Which methods are suitable for pricing an American put option? Tick all correct answers.

Bob priced an American put option on a tree and obtained the result of 2.53.

Pricing a European put option with the same parameters gave him 2.14 using the same tree (i.e., the tree build using the same parameters) and 2.18 using the Black-Schole formula.

Use the control variate technique to improve the price of the American put. In your answer give the improved price.

Consider a tree model where a stock price can go up by 10% over one time step lasting for one year (as in our examples in Class 4). Assuming the usual approach to calculating u, what is the corresponding value of volatility? Give the answer as yearly volatility. Calculate the result to four decimal points.

Consider a European put option with the strike price of 150 maturing in 3 months from now on a share worth 120. Assuming the volatility of the share of 0.2 and the interest rate (with continuous compounding) of 5% calculate the option price using the Black-Scholes formula. Use the tables at the end of Hull's book to get the values of N (or some other tool). Calculate the result to four decimal places.