Question

Suppose, you are an investment broker. Your client wants to take five option positions on the stock of Plumbus. The stock is currently trading at $40.

(1) She wants to buy a call option with a strike price of $40 at an option price of $4.

(2) She also wants to buy a put option with a strike of $45 at an option price of $10.

(3) She also wants to sell a second call option with a strike of $30, and an option price of $14.

(4) She also wants to sell a put option with a strike of $44, and an option price of $8.

(5) Finally, she wants to buy a call option with a strike price of $43, and an option price of $3.

Construct a profit diagram for this investment strategy. Create a graph of the portfolio payouts.

Answer 1

Payoff of a long call option = Max[S-X, 0] - P

Payoff of a short call option = P - Max[0, S-X]

Payoff of a long put option = Max[X-S, 0] - P

Payoff of a short put option = P - Max[0, X-S]

S = underlying price at expiry,

X = strike price

P = premium paid or received (long options involve paying premium, and short options receive premium)

$14 $6 $0 $7 $2 ($31 - в C D E F Stock Long Short Long Short Long price Call Call Put PutCall Net ($40) ($30) ($45) ($44) ($43) Payoff $30 ($41 $5 ($6) ($3) $31 ($4) $13 $4 ($5) ($3) $32 ($4) $12 $3 ($4) ($3) $33 ($4) $2 ($3) ($3] $34 (84) $10 ($2) (83) $35 ($4) ($3) $36 ($4) $8 ($3) $37 ($4) ($2) (43) ($1) $38 ($4) ($3) ($3) (52) $39 ($4) ($4) ($3) ($3) $40 ($4) ($5) (34) $41 ($3) ($6) ($3) ($4) $42 ($2) ($7) ($3) ($4) $43 ($8) ($3) ($4) $44 ($9) ($2) ($3) $45 ($10 ($1) ($3) $46 ($2) ($10) $0 (82) $47 ($10) ($4) ($10) ($10) $3 $50 ($6) ($10) $51 ($7) $52 ($8) ($10) $6 $53 ($9) ($10) $54 $10 ($10) ($10) $8 $55 $11 ($11 ($10) $8 $9 ($3) ($1) $4 ($10

A 1 2 3 4 5 6 10 Stock price at expiry Long Call ($40) 30 =MAX(A2-40,0)-4 31 =MAX(A3-40,0)-4 32 =MAX(A4-40,0)-4 33 =MAX(A5-40,0)-4 34 =MAX(A6-40,0)-4 =MAX(A7-40,0)-4 =MAX(A8-40,0)-4 =MAX(A9-40,0)-4 38 =MAX(A10-40,0)-4 =MAX(A11-40,0)-4 =MAX(A12-40,0)-4 =MAX(A13-40,0)-4 =MAX(A14-40,0)-4 =MAX(A15-40,0)-4 44 =MAX(A16-40,0)-4 45 =MAX(A17-40,0)-4 46 =MAX(A18-40,0)-4 =MAX(A19-40,0)-4 =MAX(A20-40,0)-4 =MAX(A21-40,0)-4 =MAX(A22-40,0)-4 =MAX(A23-40,0)-4 =MAX(A24-40,0)-4 =MAX(A25-40,0)-4 =MAX(A26-40,0)-4 =MAX(A27-40,0)-4 9448 SSBBSB888 Short Call (30) Long Put ($45) =14-MAX(0, A2-30) =MAX(45-A2,0)-10 =14-MAX(O, A3-30) =MAX(45-A3,0)-10 = 14-MAX(O,A4-30) =MAX(45-A4,0)-10 =14-MAX(0,A5-30) =MAX(45-A5,0)-10 =14-MAX(0,A6-30) =MAX(45-A6,0)-10 = 14-MAX(O,A7-30) =MAX(45-A7,0)-10 =14-MAX(0, A8-30) =MAX(45-A8,0)-10 = 14-MAX(O.A9-30) =MAX(45-49,0)-10 =14-MAX(O, A10-30) =MAX(45-A10,0)-10 = 14-MAX(O,A11-30) =MAX(45-A11,0)-10 =14-MAX(O, A12-30) =MAX(45-A12,0)-10 =14-MAX(O A13-30) =MAX(45-A13,0)-10 =14-MAX(O, A14-30) =MAX(45-A14,0)-10 = 14-MAX(O, A15-30) =MAX(45-A15,0)-10 = 14-MAX(O,A16-30) =MAX(45-A16,0)-10 =14-MAX(0, A17-30) =MAX(45-A17,0)-10 =14-MAX(O, A 18-30) =MAX(45-A18,0)-10 =14-MAX(O, A 19-30) =MAX(45-A19,0)-10 =14-MAX(O,A20-30) =MAX(45-A20,0)-10 =14-MAX(0, A21-30) =MAX(45-A21,0)-10 = 14-MAX(O,A22-30) =MAX(45-A22,0)-10 =14-MAX(0, A23-30) =MAX(45-A23,0)-10 =14-MAX(O, A24-30) =MAX(45-A24,0)-10 =14-MAX(O, A25-30) =MAX(45-A25,0)-10 =14-MAX(O, A26-30) =MAX(45-A26,0)-10 =14-MAXIO,A27-30)=MAX(45-A27,0)-10 Short Put ($44) Long Call ($43) =8-MAX(0,44-A2) =MAX(A2-43,0)-3 =8-MAX(0.44-A3) =MAX(A3-43,0)-3 =8-MAX(0,44-44) =MAX(A4-43,0)-3 =8-MAX(0.44-A5) =MAX(A5-43,0)-3 =8-MAX(0,44-46) =MAX(A6-43,0)-3 = 8-MAX(0.44-A7) =MAX(A7-43,0)-3 =8-MAX(0.44-A8) =MAX(A8-43,0)-3 =8-MAX(0.44-A9) =MAX(A9-43,0)-3 =8-MAX(0.44-A10) =MAX(A10-43,0)-3 = 8-MAX(0.44-A11) =MAX(A11-43,0)-3 =8-MAX(0.44-A12) =MAX(A12-43,0)-3 = 8-MAX(0.44-A13) =MAX(A13-43,0)-3 =8-MAX(0.44-A14) =MAX(A14-43,0)-3 =8-MAX(0.44-A15) =MAX(A15-43,0)-3 =8-MAX(0.44-A16) =MAX(A16-43,0)-3 = 8-MAX(0.44-A17) =MAX(A17-43,0)-3 =8-MAX(0,44-A18) =MAX(A18-43,0)-3 = 8-MAX(0.44-A19) =MAX(A 19-43,0)-3 =8-MAX(0.44-A20) =MAX(A20-43,0)-3 = 8-MAX(0.44-A21) =MAX(A21-43,0)-3 =8-MAX(0.44-A22) =MAX(A22-43,0)-3 = 8-MAX(0.44-A23) =MAX(A23-43,0)-3 =8-MAX(0,44-A24) =MAX(A24-43,0)-3 =8-MAX(0.44-A25) =MAX(A25-43,0)-3 =8-MAX(0,44-A26) =MAX(A26-43,0)-3 =8-MAX(0,44-A27) =MAX(A27-43,0)-3 Net Payoff =SUM(B2:F2) = SUM(B3:F3) SUM(B4:F4) = SUM(B5:F5) =SUM(B6:F6) ESUM(B7:F7) =SUM(B8:F8) SUM(B9:F9) = SUM(B10:F10) = SUM(B11:F11) = SUM(B12:F12) = SUM(B13:F13) = SUM(B14:F14) = SUM(B15:F15) =SUM(B16:F16) SUM(B17:F17) = SUM(B18:F18) = SUM(B19:F19) = SUM(B20:F20) SUM(B21:F21) SUM(B22:F22) = SUM(B23:F23) = SUM(B24:F24) = SUM(B25:F25) = SUM(B26:F26) =SUM(B27:F27) 16 17 18