Homework Derivatives

Each question is worth 25 points.  Answer all four questions.

Question #1                       (25 points)

Use the following data for this question.   

X = 25, , and .  Use stock prices of $17.50, 20, 22.50, 25, 27.50, 30, and 32.50.  

Note:  Diagrams are required as well as the payoff table.

a.                                           Show the payoff to the holder of a call option on this stock. (5 points)

b.                                          Show the payoff to the writer of a put option (5 points)

c.                                           Combine your answers to parts (a) and (b).  (5 points)

d.                  Explain whether your solution to part (c) is almost identical to either a long position in the stock or a short position in the stock.  (5 points)

e.                   Does this strategy have more risk than buying (or selling) the stock or is it the same?  (5 points)

Question #2                       (25 points) 

 Use the following data for this question.   

X = 25, , and .  Use stock prices of $17.50, 20, 22.50, 25, 27.50, 30, and 32.50.

1. Construct a straddle and show its payoff and diagram.  (8 points)

1. Construct a sketch and show its payoff.  Draw the payoff on the same diagram as in part (a).  (8 points)

1. Find the break-even points for the straddle and the sketch.  (4 points)

1. How do the straddle and sketch relate to each other?  What is the expectation of changes in S for each trader?  (5 points)

Question #3               (25 points)

Use the following data for this question.   

            X = 50                               

a.                                           (i)         Find the price of a call option on this stock.  (5 points)

            (ii)        Show its intrinsic value and time premium (3 points)

b.         (i)         Find the price of a put option on this stock using put-call parity.  (5 points) 

            (ii)        Show its intrinsic value and time premium (3 points)

c.                   Why is the time premium larger for the call option?  (5 points)

d.                  What is the lowest price for a call or put option?  (2 points)

e.        Can the time premium ever be negative?  Hint:  Find the price of a put option with S= $0.00 and compare it to its intrinsic value.  (2 points)

Question #4                  (25 points)

Use the following data for this question.   

DELL  C₁ = $2.95 with X₁ = $25

DELL  C₂ = $0.50 with X₂ = $30

a.                Compute the intrinsic value of a bull call position using prices of $15, 20, 25, 30, 35, and 40.  Graph the results.  (8 points)

b.               What are the maximum and minimum intrinsic values?  (3 points)

c.                   Now compute the cost of the position and add it to your solution in part (a).  Graph the results.  (5 points)

d.                  What is the maximum profit and maximum loss?  (4 points)

e.                   This position could be replicated using put options instead of call options.  Explain how you would do this.  (5 points)

f.                   Use the hedge ratio to show the loss on a portfolio of 200 shares if the portfolio is hedged with put options.  The percentage loss on the shares is 2%.  (7 points)

g.                  Use the hedge ratio to show the loss on a portfolio of 200 shares if the hedge ratio is used to convert a portion of the shares to T-Bills.  The percentage loss on the shares is 2%.  (7 points)

d.         What's the difference between (b) and (c)?  (2 points)