Answer-first summary for fast verification
Answer: $5.95.
Using the single-period binomial model: **Step 1: Calculate stock prices at expiration** - Up state: $50 × 1.25 = $62.50 - Down state: $50 × 0.85 = $42.50 **Step 2: Calculate option payoffs at expiration** - Up state payoff: max($62.50 - $50, 0) = $12.50 - Down state payoff: max($42.50 - $50, 0) = $0 **Step 3: Calculate risk-neutral probability** Risk-free rate = 5% = 0.05 Risk-neutral probability (p) = (1 + r - d) / (u - d) = (1.05 - 0.85) / (1.25 - 0.85) = 0.20 / 0.40 = 0.50 **Step 4: Calculate expected payoff and present value** Expected payoff = (0.50 × $12.50) + (0.50 × $0) = $6.25 Present value = $6.25 / (1.05) = $5.95 Therefore, the call option value is $5.95.
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Stock price: $50.00
Periodically compounded 1-year risk-free interest rate: 5.00%
Total return when an up move occurs (1 + return): 1.25
Total return when a down move occurs (1 + return): 0.85
Using a single-period binomial option valuation model and a strike price of $50.00, the value of a 1-year call option on the stock is closest to:
A
$5.95.
B
$6.25.
C
$6.56.
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