Exam 23: Options, Caps, Floors, and Collars

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?

A bond call option gives the holder the right to sell the underlying bond at a pre-specified exercise price.

The gain to a buyer of bond call options is unlimited, even if interest rates decrease to zero.

An FI manager purchases a zero-coupon bond that has two years to maturity. The manager paid $826.45 per $1,000 for the bond. The current yield on a one-year bond of equal risk is 9 percent, and the one-year rate in one year is expected to be either 11.60 percent or 10.40 percent. Either rate is equally probable. Given the expected one-year rates in one year, what are the possible bond prices in one year?

The gain to the writer of a bond option is unlimited.

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

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. If rates increase 1 percent, what will be the change in value of the option position?

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?

Buying a call option on a bond ensures a bank that it will be able to sell the bond at a given point in time for a price at least equal to the exercise price of the option.

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. At the time of placement, the premium on the options are quoted at 1¾. What is the cost to Allright in placing the hedge?

The combination of being long in the bond and buying a put option on a bond mimics the profit function of

Most bond options trade on the over the counter markets as opposed to organized exchanges such as the Montreal Exchange.

The buyer of a bond call 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. Using the above information and your answer to the previous question, will the investment company gain or lose on the option position if interest rates decrease 1 percent to 9 percent?

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: In addition to purchasing the cap, if the bank also sells 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

Managing interest rate risk for less creditworthy FI's by running a cap/floor book may require the backing of external guarantees such as standby letters of credit because of the nature of the options.

An FI manager purchases a zero-coupon bond that has two years to maturity. The manager paid $826.45 per $1,000 for the bond. The current yield on a one-year bond of equal risk is 9 percent, and the one-year rate in one year is expected to be either 11.60 percent or 10.40 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?

In April 2012, an FI bought a one-month sterling T-bill paying £100 million in May 2012. The FI's liabilities are in dollars, and current exchange rate is $1.6401/£1. The bank can buy one-month options on sterling at an exercise price of $1.60/£1. Each contract has a size of £31,250, and the contracts currently have a premium of $0.014 per £. Alternatively, options on foreign currency futures contracts, which have a size of £62,500, are available for $0.0106 per £. What is the foreign exchange risk that the FI is facing, and what type of currency option should be purchased to hedge this risk?

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: Assume interest rates are 5 percent in year 2 and 7 percent in year 3. Which of the following is true?