Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Use DerivaGem to calculate the cost of setting up the following positions:
(a) A bull spread using European call options with strike prices of $25 and $30 and a maturity of 6 months
(b) A bear spread using European put options with strike prices of $25 and $30 and a maturity of 6 months
(c) A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of 1 year
(d) A butterfly spread using European put options with strike prices of $25, $30, and $35 and a maturity of 1 year
(e) A straddle using options with a strike price of $30 and a 6-month maturity
(f ) A strangle using options with strike prices of $25 and $35 and a 6-month maturity. In each case provide a table showing the relationship between profit and final stock price. Ignore the impact of discounting.