Draw the tree for a put 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 put option on $20,000 with a strike price of £10,000 would be as follows:

$40,000
                            /        \
                   £20,000          £5,000
                     /   \          /   \
              $0     $20,000   $10,000   $0

At each node, we calculate the value of the put option as the maximum of 0 and the difference between the strike price (£10,000) and the dollar value of the pound at that node, converted to dollars using the current exchange rate (£1.00 = $2.00) and discounted back to the present using the relevant interest rates.

For example, at the £20,000 node, the dollar value of the pound could be either $40,000 (if it doubles) or $10,000 (if it is cut in half). Assuming no arbitrage opportunities, the put option would be exercised in the second case, giving a value of $10,000 - £10,000/$2.00 = $5,000. Discounting this back to the present using the interest rates, we get:

$5,000/(1 + 3%) = $4,854.37

Similarly, at the £5,000 node, the put option would be exercised, giving a value of $20,000 - £10,000/$0.50 = $0. Discounting this back to the present, we get:

$0/(1 + 2%) = $0

Therefore, the value of the put option today would be the expected value of the option at the root node, taking into account the probabilities of the different outcomes:

($4,854.37 + $0)/2 = $2,427.19

This means that the put option is worth $2,427.19 today, and the best choice is B.

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