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)None of the above

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Quizplus · Accepted Answer

The tree for the call option: $40,000 / \ $20,000 $20,000 / \ / \ $10,000 $10,000 $10,000 $10,000 Using the current exchange rate, the strike price is £5,000. In the up state, the exchange rate is £1.00 = $4.00, making the option worth $20,000, and in the down state, the exchange rate is £1.00 = $1.00, making the option worthless. To calculate the risk-neutral probabilities, we use the following formulas: p = (1 + i_$ - d_$ - 1/RF) / (u_$ - d_$) q = 1 - p where i_$ is the dollar interest rate, u_$ is the up-state factor for the dollar, d_$ is the down-state factor for the dollar, and RF is the risk-free factor. In this case, we have: u_$ = 2 d_$ = 0.5 i_$ = 0.03 RF = 1.02 Plugging in the numbers, we get: p = 0.538 q = 0.462 Therefore, the value of the call option today is: V0 = (0.538 * $20,000) + (0.462 * 0) / 1.02 = $10,494.12 Option B is the best choice because it correctly represents the outcomes of the option at the end of the period and uses the correct risk-neutral probabilities to calculate the value of the option today.

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