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Answer: $19.32
## Explanation **Given:** - S = $30 - σ = 22% = 0.22 - q = 1.0% = 0.01 (dividend yield) - r = 3.0% = 0.03 - T = 2 years - n = 2 steps - Δt = 1 year **Step 1: Calculate u and d** - u = e^(σ√Δt) = e^(0.22 × √1) = e^0.22 = 1.2461 - d = 1/u = 1/1.2461 = 0.8025 **Step 2: Build the binomial tree** The lowest stock price occurs after two consecutive down movements: - After first down: S × d = 30 × 0.8025 = $24.075 - After second down: S × d × d = 30 × 0.8025 × 0.8025 = 30 × 0.6440 = $19.32 Therefore, the stock price at the node with the lowest stock price is $19.32.
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A stock with a (continuous) dividend yield of 1.0% has a current price of $30 and volatility of 22%. We use a two-step binomial model to value a two-year European style call option on the stock; i.e., each time step is one year. The risk-free rate is 3.0%. In the binomial tree, what is the stock price at the node with the lowest stock price?
A
$14.78
B
$19.32
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