Suppose that the price of a non-dividend-paying stock is $30, its volatility is 25%, and the risk-free rate for all maturities is 4% per annum. Use DerivaGem European binomial with 60 steps 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.
a. A bear spread using European call options with strike prices of $25 and $30 and a maturity of one month.
b. A bull spread using European put options with strike prices of $30 and $35 and a maturity of one month.
c. A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of three months.
d. A butterfly spread using European put options with strike prices of $25, $30, and $35 and a maturity of one month.
e. A strangle using options with strike prices of $25 and $35 and a maturity of one month.