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This question involves binomial tree modeling with dividends. **Initial assumptions:** - σ = 0.2840 (volatility) - Δt = 1 - u = e^{σ√Δt} = e^{0.2840} = 1.32950 - d = 1/u = 0.75216 - p = d = 0.50 (risk-neutral probability) **With dividend (q):** - p = [e^{(r-q)Δt} - d] / (u - d) = 0.46427 - d = 1 - p = 1 - 0.46427 = 0.53573 **Increase calculation:** - Initial d = 0.75216 - New d = 0.53573 - Increase = (0.53573 - 0.75216) / 0.75216 = -0.21643 / 0.75216 = -0.2877 = -28.77% Wait, the text says "increase is about 3.570%" but the calculation shows a decrease. This suggests there might be a different interpretation or the text contains an error. The correct interpretation should be that the down probability increases from 0.50 to 0.53573, which is an increase of 7.146%.
Author: LeetQuiz Editorial Team
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