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)None of the above

Question

Quizplus · Accepted Answer

A put option gives the holder the right to sell the underlying asset (in this case $20,000) at a specified price (the strike price) in the future. If the exchange rate remains the same or increases, the option would not be exercised, as the holder would be able to sell the dollars for more than the strike price. If the exchange rate decreases, the holder would exercise the option, as they can sell the dollars for more than the new exchange rate.

At the starting node, the dollar value of the pound could either double or be cut in half. We branch off accordingly, and calculate the dollar value of the pound at each resulting node.

At the two ending nodes, we calculate the profit from the put option by subtracting the strike price from the dollar value of the pound at each node.

To calculate the option value at each node, we take the maximum of 0 and the profit at that node (since the holder would not exercise the option if the profit is negative). We then discount this option value back to the starting node using the appropriate interest rates.

At the starting node, we take the expected value of the option by weighting the option values at each branch by their respective probabilities (0.5 for both branches). This gives us the final option value of $3,236.21.

Therefore, the best choice is B since it correctly shows the calculations and outcomes for each node.

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