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. Given this information, what type of T-bond option, and how many options should be purchased, to hedge this investment?

Question

Quizplus · Accepted Answer

First, we need to calculate the duration of the bonds that we want to hedge:
Duration of Eurobonds = 4.79 years
Duration of Treasury bond = 8.82 years

Next, we need to calculate the value of the Eurobonds:
Value of Eurobonds = $100 million

Then, we need to calculate the value of the Treasury bond options that we need to purchase:
Value of Treasury bond options = Value of Eurobonds x (Duration of Eurobonds / Duration of Treasury bond) x Delta
Value of Treasury bond options = $100 million x (4.79 / 8.82) x 0.7
Value of Treasury bond options = $42.84 million

Now, we need to calculate the number of Treasury bond options to purchase:
Number of Treasury bond options = Value of Treasury bond options / (Underlying asset value x 0.01 x Volatility)
Number of Treasury bond options = $42.84 million / ($98,000 x 0.01 x 0.84)
Number of Treasury bond options = 941.89

Since we can only purchase a whole number of options, we should round up to 942 put options.

Therefore, the best choice is C, 942 put options.

An Investment Company Has Purchased $100 Million of 10 Percent