Exam 23: Options, Caps, Floors, and Collars

Buying a cap is like buying insurance against a decrease in interest rates.

Banks that are more exposed to rising interest rates than falling interest rates may seek to finance a cap by selling a floor.

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 cap if the current (spot) rates are also 6 percent? The face value is $5,000,000, and time periods are zero, one, and two.

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. -On the advice of its chief financial officer, Allright wants to hedge the balance sheet with T-bond option contracts. The underlying bonds currently have a duration of 8.82 years and a market value of $97,000 per $100,000 face value. Further, the delta of the options is 0.5. What type of contract, and how many contracts should Allright use to hedge this balance sheet?

Which of the following holds true for the writer of a bond call option if interest rates decrease?

Simultaneously buying a bond and a put option on a bond produces the same payoff as buying a call option on a bond.

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 exercise price of the option, what premium should be paid for this option?

An FI concerned that the risk on a loan will increase can

Identify a problem associated with using the Black-Scholes model to value bond options.

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?

An FI would normally purchase a cap if it was funding fixed-rate assets with variable-rate liabilities.

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

A hedge with a futures contract reduces volatility in payoff gains on both the upside and downside of interest rate movements.

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. -Market interest rates are expected to increase 1 percent to 11 percent in the next year. If this occurs, what will be the effect on the market value of equity of Allright?

A digital default option pays a stated amount in the event that a portion of the loan is not paid.

A hedge using a put option contract completely offsets gains but only but only partially offsets losses on an FIs balance sheet.

An option's delta has a value between 0 and 100.

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?

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?

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 £. -How many options should the FI purchase, and what will be the cost?