Answer: $19.32

## Explanation To calculate the stock price at the lowest node in a two-step binomial tree, we need to determine the down factor and apply it twice. ### Step 1: Calculate the up and down factors For a binomial tree with continuous dividend yield, the formulas are: - **Up factor (u)**: \(u = e^{\sigma\sqrt{\Delta t}}\) - **Down factor (d)**: \(d = \frac{1}{u}\) Where: - \(\sigma = 22\% = 0.22\) (volatility) - \(\Delta t = 1\) year (time step) \[u = e^{0.22 \times \sqrt{1}} = e^{0.22} \approx 1.2461\] \[d = \frac{1}{1.2461} \approx 0.8025\] ### Step 2: Calculate the lowest stock price Starting price: $30 Lowest node occurs after two down moves: \[S_{dd} = S_0 \times d \times d = 30 \times 0.8025 \times 0.8025\] \[S_{dd} = 30 \times (0.8025)^2 = 30 \times 0.6440 \approx 19.32\] Therefore, the stock price at the lowest node is **$19.32**. **Note**: The risk-free rate (3.0%) and dividend yield (1.0%) are not needed for calculating the stock prices in the binomial tree - they are used for calculating risk-neutral probabilities, but the tree structure itself depends only on volatility and time step.

Author: LeetQuiz .