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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
e) A strangle using options with a strike prices of \$25 and \$35 and a 6-month maturity

Solution Summary

The solution provides a table showing the relationship between the profit and final stock price for the following: bull spread using European call options, bear spread using European put options, butterfly spread using European call options, butterfly spread using european put options, straddle using options, strangle using options.

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AD 10: Suppose that the price of a non-dividend-paying stock is \$38, its volatility is 35%, and the risk-free rate for all maturities is 4% per annum. Use Derivagem (Analytic European) to calculate the cost of setting up the following positions. In each case provide a spreadsheet showing the relationship between profit and final stock price. Hint: use the strategy developed for AD 8 from Hull Chapter 8.

Q1: A bull spread using European call options with strike prices of \$35 and \$40 and an expiration of 6 months.

Q2: A bear spread using European put options with strike prices of \$35 and \$40 and an expiration of 6 months.

Q3: A butterfly spread using European call options with strike prices of \$35, \$40 and \$45 and an expiration of one year.

Q4: A butterfly spread using European put options with strike prices of \$35, \$40 and \$45 and an expiration of one year.

Q5: A straddle using options with a strike price of \$35 and a six-month expiration.

Q6: A strangle using options with a strike prices of \$35 and \$40 and a six-month expiration.

Adapted from Fundamentals of Futures and Options Markets, 6th ed., John C. Hull.

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