A stock price is currently $52. The volatility is 36.46% per year. The risk-free interest rate is I 0% per annum with continuous compounding and the dividend yield is 0%.

1. 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.

2. 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 replicating portfolio

3. 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 portion

4. 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 Share of Replicating Portfolio at date I when the tock is at the lower node.
Dollar Value of Position in Shares
Amount of Fund Borrowed
Total Value of Portion

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.

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

F. Use Put call parity to compute the fair price of an European call option with the same strike and the same maturity as the European put