Draw the tree for a call option on $20,000 with a strike price of £10,000.The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half.The current interest rates are i_$ = 3% and are i_£ = 2%. C)both of the options D)none of the options

Question

Quizplus · Accepted Answer

The tree for the call option would look like this:

$40,000
                                          /         \
                                       $20,000    $10,000

If the exchange rate doubles (i.e. £1.00 = $4.00), the option would be worth:

Max($40,000 - £10,000/4.00,0) = Max($37,500,0) = $37,500

If the exchange rate is cut in half (i.e. £1.00 = $1.00), the option would be worth:

Max($20,000 - £10,000/1.00,0) = Max($10,000,0) = $10,000

Using this tree, we can calculate the expected value of the call option:

Expected value = ($37,500 x 0.5) + ($10,000 x 0.5) = $23,750

To determine whether the option is worth purchasing or not, we compare the expected value to the price of the option. Assuming that the price of the option is less than $23,750, then it would be a good choice to purchase the call option.

Therefore, Option B is the best choice as it accurately shows the expected value of the call option.

Draw the Tree for a Call Option on $20,000 with a Strike