Suppose the stock price is currently $75. For the next six months there is 7.5% probability that the stock will appreciate 8% with 4% annualized drift. The risk-free rate is 1.53% per year with continuous compounding. The dividend yield is 1 p.a.%. Value the following option using binomial tress and 12-time steps. 

a.) What is the value of a six-month European put option with a strike price of $86. 

b.) What is the value of a six-month American put option with a strike price of $70. 

c.) What is the value of a six-month European call option with a strike price of $86. 

d.) What is the value of a six-month European put option with a strike price of $70. 

e.) Estimate how high the minimum strike price must be for it to be optimal to exercise the put option immediately