Question

Financial Derivatives (4) T=1/4 year, three call options - cl,c2 and 3. K1 = $20. K2 - $30, K3 = 50, c1 - $15, and c2 S5, c3 = $1. (10 points) a. An investor buys one cl and c3, and short 2 c2. please draw a diagram illustrating how the investor's profitloss varies with the nice of the underlying asset on the day of maturity. points) b. Under what circumstances you expect to use this trading strategy? (2 points)

Answer 1

a]

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

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

S = underlying price at expiry,

X = strike price

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

at 2 $12 $14 I A B C D E Payoffs Stock price Long Call Long Call Short Call Net expiration (c1) *1 (3)*1 (C2) 2 Payoff $10 ($15) ($1) $10 ($6) $11 ($15) ($1) $10 (96) ($15) ($1) $10 ($6) $13 ($15) ($1) $10 ($6) ($15) ($1) ($6) $15 ($15) ($1) ($6) $16 ($15) ($1) $10 ($6) $17 ($15) ($1) $10 ($6) $18 ($15) ($1) $10 ($6) ($15) ($1) $10 ($6) $20 ($15) ($1) $10 ($6) $21 ($14) ($1) $10 ($5) ($13) ($1) $10 ($4) $23 ($12) ($1) $10 ($3) $24 ($11) ($1) $10 ($10) ($1) $10 $26 ($9) ($1) $27 ($8) ($1) $10 $28 ($7) ($1) $29 ($1) $10 $3 $30 ($5) ($1) $10 ($2) $10 $10

($1) A B Payoffs Stock price Long Call Long Call Short Call Net expiration (1) 1 (13)*1 (c2) 2 Payoff (54) ($1) $8 ($3) ($1) ($2) ($1) $4 $1 ($1) ($1) ($1) ($1) ($2) ($2) ($4) ($3) ($6) ($4) ($8) ($5) ($10) ($6) ($1) ($12) ($7) ($1) ($14) ($8) ($1) ($16) ($9) $9 ($18) ($10) $10 ($1) ($20) ($11) $11 ($22) ($12) $47 $12 ($1) ($24) ($13) $48 $13 ($1) ($26) ($14) $14 ($1) ($28) ($15) ($1) ($30) ($16) ($32) ($16) ($1) ($1) ($1) (51) $25 $51 $16

E at 2 $53 A B C D Payoffs Stock price Long Call Long Call Short Call Net expiration (c1) *1 (13) *1 (c2)* 2_Payoff $49 $14 ($1) ($28) ($15) $50 $15 ($1) ($30) ($16) $51 $16 $o ($32) ($16) $52 $17 ($34) ($16) $18 ($36) ($16) $54 $19 ($38) ($16) $55 $20 ($40) ($16) $56 ($42) ($16) $57 $22 ($44) ($16) $58 $23 ($46) ($16) $59 $24 ($48) ($16) $60 ($50) ($16) $61 $26 $10 ($52) ($16) $62 $11 ($54) ($16) $63 $28 $12 ($56) ($16) $64 $29 $13 ($58) ($16) $65 $14 ($60) ($16) $21 $25 $27

$10_$12_$14 $16_$18_$20 $22 $24 $26 $28 $30 $32 $34 $36 $38 $40_542 544 $46 $48 $50 $52 $54 $56 $58 $60 562 564 payoffs (540) ($50) (560) ($70) stock price at expiration Long Call (c1) *1 — Long Call (C3) 1 - Short Call (2) *2 — Net Payoff

b]

This is a long butterfly call spread.

This is used when one is not expecting the stock price to change a lot before expiration.