$1.$ Consider a swap where one party receives six$-$month LIBOR, pay $3\%($s$.$a$.$ compounding$)$ on a principal of $$100$ million, remaining life is $1\mathrm{.}25$ years, LIBOR zero rates for $3-$months, $9-$months and $15-$months are $2\mathrm{.}8\%,3\mathrm{.}2\%,$ and $3\mathrm{.}4\%($cont comp$)$ and $6-$month LIBOR on last payment date was $2\mathrm{.}9\%($s$.$a$.$ compounding$).$ What is the value of the swap?

$2.$ Consider a share of stock currently priced at $$30.$ The size of the possible price changes, and the probabilities of these changes occurring, are as follows:

Size of the up move: $1\mathrm{.}333,$ probability of up move: $55\%.$ Calculate the value of the PUT option on the stock with an exercise price of $$30.$