I give you a flat yield curve from 0 to 4 years: 2%. You have a five year swap contract that pays annually and want to use it to extend the curve to 5 years. How low can the swap par rate go before forward between 4 and 5 years goes negative?
To solve this problem, we need to understand how swap contracts work and how to calculate the swap par rate. Here's how you can approach this:
Step 1: Understand Swap Contracts
A swap contract is an agreement between two parties to exchange future cash flows based on different types of interest rates. In this case, you have a five-year swap contract that pays annually, meaning there will be five cash flow exchanges between the two parties over the contract period.
Step 2: Calculate the Swap Par Rate
The swap par rate is the fixed interest rate at which the two parties would have a net present value of zero for the swap contract. It is determined by equalizing the present value of the fixed-rate cash flows with the present value of the floating-rate cash flows.
In this scenario, since the flat yield curve from 0 to 4 years is 2%, it means that the risk-free interest rate is 2% for all maturities between 0 and 4 years.
Step 3: Calculate the Forward Rate from 4 to 5 years
To determine the swap par rate that would make the forward rate between 4 and 5 years negative, we need to calculate the forward rate first. The forward rate is the implied interest rate for a specific period in the future, based on the current yield curve.
Given that the yield curve is flat at 2% for all maturities between 0 and 4 years, the forward rate from 4 to 5 years would also be 2%.
Step 4: Determine the Lowest Swap Par Rate
To make the forward rate between 4 and 5 years negative, the swap par rate would need to be lower than 2%. Therefore, the lowest swap par rate that would achieve this is anything below 2%.
In conclusion, the swap par rate can go as low as anything below 2% to make the forward rate between 4 and 5 years negative.