Currently, shares of ABC trade at 100. The monthly risk nuetral probability of shares going by 10 is 30%, and the probability of share declining by 10 is 70%. what is the mean and standard deviation of the price after 2 months if the price changes of consecutive months are independent ? Mean Standard Deviation a) 70, 11.32 b) 70, 12.96 c) 92, 11.32 d) 92, 12.36
Up, up: price = 100 + 10 + 10 = 120, probability = 30% × 30% = 9%
Up, down: price = 100 + 10 – 10 = 100, probability = 30% × 70% = 21%
Down, up: price = 100 – 10 + 10 = 100, probability = 70% × 30% = 21%
Down, down: price = 100 – 10 – 10 = 80, probability = 70% × 70% = 49%
μ = 9%(120) + 21%(100) + 21%(100) + 49%(80) = 92
σ² = 9%(120 – 92)² + 21%(100 – 92)² + 21%(100 – 92)² + 49%(80 – 92)² = 168
σ = √168 = 12.96.
I assume that the answer’s d) and that there’s a typo.
Its a typo. Thanks Magician
You’re welcome.