1. Which of the following can be estimated for an American option by constructing a single binomial tree: delta, gamma, vega, theta, rho?
2. Calculate the price of a 3-month American put option on a non-dividend-paying stock when the stock price is $60, the strike price is $60, the risk-free interest rate is 10% per annum, and the volatility is 45% per annum. Use a binomial tree with a time interval of 1 month.
3. Explain how the control variate technique is implemented when a tree is used to value American options.