Ms. Jeff,  newly recruited staff member of your team at Royal Investments Inc.comes and seeks your help on option pricing using the Binomial Tree method.  She provides you with the following information: the current market price of stock is $110.00, its annualized return volatility is 0.3810, the annually compounded risk-free rate is 0.0582, the option is a European option with an exercise price of $108 and a time to maturity of 125 days. Jeff would like you to use a two-step binomial tree to show her the following:

(1) The periodic risk-free rate (a), the up factor (u), the down factor and the probability of price increase (p). 

(2) Construct trees by estimating stock prices, call option prices and hedge ratios for each node of the trees using a two-period binomial pricing model. 

(3) Also estimate put option prices and its hedge ratios for each node of the trees using a two-period binomial pricing model.