risk-free rate

1 .(Concept Problem) Show how a delta hedge using a position in the stock and a long position in a put would be set up.
2 .Concept Problem) Suppose that a stock is priced at 80 and has a volatility of 0.35. You buy a call option with an exercise price of 80 that expires in 3 months. The risk-free rate is 5 percent. Answer the following questions:
a. Determine the theoretical value of the call. Use BSMbin8e.xls.
b. Suppose that the actual call is selling for $5. Suggest a strategy, but do not worry about hedging the risk. Simply buy or sell 100 calls.
c. After purchasing the call, you investigate your possible profits. You expect to unwind the position one month later, at which time you expect the call to have converged to its Black-Scholes-Merton value. Of course you do not know what the stock price will be, but you can calculate the profits for stock prices over a reasonable range. You expect that the stock will not vary beyond $60 and $100. Determine your profit in increments of $10 of the stock price. Comment on your results.