STAT 473 S24 Chapter 10 Quiz - Sample - Solutions

NAME: _____________________ STAT 473 Spring 2024 Chapter 10 Quiz – There is Trouble with the (Binomial) Trees Given: r = 0.02, δ = 0.04, ơ = 0.15, n = 3, T = 0.75 h = T /n = 0.75 / 3 = 0.25 u = e (r-δ)h + ơ*SRT(h) = e (0.02 - 0.04)*0.25 + 0.15*SQRT(0.25) = 1.0725 d = e (r-δ)h - ơ*SRT(h) = e (0.02 - 0.04)*0.25 - 0.15*SQRT(0.25) = 0.9231 u S = S * e (r-δ)h + ơ*SRT(h) = 50 * e (0.02 – 0.04)*0.25 + 0.15*SQRT(0.25) = 50 * 1.0725 = 53.6254 d S = S * e (r-δ)h - ơ*SRT(h) = 50 * e (0.02 – 0.04)*0.25 - 0.15*SQRT(0.25) = 50 * 0.9231 = 46.1558 uu S = u S * 1.0725 = 57.5317 ud S = du S = u S * 0.9231 = d S * 1.0725 = 49.5025 dd S = d S * 0.9231 = 42.6072 uuu S = uu S * 1.0725 = 61.6839 uud S = uu S * 0.9231 = 53.0918 udd S = ud S * 0.9231 = 45.6966 ddd S = dd S * 0.9231 = 39.3314 C u = Max(0, 53.6254 – 45.00) = 8.6254 C d = Max(0, 46.1558 – 45.00) = 1.1558 C uu = Max(0, 57.5137 – 45.00) = 12.5137 C ud = Max(0, 49.5025 – 45.00) = 4.5025 C dd = Max(0, 42.6072 – 45.00) = 0 C uuu = Max(0, 61.6839 – 45.00) = 16.6839 C uud = Max(0, 53.0918 – 45.00) = 8.0918 C udd = Max(0, 45.6966 – 45.00) = 0.6966 C ddd = Max(0, 39.3314 – 45.00) = 0 p* = e (0.02-0.04)*0.25 – 0.9231 = 0.48126 1.0725 - 0.9231 Option Value (57.5137) = e -0.02 * 0.25 * [ (16.6839 * 0.48126) + (8.0918 * 0.51874) ] = 12.1659 Option Value (49.5025) = e -0.02 * 0.25 * [ (8.0918 * 0.48126) + (0.6966 * 0.51874) ] = 4.2344 Option Value (42.6072) = e -0.02 * 0.25 * [ (0.6966 * 0.48126) + (0.000 * 0.51874) ] = 0.3336 Option Value (57.5137) = Max(12.5737, 12.1659) = 12.5737 (Amer: Use Exercise Value since Greater) Option Value (49.5025) = Max(4.5025, 4.2344) = 4.5025 (Amer: Use Exercise Value since Greater) Option Value (53.6254) = e -0.02 * 0.25 * [ (12.5737 * 0.48126) + (4.5025 * 0.51874) ] = 8.3163 Option Value (46.1558) = e -0.02 * 0.25 * [ (4.5025 * 0.48126) + (0.3336 * 0.51874) ] = 2.3282 Option Value (53.6254) = Max(8.6254, 8.3163) = 8.6254 (Amer: Use Exercise Value since Greater) Option Value (50.000) = e -0.02 * 0.25 * [ (8.6254 * 0.48126) + (2.3282 * 0.51874) ] = 5.3321