Explanation:
To find the no-arbitrage price of the option using the one-step binomial model, we must first calculate the risk-neutral probability of an up move.
Given parameters:
$47$47 + $8 = $55$47 - $8 = $39$45First, calculate the payoff of the put option in up and down states:
Next, calculate the risk-neutral probability (p) of an up move: p = (S0 * e^(r*T) - Sd) / (Su - Sd) = (47 * e^(0.021 * 1) - 39) / (55 - 39) = (47 * 1.02122 - 39) / 16 = (47.9974 - 39) / 16 = 8.9974 / 16 ≈ 0.5623
The risk-neutral probability of a down move is (1 - p) = 1 - 0.5623 = 0.4377.
Finally, calculate the present value of the expected option payoff: Put Price = e^(-r*T) * [p * Pu + (1 - p) * Pd] = e^(-0.021) * [0.5623 * 0 + 0.4377 * 6] = 0.9792 * 2.6262 ≈ 2.5716
The correct price is approximately $2.57, which corresponds to choice B.
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Q.56 Frank Ort is a junior trader at the options trading desk of an investment bank. He is reviewing a recent analysis of Tempo Construction LLC. Stocks of Tempo are currently trading at $47. According to the bank’s analysts, the price of the stock will either go up or down by $8 in one year depending on the revenues that the company will generate. Since Ort is quite pessimistic on the future development of the company, he is thinking about opening a short position by buying put options on Tempo’s stocks with a strike price of $45. The risk-free rate is assumed to be 2.1% per year. What is the no-arbitrage price of the option that Ort is looking to buy?
A
$2.55
B
$2.57
C
$2.77
D
$2.97
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