Question

# An investor has the following information about a zero-coupon bond curve: Years to maturity 1 2...

An investor has the following information about a zero-coupon bond curve: Years to maturity 1 2 3 4 Spot rates 3.23% 3.65% 4.05% 4.30% The investor enters into a 4-year interest rate swap to pay a fixed rate and receive a floating rate based on future 1-year LIBOR rates. If the swap has annual payments, what is the fixed rate you should pay? Six months into the swap the term structure is now: Years to maturity 0.5 1.5 2.5 3.5 Spot rates 3.44% 3.92% 4.20% 4.50% What is the value of the swap at this time?

First we need to calculate Swap Fixed rate we need to pay. This swap rate is calculated using discount factors obtained from the LIBOR Spot Curve. Once we calculate the swap fixed rate at t=0, the swap fixed rate is compared to the swap fixed rate six months in to the Swap term to find out the value of the swap at t= 0.5 (6 months). The working for the same is shown in the image

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