An underlying asset is priced today at $100. A European call option on the asset has strike price $105. Consider a three-step binomial tree in which at each step, the price either increases 4% or decreases 4%. Assume that the continuously compounded risk-free rate is 4% per annum and the time between steps is delta t = 0.25 year, so that one dollar increase in value to exp(0.04 times 0.25) dollars after one time step. a What are the risk-neutral probabilities? Are they the same at all nodes? Explain your reasoning. b What is the initial price of the option? Obtain the price by working backwards through the nodes and also by using the binomial distribution without calculating the prices at the intermediate nodes. c How much stock and risk-free asset would the replicating portfolio hold initially? Explain your reasoning. d How would the replicating portfolio be adjusted if the price of the stock went up on the first step? Confirm that these adjustments to the replicating portfolio are self-financing