1.A stock price is currently $30. During the next six months it is expected to increase by 8% or decrease by 10%. No dividend payment is expected during these six month. The risk-free interest rate is 5% per annum. What is the risk neutral probability of the stock price moving up?

2.The volatility of a stock is 0.3 per annum. In a Cox-Ross-Rubinstein binomial tree in which one step represents a time interval of 6 months, what are the proportional up-movement and down-movement factors, u and d, respectively?

3.The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with one time step to do the valuation, what is the value of a call option with a strike price of 32 that expires in 6 months?