6.6. APPENDIX: EUROCURRENCY FUTURES CONTRACTS 249
the two spot rates then gives us the link with the forward rate:
Vt,Tf 1 ,T 2 = Vt(1 +rt,T 1 )=1 +rt,T 1
1 +rt,T 2
, see [6.18],=
1
1 +rft,T 1 ,T 2, see [4.48]. (6.19)Example 6.16
Consider a six-month forward on a nine-month bill with face valueusd1. Let the
p.a. interest rates be 4 percent for nine months, and 3.9 percent for six months.
Thenrt,T 2 = (9/12)×4% = 0.03, so that the spot price (quoted as a percentage)
is equal to:
Vt=100%
1. 03
= 97.087%. (6.20)
Also,rt,T 1 = (6/12)×3.9% = 0.0195; thus, the forward price today is:
Vt,Tf 1 ,T 2 = 97. 087 × 1 .0195 = 98.981%. (6.21)Alternatively, we can compute the six-month forward price on a nine-month T-bill
via the forward rate of return:
1 +rft,T 1 ,T 2 =1. 03
1. 0195
= 1. 010 , 299 ⇒Vt,Tf 1 ,T 2 =1
1. 010 , 299
= 98,981%. (6.22)
For some time, interest rate futures markets in Sydney were based on this system
of forward prices forCDs. Although the system is perfectly logical, traders and
investors are not fond of quoting prices in this way. One reason is that traders
and dealers are more familiar withp.a. interest rates than with forward prices for
deposits orCDs. The process of translating the forward interest rate into a forward
price is somewhat laborious: Equation [6.19] tells us that the unfortunate trader
has to divide the per annum forward rate by four, add unity, and take the inverse
to compute the normal forward price as the basis for trading. A second problem is
that real-world interest rates are typically rounded to one basis point (0.01 percent).
Thus, unless forward prices are also rounded, marking to market will result in odd
amounts. These very practical considerations lead to a more user-friendly manner
of quoting prices for futures onCDs.
6.6.2 Modern Eurodollar Futures Quotes
To make life easier for the traders, rather than quoting a true futures price, most
exchanges quote three-month eurodollar futures contract prices as:
Quote = 100−[per annum forward interest rate], (6.23)