Two-period binomial tree.

A stock has a price of $35, and a standard deviation of 29%. The continuous risk-free rate is 10%. There are European and American call and put options with a strike price of $37 and time to expiration of 3 years written on the stock. Using a two-step recombining CRR binomial tree, answer the following:

a. What is the risk-neutral probability of the stock price going up in a single step?

Round your answer to two decimals.

b. What is the theoretical value of the European call?

$

Round your answer to the nearest cent.

c. What is the theoretical value of the European put?

$

Round your answer to the nearest cent.

d. What is the theoretical value of the American put??

$

Round your answer to the nearest cent.