Question

Suppose a stock’s price S(0) = $23 and you purchase a call option with strike X = 25 for $5 and also sell a call option with strike X = 35 for $1. Draw the hockey-stick/payoff diagram.

Answer 1

Basically lets understand the question first:

• We have bought the call with an exercise price of 25 and sold a call with the exercise price of 35
• So below 25 none of the options will be exercised
  • Payoff = 0
• Between 25 and 35, only long will be exercised
  • Payoff = Spot - exercise
  • So if Spot = 34, the payoff =34-25 = 9
• And from 35 and above both the options will be exercised
  • Payoff for long = Spot - exercise
    • So if spot = 40, then payoff = 40-25 = 15
  • Payoff for short = exercise-Spot
    • So if spot = 40, then payoff = 35-40= -5
  • So total pay off = 15-5 = 10
  • Basically in this case, we will always buy the stock for 25 and sell for 35 so the payoff will be fixed at 10 no matter how high the price goes
• Following is the table with some assumed data points

• Price	Long Payoff	Short Payoff	Total Payoff
  40	15	-5	10
  39	14	-4	10
  38	13	-3	10
  37	12	-2	10
  36	11	-1	10
  35	10	0	10
  34	9	0	9
  33	8	0	8
  32	7	0	7
  31	6	0	6
  30	5	0	5
  29	4	0	4
  28	3	0	3
  27	2	0	2
  26	1	0	1
  25	0	0	0
  24	0	0	0
  23	0	0	0
  22	0	0	0
  21	0	0	0
  20	0	0	0
  19	0	0	0

• So the graph will be:
• 
  Total Payoff 35, 10 34,9 33,8 32,7 31,6 30,5 29,4 28,3 27,2 26,1 25,0 30 35 5 10 15 20 25 40 45