Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the riskfree rate for all maturities is 5% per annum. Use DerivaGem to calculate the cost of setting up the following positions. In each case provide a table showing the relationship between profit and final stock price. Ignore the impact of discounting.

a. A bull spread using European call options with strike prices of $25 and $30 and a maturity of six months.

b. A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of one year.

c. A straddle using options with a strike price of $30 and a six-month maturity.

d. A strangle using options with strike prices of $25 and $35 and a six-month maturity.