Exam 24: Options, Caps, Floors, and Collars

A bank purchases a 3-year, 6 percent $5 million cap (call options on interest rates), where payments are paid or received at the end of year 2 and 3 as shown below: End of Year: 0 1 2 3 Cash Flow at end of year: - - In addition to purchasing the cap, if the bank also purchases a 3-year 6 percent floor and interest rates are 5 percent and 7 percent in years 2 and 3, respectively, what are the payoffs to the bank? Specifically, the bank will

A hedge with futures contracts increases volatility in profit gains on both the upside and downside of interest rate movements, whereas in comparison, the hedge with the put option contract completely offsets the gains but only partially offsets the losses.

The profit on bond call options moves asymmetrically with interest rates.

Assume a binomial pricing model where there is an equal probability of interest rates increasing or decreasing 1 percent per year. What should be the price of a three-year 6 percent floor if the current (spot) rates are also 6 percent? The face value is $5,000,000, and time periods are zero, one, and two.

The Black-Scholes model does not work well to value bond options because of violations of the underlying assumption of a constant variance of returns on the underlying asset.

Most pure bond options trade on the over the counter markets as opposed to organized exchanges such as the Chicago Board Options Exchange.

For put options, the delta has a negative sign

Giving the purchaser the right to buy the underlying security at a prespecified price is a

Allright Insurance has total assets of $140 million consisting of $50 million in 2-year, 6 percent Treasury notes and $90 million in 10-year, 7.2 percent fixed-rate Baa bonds.These assets are funded by $100 million 5-year, 5 percent fixed rate GICs and equity. The duration of the T-notes, Baa bonds, and GICs is 1.93 years, 6.9 years, and 4.5 years respectively.What is the leverage-adjusted duration gap for Allright?

An FI manager purchases a zero-coupon bond that has two years to maturity.The manager paid $76.95 per $100 for the bond.The current yield on a one-year bond of equal risk is 12 percent, and the one-year rate in one year is expected to be either 16.65 percent or 15.35 percent.Either rate is equally probable. What is the yield to maturity for the two-year bond if held to maturity?

The preferred method of FIs when hedging interest rates is an option on interest rate futures rather than using a pure bond option.

An investment company has purchased $100 million of 10 percent annual coupon, 6-year Eurobonds.The bonds have a duration of 4.79 years at the current market yields of 10 percent.The company wishes to hedge these bonds with Treasury-bond options that have a delta of 0.7.The duration of the underlying asset is 8.82, and the market value of the underlying asset is $98,000 per $100,000 face value.Finally, the volatility of the interest rates on the underlying bond of the options and the Eurobond is 0.84. What is the net gain or loss to the investment company resulting from the change in rates given that the hedge was placed?

Contrast the marking to market characteristics of options versus futures contracts.

An FI manager purchases a zero-coupon bond that has two years to maturity.The manager paid $76.95 per $100 for the bond.The current yield on a one-year bond of equal risk is 12 percent, and the one-year rate in one year is expected to be either 16.65 percent or 15.35 percent.Either rate is equally probable. If the manager buys a one-year option with an exercise price equal to the expected price of the bond in one year, what will be the exercise price of the option?

The purchase often of a series of put options with multiple exercise dates results in a

The buyer of a bond put option

An option that does NOT identifiably hedge an underlying asset is a

An investment company has purchased $100 million of 10 percent annual coupon, 6-year Eurobonds.The bonds have a duration of 4.79 years at the current market yields of 10 percent.The company wishes to hedge these bonds with Treasury-bond options that have a delta of 0.7.The duration of the underlying asset is 8.82, and the market value of the underlying asset is $98,000 per $100,000 face value.Finally, the volatility of the interest rates on the underlying bond of the options and the Eurobond is 0.84. Using the above information, what will happen to the market value of the Eurobonds if market interest rates fall 1 percent to 9 percent?

An FI manager purchases a zero-coupon bond that has two years to maturity.The manager paid $76.95 per $100 for the bond.The current yield on a one-year bond of equal risk is 12 percent, and the one-year rate in one year is expected to be either 16.65 percent or 15.35 percent.Either rate is equally probable. Given the exercise price of the option, what premium should be paid for this option?

The purchaser of an option must pay the writer a