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 1

(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.