9. There are call and put options on a stock with strike 40, 50, and 55. Which of the foll...

9. There are call and put options on a stock with strike 40, 50, and 55. Which of the following inequalities must hold?

(a) 0.5C(40) + 0.5C(55) > C(50).

(b) (1/3)C(40) + (2/3)C(55) > C(50)

(c) (2/3)C(40) + (1/3)C(55) > C(50)

(d) 0.5P(40) + 0.5P(55) > P(50)

(e) (1/3)P(40) + (2/3)P(55) > P(50)

(f) (2/3)P(40) + (1/3)P(55) > P(50)

Note: This question uses the general form of convexity in the strike for options:

and

where