Use Python or R to perform the following

1.Build a binomial tree for stock price evolution.

u = (1.10+18/100)

a. Calculate and show the new Binomial tree for N=6.

b. What are the terminal values of each path? Define the appropriate filtrations for each of these values.

2. Finally, recalculate the tree for N=4,000.

a.Plot the terminal prices produced by the model (You may use a histogram for this).

b.Can you identify what type of statistical distribution do these prices resemble to?

c. If we defined, Return = ln(price_{t}/price_{t-1}), this is, using a log-function from previous prices, which statistical distribution would Returns follow? Indicate the appropriate Probability Density Function for it.

3. Market completeness

a. How many fundamental securities are there in the market? (Hint: a derivative, such

as an option, is NOT a fundamental security. Derivatives are derived from fundamental securities).

b. At any given node, how many states of the world are there in the binomial tree?

c. Define market completeness using parts a and b.

d. Suppose the underlying stock price jumped. By jumps, we mean that it moves by a

factor larger than u (or smaller than d) from 1 node to the next. Would that market

still be complete? Why or why not?