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.