You wish to establish the theoretical futures price on a Euribor contract quoted on the London International Financial Futures Exchange (LIFFE) in London. The futures contract is for a 90-day Euribor rate at expiration of the futures contract. You look at the current term structure of Euribor interest rates. Following the standard conventions for short-term rates, all interest rates are quoted as annualized linear rates. In other words, the interest paid for a maturity of T days is equal to the annualized rate quoted, divided by 360 and multiplied by T. The observed rates are as follows:
$$\begin{array} { l l l l l }
\hline & \text { 60-Day } & 90 - D \pi & 150 - D a y & 180 - D a \% \
\hline \text { Euribar Rate } & 4.125 \% & 4.250 \% & 4.500 \% & 4.550 \% \
\hline
\end{array}$$ a. What should be the Euribor futures price quoted today with an expiration date in exactly
90 days?
b. What should be the Euribor futures price quoted today with an expiration date in exactly
60 days?

Question

You wish to establish the theoretical futures price on a Euribor contract quoted on the London International Financial Futures Exchange (LIFFE) in London. The futures contract is for a 90-day Euribor rate at expiration of the futures contract. You look at the current term structure of Euribor interest rates. Following the standard conventions for short-term rates, all interest rates are quoted as annualized linear rates. In other words, the interest paid for a maturity of T days is equal to the annualized rate quoted, divided by 360 and multiplied by T. The observed rates are as follows:
 $$\begin{array} { l l l l l } 
\hline & \text { 60-Day } & 90 - D \pi & 150 - D a y & 180 - D a \% \
\hline \text { Euribar Rate } & 4.125 \% & 4.250 \% & 4.500 \% & 4.550 \% \
\hline
\end{array}$$ a. What should be the Euribor futures price quoted today with an expiration date in exactly
90 days?
b. What should be the Euribor futures price quoted today with an expiration date in exactly
60 days?

Quizplus · Accepted Answer

The Answer is a. This futures contract is for a 90-day bill issued in 90 days and maturing in 180 days. The annualized forward interest rate r_F is given by:

1 + \frac { r _ { F } } { 4 } = \frac { 1 + 4.55 \% \frac { 100 } { 360 } } { 1 + 4.25 \% \frac { 90 } { 360 } } = 1.011998

r_F =4.80%
F=100% - 4.80% = 95.20%.
b. This futures contract is for a 90-day bill issued in 60 days and maturing in 150 days. The annualized forward interest rate r_F is given by:

1 + \frac { r _ { F } } { 4 } = \frac { 1 + 4.5 \% \frac { 150 } { 30 } } { 1 + 4.125 \% \frac { 60 } { 300 } } imes 1.011794

r_F = 4.72%
F = 100% - 4.72% = 95.28%.

You Wish to Establish the Theoretical Futures Price on a Euribor