Your bank entered into a standard floating$-$for$-$fixed interest rate swap $6-$months ago $($i$.$e$.$ the bank pays the floating and receives fixed$).$ There are two payments remaining that occur $6-$months and $1-$year from now. The fixed$-$rate on the swap is $3\mathrm{.}1\%,$ the floating rate is $6-$month SOFR $+0\mathrm{.}4\%,$ and the principle is $100$ million. The current forward curve for the $6-$month SOFR is $2\mathrm{.}6\%,3\mathrm{.}0\%,$ and $3\mathrm{.}2\%$ for $6-$months, $12$ months, and $18$ months, respectively. You can assume a constant risk$-$free rate of $1\mathrm{.}5\%.$ All rates are annualized. $(22$ points$)$

$($a$)$ Calculate the value of the swap to the bank today. $(6$ points$)$

$-$$$98140.$ Apply normal swap valuation $($see Lecture $3)$

$($b$)$ If in $6-$months $($immediately after the next payment$)$ the interest rate curve increase for the following six months to $3\mathrm{.}3\%,$ how much different would the value of the swap change, relative to what you expect it to be in $6-$months, today? Why? $(5$ points$)-$ Hint compare the value of the swap in $6-$months under the initial interest rate scenario to this updated scenario.

See lecture $3.$ The swap decreases by an additional $$148879.$ One less period of payment, updated discounting, and higher floating rate.

$($c$)$ Suppose the counterparty to the swap primarily has assets which are unrelated to interest rate fluctuations, and its liabilities consist of floating rate bonds. Given this information, explain how it affects your evaluation of the counterparty risk of the swap? $(5$ points$)$

See Lecture $10$ & $11.$ Likely should reduce risks, since they are hedging, when value of swap to bank goes up $($i$.$e$.,$ when rates are down$),$ the firm has lower liabilities, and vice versa, also might have thought they had wrong$-$way risk before.

$($d$)$ Another firm approaches your bank looking to enter into a fixed$-$for$-$floating swap with the same parameters as the original swap. This firm has a higher credit risk than your current counterparty and offers to pay SOFR$+0\mathrm{.}25\%.$ Explain what factors you need to consider before deciding to enter this swap and why? $(6$ points$)$

See Lecture $3$ & $10.$ The swap is paying a lower spread, despite being a higher credit risk. Need consider the value of this credit risk vs$.$ the value of facing interest rate risks. This is the question with the main answers, please show how they came to these conclusion, and this is a whole task with sidequestions please answer them