The current price of a stock is 1,000. In three months from now its price will either be 1,250 or 800. The constant risk-free interest rate is 18.562% per year with continuous compounding. Using a two-period binomial model, answer the following questions (show the details of your calculations and present them with four decimal places)

i. Calculate the upward move 'u' and the downward move 'd'.

ii. Calculate the risk-neutral probability 'p'.

iii. Calculate the price of a European put option with a strike price of 1,100 and a maturity of six months.

iv. Calculate the gamma of the put option in (iii).

v. Calculate the price of an American put option with a strike price of 1,100 and a

maturity of six months