A stock price is currently $52. The volatility is 36.46% per year. The risk-free interest rate is 10% per annum with continuous compounding and the dividend yield is 0%. [ a) Set up a two period binomial lattice for pricing a six month at the money European put option. Show the complete lattice of stock and option prices. Indicate the risk neutral probability of an up-jump.

b) Establish the replicating portfolio at date 0. Show your work and then fill out the table below

Number of Shares Purchased
Amount of Funds Borrowed
Total Value of the Replicating Portfolio

c) Assume you own the replicating portfolio at date 0. Assume the stock goes down in the first period. At this node, compute the value of the replicating portfolio and complete the Table:

Value of Shares of Replicating Portfolio initiated at date 0
Amount Owed
Total Value of Position

d) Now, at this down node compute the new replicating position that mimics the payout of the put option in the second period. Explain how you got the values

Number of Shares of Replicating Portfolio at date 1 when the stock is at the lower node.
Dollar Value of Position in Shares
Amount of Funds Borrowed
Total Value of Position

e) Finally, go through the exact transactions that need to take place at the node to update the original replicating position to the new replicating position. Specifically how many more (or less) shares need to traded and how much more money (or less money) needs to be borrowed.

Use this space to explain your computations and complete then complete the Table below.

How many extra shares need to be purchased or sold short
Cost or money received from share transactions
Amount of extra borrowing or lending that needs to take place