Question

#1 The following options on American Euro Call options are available. The current spot price of the Euro is $1.00/Euro. You care going to construct a short butterfly spread that entails: Sell 1 in the money call Buy 2 at the money Calls (lower strike than sold call above) Sell 1 out of the money call This strategy is outlined below in the table, the first column tells you which position to take in each option contract. Decision Type Premium Strike Sell 1 Call $.08 $.95/Euro Buy 2 Call $.03 $1.00/Euro Sell 1 Call $.01 $1.05/Euro a) Construct the payoff diagram for the short butterfly spread. Be sure and label the axis as well as the values on the x and y-axis. SHOW WORK Make payoff diagram b) At what spot rate will the position make the maximum profit? c) At what spot rate will the position make the minimum profit (or biggest loss)? d) An investor constructing this position and wishing to make a profit would likely believe the $/euro exchange rate would appreciate/depreciate/stay the same/or make a large move? (circle one)

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)

A B C D E Payoffs 3 Stock price at 2 expiry $0.75 $0.80 $0.85 $0.90 $0.95 $1.00 $1.05 10 $1.10 $1.15 $1.20 $1.25 Long Call Short Call Short Call Net ($1.00) ($0.95) ($1.05) Payoff ($0.06) $0.08 $0.01 $0.03 ($0.06) $0.08 $0.01 $0.03 ($0.06) $0.08 $0.01 $0.03 ($0.06) $0.08 $0.01 $0.03 ($0.06) $0.08 $0.01 $0.03 ($0.06) $0.03 $0.01 ($0.02) $0.04 ($0.02) $0.01 $0.03 $0.14 ($0.07) ($0.04) $0.03 $0.24 ($0.12) ($0.09) $0.03 $0.34 ($0.17) ($0.14) $0.03 $0.44 ($0.22) ($0.19) $0.03

B с E Payoffs 2 Stock price at expiry Long Call ($1.00) Short Call ($0.95) Short Call ($1.05) Net Payoff 3 0.75 =(MAX(A3-1,0)-0.03)*2 =0.08-MAX(0,A3-0.95) =0.01-MAX(0, A3-1.05) =SUM(B3:03) 4 0.8 =(MAX(A4-1,0) -0.03)*2 =0.08-MAX(0,A4-0.95) =0.01-MAX(0,A4-1.05) =SUM(B4:04) 5 0.85 =(MAX(A5-1,0)-0.03)*2 =0.08-MAX(0,45-0.95) =0.01-MAX(0, A5-1.05) =SUM(B5:05) 6 0.9 =(MAX(A6-1,0)-0.03)*2 =0.08-MAX(0,A6-0.95) =0.01-MAX(0,A6-1.05) =SUM(B6:06) 7 0.95 =(MAX(A7-1,0)-0.03)*2 =0.08-MAX(0,A7-0.95) =0.01-MAX(0, A7-1.05) =SUM(B7:07) 8 1 =(MAX(A8-1,0) -0.03)*2 =0.08-MAX(0,A8-0.95) =0.01-MAX(0,A8-1.05) =SUM(B8:08) 9 1.05 =(MAX(A9-1,0)-0.03)*2 =0.08-MAX(0, A9-0.95) =0.01-MAX(0,49-1.05) SUM(B9:D9) 10 1.1 =(MAX(A10-1,0)-0.03)*2 =0.08-MAX(0,A10-0.95) =0.01-MAX(0,A10-1.05) =SUM(B10:D10) 11 1.15 =(MAX(A11-1,0)-0.03)*2 =0.08-MAX(0,A11-0.95) =0.01-MAX(0,A11-1.05) =SUM(B11:011) 12 1.2 =(MAX(A12-1,0)-0.03)*2 =0.08-MAX(0,A12-0.95) =0.01-MAX(0, A12-1.05) =SUM(B12:012) 13 1.25 =(MAX(A13-1,0)-0.03)*2 =0.08-MAX(0,A13-0.95) =0.01-MAX(0,A13-1.05) =SUM(B13:013)

$0.50 $0.40 $0.30 $0.20 - Long Call ($1.00) Short Call ($0.95) Short Call ($1.05) $0.10 Net Payoff $0.00 $0.75 $0.80 $0.85 $0.90 $0.95 $1.00 $1.05 1.10 $1.15 $1.20 $1.25 ($0.10) ($0.20) ($0.30)

b]

The position will make maximum profit when the spot price is $0.95 and below or $1.05 and above.

c]

The position will make maximum loss when the spot price is $1.00

d]

An investor taking this position would likely believe the spot rate would stay the same.