Question $6$

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Homework due Aug $1,202402$:$12$ CDT Question $6$

$0\mathrm{.}0/15\mathrm{.}0$ points $($graded$)$

Consider a swap contract. The floating leg of the contract makes a payment at the end of each month, starting one month from now, equal to the spot price of natural gas at that time. The last payment on the swap contract will be $3$ months from now. The fixed leg of the contract pays the same amount $$x$ at the end of each month. Current futures prices for natural gas are $F_1=$$$38\mathrm{.}9,F_2=$$$42\mathrm{.}2,F_3=$$$44\mathrm{.}5$ for the $1-,2-,$ and $3-$month contracts, respectively. Assume that the term structure of risk$-$free interest rates is flat, with the annual rate $($continuously compounded$)$ equal to $r_f=3\%.$

Compute the value of the fixed leg of the forward contract. $x=$

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