Question

2. Assume there are two Call options for Intel stock at CBOE with strike price 100 and 120. The current stock price for Intel is 110. Construct a Bull Spread using these options. Specify the option positions you hold. Draw the terminal payoff graph for the bull spread. (1)

Answer 1

A bull spread is constructed by buying a call option with a lower strike price and selling a call option with a higher strike price.

The 100 call option will be bought, and the 120 call option will be sold.

S = underlying price at expiry,

X = strike price

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

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

A B C D Payoffs Long Call Short Call Net ($100) ($120) Payoff $0 SO SO 10 Stock price at expiry $95 $96 $97 $98 $99 $100 $101 $102 $103 $104 $105 $106 $107 $108 $109 $110 $111 $112 $113 $114 $115 $116 $117 $6 15 16 17 $9 $10 $11 $12 $13 $14 $15 $16 $17 $10 $11 $12 $13 $14 $15 $16 $17

A B C D | Payoffs $21 30 (52) 31 32 (54) (55) $20 Stock price at expiry 27 $119 28 $120 29 $121 $122 $123 $124 33 $125 $126 $127 $128 $129 $130 $131 $132 $133 $134 $135 $136 $137 46 $138 $139 48 $140 49 Long Call Short Call Net ($100) ($120) Payoff $19 $0 $19 $20 $0 $20 ($1) $20 $22 $20 $23 ($3) $20 $24 $20 $25 $20 $26 ($6) $20 $27 ($7) $28 ($8) $20 $29 ($9) $20 $30 ($10) $20 $31 ($11) $20 $32 ($12) $20 ($13) $20 $34 ($14) $20 $35 ($15) $36 ($16) $20 $37 ($17) $38 ($18) $20 $39 ($19) $20 $40 ($20) $20 $33 $20

Payoffs 13 105 2 Stock price at expiry Long Call ($100) I=MAX(A3-100,0) 4 96 =MAX(A4-100,0) =MAX(A5-100,0) =MAX(A6-100,0) =MAX(A7-100,0) =MAX(A8-100,0) 9 101 =MAX(A9-100,0) =MAX(A10-100,0) 103 =MAX(A11-100,0) =MAX(A12-100,0) =MAX(A13-100,0) =MAX(A14-100,0) =MAX(A15-100,0) =MAX(A16-100,0) =MAX(A17-100,0) =MAX(A18-100,0) =MAX(A19-100,0) =MAX(A20-100,0) 21 113 =MAX(A21-100,0) =MAX(A22-100,0) =MAX(A23-100,0) 24 116 =MAX(A24-100,0) 25 117 =MAX(A25-100,0) Short Call ($120) --MAX(0,A3-120) --MAX(0,A4-120) --MAX(0,45-120) --MAX(0,A6-120) --MAX(0,A7-120) --MAX(0,A8-120) =-MAX(0,49-120) --MAX(0,A10-120) --MAX(0,A11-120) =-MAX(0,A12-120) --MAX(0,A13-120) --MAX(0,A14-120) --MAX(0,A15-120) --MAX(0,A16-120) =-MAX(0, A17-120) --MAX(0,A18-120) =-MAX(0, A19-120) =-MAX(0, A20-120) =MAX(0,A21-120) --MAX(0,A22-120) --MAX(0, A23-120) - MAX(0, A24-120) --MAX(0,A25-120) Net Payoff I=SUM(B3:03) SUM(B4:04) =SUM(B5:C5) -SUM(B6:06) ESUM(B7:07) =SUM(B8:08) SUM(B9:09) =SUM(B10:010) =SUM(B11:011) =SUM(B12:C12) =SUM(B13:013) ESUM(B14:C14) =SUM(B15:C15) =SUM(816:C16) ESUM(B17:C17) =SUM(B18:C18) =SUM(B19:C19) =SUM(B20:C20) SUM(B21:C21) =SUM(B22:C22) =SUM(B23:023) =SUM(B24:C24) =SUM(B25:C25) 106 17 109 112 22 114 23 115

$117 $118 $119 $120 Net Payoff $131 $132 $133 $134 $135 $138 $140 - Net Payoff