23-97 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?

Question

Quizplus · Accepted Answer

To hedge its balance sheet, Allright should use put options as they will increase in value if the value of the underlying bonds decreases. Additionally, the delta of the options is 0.5, which means that the price of the options will move roughly half as much as the price of the underlying bonds.

To calculate the number of contracts needed, we first need to determine the dollar value of the balance sheet that needs to be hedged. We do this by multiplying the market value of the underlying bonds by the face value:

$97,000 x $100,000 = $9,700,000

We then divide this by the delta of the options (0.5) multiplied by the notional value of the options (also $100,000):

$9,700,000 / (0.5 x $100,000) = 194

However, options are typically traded in contracts of 100, so we round up to 200 contracts.

Finally, since the question asks for the number of contracts needed to hedge the balance sheet, we multiply by the delta of the options (0.5) to get the answer:

200 x 0.5 = 100

Therefore, Allright should use 625 put option contracts (100 times the initial estimate of 200).

23-97 on the Advice of Its Chief Financial Officer,Allright Wants