Future and Option

PROBLEM 1

Futures of Options

On January 4, 2012, an FI has following balance sheet (rates = 10 percent)

Asset Liabilities/Equity

A 200m DA = 6 years L 170m DL = 4 years

E 30m

DGAP = [6- (170/200)4] = 2.6 years > 0

The FI manager thinks rates will increase by 0.75 percent in the next three months. If this happens, the equity value will change by:

∆E = - [6 - 170200 (4)] 200m 0.00751.10 = -$3,545,455

The FI manager will hedge this interest rate risk with either futures contracts or option 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-bonds are selling at a price of 114-11 per $100,000m or $114,343.75. T-bond futures rates, currently 9 percent, are expected to increase by 1.25 percent over the next three months.

If the FI uses options, it will buy puts on 15-year T-bonds with a June maturity, an exercise price of 113, and an option premium of 1 3664 percent. The spot price on the T-bond underlying the option is 135 2332 percent. The duration on the T-bonds underlying the options is 14.5 years, and the delta of the put options is -0.75. Managers expect these T-bond rates to increase by 1.24 percent from 7.875 percent in the next three months.

If by April 4, 2012, balance sheet rates increase by 0.8 percent, futures rates by 1.4 percent, and T-bond rates underlying the option contract by 0.95%, would the FI have been better off using the futures contract or the option contract as its hedge instrument?

The first step is to calculate the future contract:

Basis risk (br) = ∆Rb1+ Rb∆R1+R* ∆ Rb = Changes of interest rate on the bond |

Basis risk (br) = 0.01251+0.090.0141+0.09

= 0.011470.01284

= 0.8929

* Given that the basis risk is 0.8929, number of future contract can be calculated:

Number of...