Home Business & Finance The mathematics of financial models

# MARKET INSTRUMENTS

There are many instruments that are traded in the financial markets. Since the concept of calculating the present value of cash flow involves the use of interest rates, I will restrict my discussion to interest-bearing instruments. As this comprises a very broad universe of instruments, for the purposes of illustration, I will focus on treasury bills, treasury bonds, euro-dollar futures, and swaps.

## Treasury Bills

Treasury bills (or T-bills) are short-term debt instruments that are issued by the U.S. Treasury. With maturities of less than a year, these zero-coupon bonds are usually issued with maturities of 1, 3, 6, and 12 months. While 12-month T-bills are auctioned monthly, T-bills of other maturities are auctioned weekly.[1] As stated in the T-bill settlement calculation put out by the U.S. Treasury, the formula used to convert a discount yield into a settlement price is given by the expression

(2.1)

TABLE 2.1 Calculating the Cash Price of a Treasury Bill

where DY represents the discount yield (or quoted price[2]), Price represents the cash (or settlement) price associated with the Treasury bill, and T represents the number of calendar days from today to the maturity date.[3] Table 2.1 shows the use of equation (2.1) when DY = 0.05 and T = 30 days.

As can be seen from Table 2.1, when the quoted price is 5 percent, the cash price paid for this T-bill is USD99.5833 so as to receive USD100 in 30 days.

• [1] For more details associated with Treasury bills, go to treasurydirect.gov/ indiv/research/indepth/tbills/res_tbill.htm.
• [2] Quoted price is the terminology that is used to refer to a traded price (i.e., the price seen on a trading screen) although in this instance the quoted price refers to the yield and not the price.
• [3] For the purposes of settlement, T is calculated from the day the transaction is settled-which is one business day following the trade date.

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