose to 6.04%, we would redo the calculation and come up with $984,900.
Tips & Tricks
For every basis point increase â€“ that is, for every additional 100^{th} of a percent discount yield â€“ on a Tbill with 90 days to maturity, the Tbill's price declines by $25.
Knowing how to calculate the Tbill's price as of the expiration date allows you to determine the intrinsic value of the contract to deliver it.
Tbonds and Tnotes have a somewhat different pricing structure that a futures trader would need to understand. While Tbills are traded on the CME, Tbonds and Tnotes trade on the CBOT, which has different rules. Trading Tbond futures, in fact, is perhaps the highestvolume business the CBOT does. Of course, there are differences in the structure of the bond market versus the bill market on the East Coast before the futures even enter the pits in
As opposed to Tbills, which are quoted in easytounderstand decimals, the longerterm Tbonds and Tnotes are quoted in "points and 32nds of par." As complex as that sounds, it simply means that a quote of "9824" translates as, "This bond is worth 98 and 24/32 percent of its $100,000 face value, or $98,750."
Tips & Tricks
The minimum tick for a Tbond is $31.25 (one thirtysecond of one percent of $100,000).
There is a specific procedure for delivering Tbond futures:
 Two days before the delivery day, the parties taking the long and short positions each declare their positions and notify the clearinghouse of their willingness to take delivery and intention to make delivery.
 The next day, the "notice of intention day," the clearinghouse matches the long and the short and notifies them of each other's contact information. The short invoices the long.
 The next day, "delivery day," the short acquires the bonds and delivers them to the long, who makes payment to the short. Title passes and the long assumes ownership of the bonds.
Interest rates for U.S.domiciled municipal bonds tend to follow those of the federal government's Treasury obligation. Still, the market for muni futures is unique in a number of respects.
The muni futures contract is actually indexbased, rather than tracking an underlying asset. Specifically, it is based on The Bond Buyer Municipal Bond Index (MBI), which tracks 40 investmentgrade, taxexempt bonds that pay a fixedrate semiannual coupon.
The math required to compute the MBI is more complex than a newlyminted, Series 3 futures trader is expected to master. Suffice to say, though, that muni futures are quoted in pointsand32ndsofpar, with par defined as 1,000 times the MBI. The tick size is $31.25. On the final trading day, the futures settlement price is equal to the cash value of the index to ensure convergence of the futures and cash market prices.

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