I. The volatility of a non-dividend-paying stock whose price is $80, is 35%. The risk-free rate is 2% per annum (continuously compounded) for all maturities.

Calculate values for u, d, and p when a 2-month time step is used. What is the value a 4-month European call option with a strike price of $82 given by a two-step binomial tree? Suppose a trader sells 1,000 options (10 contracts). What position in the stock is necessary to hedge the traders position at the time of the trade? What is the value of the option if it is a European put? What is the value of the option if it is an American put?