Exercise 1.2 Swaps Assume the risk-free rates and discount curve calculated in HW 1 Exercise 1a (Piecewise constant). ( LOOK AT IMAGE ))

You have a swap with the following characteristics: Receive 3% fixed and pay float Fixed and Float pay semi-annual 10-year maturity Notional is $1,000,000 For the swap above, What is the value of the swap? What is the swaps Duration? What is the swaps convexity? What 10-year zero-coupon bond position is needed to duration hedge the swap? What is the mismatch in one-year if interest rates follow the forward curve? What is the par swap rate? What is the par forward starting swap rate for a swap starting in 5 years for 10-years (5x10)?

\begin{tabular}{|r|r|r|} \hline \multicolumn{3}{|c|}{ Optimization Parameters } \\ \hline 1 & Forward Const & Linear \\ \hline 2 & 2.73% & 2.75% \\ \hline 3 & 3.23% & 3.00% \\ \hline 5 & 3.74% & 3.25% \\ \hline 7 & 3.61% & 3.40% \\ \hline 10 & 3.00% & 3.30% \\ \hline 20 & 2.91% & 3.20% \\ \hline 30 & 2.94% & 3.10% \\ \hline 2.67% & 3.00% \\ \hline \end{tabular} \begin{tabular}{|r|r|r|} \hline \multicolumn{3}{|c|}{ Optimization Parameters } \\ \hline 1 & Forward Const & Linear \\ \hline 2 & 2.73% & 2.75% \\ \hline 3 & 3.23% & 3.00% \\ \hline 5 & 3.74% & 3.25% \\ \hline 7 & 3.61% & 3.40% \\ \hline 10 & 3.00% & 3.30% \\ \hline 20 & 2.91% & 3.20% \\ \hline 30 & 2.94% & 3.10% \\ \hline 2.67% & 3.00% \\ \hline \end{tabular}