11) A stock price is currently $100 Over each of the next two three-month periods, it is expected to increase 10% or fall by 10%. Consider a six month American put option with a strike price of$99 The risk free rate i a) what is the risk neutral probability of 10% rise in each quarter? (4 points) 1-4 b) Answer the following using the diagram below Write your answers on the diagram.(12 points i) What is the value of stock at each node? ii) What is the pay-off ivalue of American put option at each node? ii) Is it ever optimal to exercise the American put option early? If so, state at which node's and why? 21