Problem$-$Solving Assignment $7$:

Hedging Interest Rate Risk with Futures versus Options versus Swaps

On January $4,2018,$ an FI has the following balance sheet $($rates $=8$ percent$)$

Assets Liabilities$/$Equity

A $450$m DA $=8$ years L $396$m DL $=4$ years

E $54$m

Duration Gap $=[8(396/450)4]=4\mathrm{.}48$ years $>0$

The FI manager thinks rates will increase by $0\mathrm{.}55$ percent in the next three months. If this happens, the equity value will change by:

The FI manager will hedge this interest rate risk with either futures contracts, option contracts, or swap contracts.

If the FI uses futures, it will select June T$-$bonds to hedge. The duration on the T$-$bonds underlying the contract is $14\mathrm{.}5$ years and the T$-$bond futures are selling at a price of $$110\mathrm{.}53125$ per $$100,$ or $$110,531\mathrm{.}25.$ T$-$bond futures rates, currently $5$ percent, are expected to increase by $0\mathrm{.}75$ percent over the next three months.

If the FI uses options, it will buy puts on $15-$year T$-$bonds futures with a June maturity, an exercise price of $109,$ and an option premium of percent. The spot price on the T$-$bond underlying the option is $$115\mathrm{.}78125$ per $$100$ of face value. The duration on the T$-$bonds underlying the options is $14\mathrm{.}5$ years and the delta of the put options is $-0\mathrm{.}85.$ Managers expect these T$-$bond rates to increase by $0\mathrm{.}7$ percent from $5\mathrm{.}25$ percent in the next three months.

If the FI uses swaps, a swap agent offers a swap involving DFixed $=8$ years $($based on the $15-$year Treasury bond rate$)$ and DFloating $=1$ year $($based on Treasury bills$).$

If by April $4,2018,$ balance sheet rates increase by $0\mathrm{.}5$ percent, futures rates by $0\mathrm{.}7$ percent, and T$-$bond rates underlying the option contracts by $0\mathrm{.}66$ percent, calculate the on$-$ and off$-$balance$-$sheet cash flows to the FI when using futures contracts, option contracts, and swap contracts as its hedge instrument. Which alternative is the best?