On January 4, 2018, an FI has the following balance sheet (rates = 8 percent)
Assets Liabilities/Equity
A 450m DA = 8 years L 396m DL = 4 years
E 54m
Duration Gap = [8 – (396/450)4] = 4.48 years > 0
The FI manager thinks rates will increase by 0.55 percent in the next three months. If this
happens, the equity value will change by:
đťš«E=-[8-0.88(4)]450m*.00509259=-$10,266,667
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 14.5 years and the T-bond futures are selling at a price of $110.53125
per $100, or $110,531.25. T-bond futures rates, currently 5 percent, are expected to increase
by 0.75 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 64
36 percent. The spot price on the T-bond
underlying the option is $115.78125 per $100 of face value. The duration on the T-bonds
underlying the options is 14.5 years and the delta of the put options is -0.85. Managers expect
these T-bond rates to increase by 0.7 percent from 5.25 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 0.5 percent, futures rates by 0.7 percent, and
T-bond rates underlying the option contracts by 0.66 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?