Market Completeness Revisited

a. Form a matrix with 2 rows and 2 columns. Each row contains a state of the world (up and down). Each column contains a security (stock and bond).

b. Pick a specific node. Write down the values for the A matrix.

c. From that node, the stock price may go up or down. Write down the b matrix (which is a column matrix). The first value in b contains the option value if the stock price went up. The second value in b contains the option value if the stock price went down.

d. The no-arbitrage equation can be written as Ax=b. How do you solve this equation for x?

e. Using matrix algebra, solve for x.

f. Show that your solution matches that from the binomial tree.