Complete a three-step binomial tree to price the options outlined below. Use the information provided to find the values for:

1. a European Call Option
2. a European Put Option
3. an American Put Option
4. the call delta at each node in the tree

Provide examples of your math/setup with your answer.

Stock Price = $80, Strike Price = $82, Volatility =0.3, Maturity = 9 months, (each step in the tree = 0.25), interest rate = 0.025

Steps to calculating binomial tree prices

1. Calculate u, d, and p
2. Calculate the stock prices at each node using u and d. For each price increase multiply by u (for example from the original price of S₀ the price would be (S₀)(u) for the branch with a price increase). This will be the same for all three of the options.
3. Find the intrinsic value of the options at maturity (the far right of the tree). For Call options, the intrinsic value is S-X, for put options the intrinsic value is X-S.
4. Use p and the intrinsic value to work right to left in the tree and find the option values at each node. Stepping one-time unit back in the tree, the equation is (c_u(p)+(1-p)c_d)e^-rh for put options you can use the same formula, just use the put option prices in place of the call options.
5. If pricing an American Put Option find the intrinsic value at each node and compare it to the calculated option value for the European put. If the intrinsic value is greater than the European option price, use the intrinsic value in the option price when you calculate the option price for the step to the left.