Discuss the below:
Q: 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 costs of setting up the following positions. In each case provide a table showing the relationship between the 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 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 one year-
e) A straddle using options with a strike price of $30 and a 6-month maturity
f) A strangle using options with a strike prices of $25 and $35 and a 6-month maturity