3. 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. 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 bear spread using European put options with strike prices of $25 and $30 and a maturity of six months. (c) A butterfly spread using European call options with strike prices of $25, $30 and $35 and a maturity of one year. (d) A butterfly spread using European put options with strike prices of $25, $30 and $35 and a maturity of one year. 3. 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. 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 bear spread using European put options with strike prices of $25 and $30 and a maturity of six months. (c) A butterfly spread using European call options with strike prices of $25, $30 and $35 and a maturity of one year. (d) A butterfly spread using European put options with strike prices of $25, $30 and $35 and a maturity of one year