Consider an up-and-out barrier call option on a non-dividend-paying stock when the stock price is 50, the strike price is 50, the volatility is 30%, the risk-free rate is 5%, the time to maturity is 1 year, and the barrier at $80. Use the DerivaGem software to value the option and graph the relationship between
(a) the option price and the stock price
(b) the delta and the stock price
(c) the option price and the time to maturity, and
(d) the option price and the volatility
(e) Provide an intuitive explanation for the results you get. Show that the delta, gamma, theta, and vega for up-and-out barrier call option can be either positive or negative.