You have written a call option on £10,000 with a strike price of $20,000. The current exchange rate is $2.00/£1.00 and in the next period the exchange rate can increase to $4.00/£1.00 or decrease to $1.00/€1.00 . The current interest rates are i_$ = 3% and are i_£ = 2%. Find the hedge ratio and use it to create a position in the underlying asset that will hedge your option position. A)Buy £10,000 today at $2.00/£1.00 B)Enter into a short position in a futures contract on £6,666.67 C)Lend the present value of £6,666.67 today at i_£ = 2% D)Enter into a long position in a futures contract on £6,666.67 E)Both c and d would work F) None of the above

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Quizplus · Accepted Answer

To find the hedge ratio, we can use the formula: Hedge Ratio = Value of Option / Value of Underlying Asset Value of Option = Max(0, $20,000 - £10,000*Current Exchange Rate) If the exchange rate increases to $4.00/£1.00, then the option value will be 0 as the strike price is higher than the current exchange rate. If the exchange rate decreases to $1.00/£1.00, then the option value will be $10,000 as the strike price is lower than the current exchange rate. Therefore, the expected value of the option is: Expected Value of Option = (0.5 * 0) + (0.5 * $10,000) = $5,000 Value of Underlying Asset = £10,000 * Current Exchange Rate If the exchange rate increases to $4.00/£1.00, then the value of the underlying asset will be £10,000 * $4.00/£1.00 = $40,000. If the exchange rate decreases to $1.00/£1.00, then the value of the underlying asset will be £10,000 * $1.00/£1.00 = $10,000. Therefore, the expected value of the underlying asset is: Expected Value of Underlying Asset = (0.5 * $40,000) + (0.5 * $10,000) = $25,000 Hedge Ratio = $5,000 / $25,000 = 0.2 This means that for every £1, we need to hedge with 0.2 units of the underlying asset. To create a position in the underlying asset that will hedge our option position, we can use a combination of options, futures, and spot transactions. One possible strategy is: 1. Buy £10,000 today at $2.00/£1.00 2. Enter into a short position in a futures contract on £6,666.67 3. Lend the present value of £6,666.67 today at i_£ = 2% 4. Enter into a long position in a futures contract on £6,666.67 Step 1 allows us to acquire the underlying asset at the current exchange rate. Steps 2 and 4 involve futures contracts that will allow us to sell and buy the underlying asset at a future date and price, effectively locking in the current exchange rate. Step 3 involves lending money at the current interest rate to generate some income that will offset the cost of the futures contracts. This strategy will effectively hedge our option position and eliminate the risk of exchange rate fluctuations.

You Have Written a Call Option on £10,000 with a Strike