Calculate 12x18 Month Forward Rate Agreement Using Zero Spot Rates
How to calculate the rate for a 12x18 month forward rate agreement based on continuously compounded zero spot rates?
Two banks want to trade a 12x18 month forward rate agreement with the following continuously compounded zero spot rates: 6 months: 5%, one year: 5.2%, 18 months: 5.5%, and two years: 5.4%. What rate will the agreement be?
Calculation of 12x18 Month Forward Rate Agreement Using Zero Spot Rates
The rate for the 12x18 month forward rate agreement can be calculated using the continuously compounded zero spot rates provided. Convert the rates into semi-annual rates since the agreement is for 12x18 months:
- For 6 months: 5% compounded semi-annually.
- For 1 year: 5.2% compounded semi-annually.
- For 18 months: 5.5% compounded semi-annually.
- For 2 years: 5.4% compounded semi-annually.
Step-by-Step Calculation:
1. Calculate the semi-annual zero spot rates for the relevant time periods:
- For 12 months: (1 + 5.2%)^(1/2) - 1
- For 18 months: (1 + 5.5%)^(1/2) - 1
2. Calculate the forward rate agreement rate using the semi-annual zero spot rates:
- The rate for the 12x18 month forward rate agreement is [(1 + 5.5%)^(1/2)] / [(1 + 5.2%)^(1/2)] - 1
Therefore, the rate for the 12x18 month forward rate agreement, based on the continuously compounded zero spot rates given, is [(1 + 5.5%)^(1/2)] / [(1 + 5.2%)^(1/2)] - 1.
When trading a 12x18 month forward rate agreement, understanding how to calculate the rate based on continuously compounded zero spot rates is crucial. By converting the rates into semi-annual rates and following the step-by-step calculation process, you can determine the rate accurately.
It's important to note that the calculation involves compounding rates over different time periods and then deriving the forward rate agreement rate using these rates. This process ensures that both banks involved in the agreement are on the same page regarding the agreed-upon rate for the specified duration.
By mastering the calculation of forward rate agreements, financial institutions can manage their interest rate risk effectively and make informed decisions when entering into such agreements. The ability to analyze and calculate rates based on zero spot rates is a valuable skill in the world of finance and helps ensure the smooth execution of financial transactions.