Mathematical Finance Problem: Binomial Trees and Security Pricing Modeling

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5.14. Consider a nondividend-paying stock with a current price of $45, an instantaneous annual expected return of 8%, and annual volatility of 15%. Assume an 80-period CRR tree. a) Can the stock price be at the same value 3 months from now? If so, how many times would the price have to increase and decrease for this to happen? b) What is the probability that the stock price will be at the same value 3 months? c) What is the probability that in 3 months the stock price is greater than its current price? 5.14. Consider a nondividend-paying stock with a current price of $45, an instantaneous annual expected return of 8%, and annual volatility of 15%. Assume an 80-period CRR tree. a) Can the stock price be at the same value 3 months from now? If so, how many times would the price have to increase and decrease for this to happen? b) What is the probability that the stock price will be at the same value 3 months? c) What is the probability that in 3 months the stock price is greater than its current price