Chapter 11

To answer Q1 ­ Q6, please provide graphs showing the relationship between the position profit (Y­axis) and the stock price at expiration (X­axis).

Suppose the price of a non­ dividend­ paying stock is currently \$50, its volatility is 25%, and the risk­free rate for all maturities is 4% per annum.

All the options below expire in 4 months (=4/12 years). The option prices are not given here but you can use Derivagem to find the option prices. Choose “Black­Scholes ­ European” for Option Type in D17 cell. We will learn how to use Derivagem this week. You must include all the Derivagem outputs (6 total) in your Excel file by copying or taking a screenshot.

Q1: A bull spread using European call options with strike prices of \$45 and \$50. (The call price for K=\$45 option should be \$6.38. If not, double check the parameters you used in Derivagem. See the attached screenshot of derivagem.)

Q2: A bear spread using European put options with strike prices of \$45 and \$50.

Q3: A butterfly spread using European call options with strike prices of \$45, \$50 and \$55.

Q4: A butterfly spread using European put options with strike prices of \$45, \$50 and \$55. (Hint: The total profit graph should be identical to Q3.)

Q5: A straddle using options with a strike price of \$50.

Q6: A strangle using options with strike prices of \$50 and \$55.

Attached are templates that have been provided

Q7 Use put–call parity to show that the cost of a butter?y spread created from European puts is identical to the cost of a butter?y spread created from European calls.

Q8 A call with a strike price of \$60 costs \$6. A put with the same strike price and expiration date costs \$4. Construct a table that shows the pro?t from a straddle. For what range of stock prices would the straddle lead to a loss?