# THE INSTRUMENTS AVAILABLE FOR CURVE CONSTRUCTION

The number of different fixed-income instruments one can trade in the market is enormous; however, allowing for variations on common characteristics, one can attempt to give a fairly complete picture. We will do so going from the simplest to the most complex instruments.

## Discount Bonds and Cash Deposits

Discount bonds are the simplest of all instruments and do not need any calculation when used for constructing a curve. As shown in the previous example, these instruments offer a unit of principal at some future time: the bond price is the discount factor itself. Discount bonds are usually available in developed markets and for very short maturities (around three months). In Figure 2.1 we see an example of quotes of U.S. Treasury debt with the quotes for discount notes highlighted (boxed). The quote is given as the difference between 100 and the note's price. For example, we see that for the note expiring on March 21, 2013, the mid quote (the mid quote is obtained by average the bid quote and the offer quote) is 0.06, meaning that the discount factor for that maturity is 0.9994.

The market information given by a cash deposit is the rate *r* at which a cash deposit will grow from today up to time T. If we know that a unit of cash will grow, assuming linear compounding, to 1 + *rT* in a period of time

**FIGURE 2.1 **Quotes for U.S. Treasury notes as of March 1, 20f3, with a few discount notes highlighted. *Source:* Thomson Reuters Eikon.

T, it must be that a unit of cash at time *T* that has grown at rate *r* must now be worth

(2.2)

our discount factor.^{[1]} Cash deposits are available in all markets and are available only for short maturities (less than one year). In Figure 2.2 we see an example of quotes of deposits in Canadian Dollars.

**FIGURE 2.2 **Quotes for Canadian Dollar cash deposits as of February 27, 2013. *Source:* Thomson Reuters Eikon.

- [1] We remind the reader of the possible type of relations, depending on the compounding chosen, between a rate
*r*T and the corresponding discount factor*D*T. With linear compounding we have with annual compounding we have and with continuous compounding For short maturities the three values would be virtually identical.