Consider the following table of prices of five-year semi-annual pay caps and floors: $$\begin{array} { | c | c | c | }
\hline \text { Strike (\%/) } & \text { Cap price } & \text { Floor price } \
\hline 4 \% & 2.50 & 0.50 \
\hline 5 \% & 1.50 & 1.50 \
\hline 6 \% / & 0.50 & 2.50 \
\hline
\end{array}$$ Assume that the caps and floors also include the first payment in 6 months, so there are 10 payment dates in each instrument. The quoted prices of the caps and floors includes this first payment for which the floating leg has already been set. What is the fixed-rate on a five-year fairly priced swap?
A) 4%
B) 5%
C) 6%
D) Not possible to determine from the available information.

Question

Consider the following table of prices of five-year semi-annual pay caps and floors: $$\begin{array} { | c | c | c | } 
\hline \text { Strike (\%/) } & \text { Cap price } & \text { Floor price } \
\hline 4 \% & 2.50 & 0.50 \
\hline 5 \% & 1.50 & 1.50 \
\hline 6 \% / & 0.50 & 2.50 \
\hline
\end{array}$$ Assume that the caps and floors also include the first payment in 6 months, so there are 10 payment dates in each instrument. The quoted prices of the caps and floors includes this first payment for which the floating leg has already been set. What is the fixed-rate on a five-year fairly priced swap?
A) 4%
B) 5%
C) 6%
D) Not possible to determine from the available information.

Quizplus · Accepted Answer

The fixed-rate on a fairly priced swap is the rate at which the cost of a cap equals the cost of a floor for the same strike. From the table, at a 5% strike, both the cap and the floor are priced at 1.50, indicating that this is the fixed rate for a fairly priced swap.

Consider the Following Table of Prices of Five-Year Semi-Annual Pay