IBM stock currently sells for 84 dollars per share. Over 8 m…

IBM stock currently sells for 84 dollars per share. Over 8 months the price will either go up by 7.5 percent or down by −3.0 percent. The risk-free rate of interest is 4.5 percent continuously compounded. A call option with strike price 83 and maturity of 8 months has a delta of 0.82766. What is the value of this call option?

IBM stock currently sells for 44 dollars per share. The impl…

IBM stock currently sells for 44 dollars per share. The implied volatility equals 45.0 percent. The risk-free rate of interest is 7.0 percent continuously compounded. If you owned 100 shares of IBM stock with strike price 45 and maturity of 5 months, how many call options would you have to buy (sell) to create a delta-neutral hedge? Assume each option controls one share of IBM stock.