For the following problems assume the eective 6-month interest rate is 2% and the S&R 6-month forward price is $1020, and use these premiums for S&R options with 6 months to expiration:

Strike         call             put

$950     $120.405    $51.777

1000     93.809         74.201

1020     84.470         84.470

1050     71.802         101.214

1107     51.873          137.167

(a) Construct payoff and profit diagrams for the purchase of a 950-strike S&R call and sale of a 1000-strike S&R call. Verify that you obtain exactly the same profit diagram for the purchase of a 950-strike S&R put and sale of a 1000-strike S&R

put. What is the dierence in the payo diagrams for the call and put spreads? Why is there a difference?

(b) Compute profit diagrams for the following ratio spreads:

i. Buy 950-strike call, sell two 1050-strike calls.

ii. Buy two 950-strike calls, sell three 1050-strike calls.

iii. Consider buying n 950-strike calls and selling m 1050-strike calls so that the premium of the position is zero. Considering your analysis in (a) and (b),

what can you say about n=m? What exact ratio gives you a zero premium?