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?

Question

Quizplus · Accepted Answer

The investment company will lose $4,352,414 on the option position if interest rates decrease 1 percent to 9 percent. This is because the delta of the options is 0.7, which means that the value of the options will change by 70% of the change in the value of the underlying bond. The duration of the underlying bond is 8.82 years, which means that the value of the bond will change by 8.82% for a 1% change in interest rates. Therefore, the value of the options will change by 70% of 8.82%, or 6.174%. The market value of the underlying asset is $98,000 per $100,000 face value, so the value of the options will change by 6.174% of $98,000, or $6,034,328. Since the investment company has purchased $100 million of Eurobonds, the value of the options will change by $6,034,328 * $100 million/$98 million = $6,156,452. However, the investment company has also purchased $100 million of Eurobonds, so the net change in the value of the investment company's position will be $6,156,452 - $100 million = -$4,352,414.

An Investment Company Has Purchased $100 Million of 10 Percent