XYZ CORP
ANSWERS TO PROBLEMS
1 (US$/Can$)(0.0118)(50,000 Can$) = $590 2 (US$/Can$)(0.0068)(50,000 Can$) = $340
3 Cost = $590
Net gain = (0.90 - 0.815)(50,000) -590 = $3,660
4 Cost = $590
Payoff = (0) – 590 = -$590 (Option expires worthless)
5 Cost = $340
Payoff = (0) – 340 = -$340 (Option expires worthless)
6 Cost = $340
Payoff = (0.82 – 0.75)(50,000) - $340= $3160
7 Long straddle: purchase one OCT 85 put and one OCT 85 call Cost of one call = 16 3/4(100) = $1,675.00
Cost of one put = 1/8(100) = $12.50
Total cost = $1,687.50
Payoff on one call = 100(101 11/16 - 85) = $1,668.75 Payoff on one put = 0, expires out of the money Net gain/loss = $1,668.75 - $1,687.50 = $18.75 loss
8 Long strap: purchase two OCT 85 calls and one OCT 85 put Cost of 2 calls = 2(16.75(100) = $3,350.00
Cost of one put = 1/8(100) = $12.50
Total cost = $3,362.50
Payoff on 2 calls = 2(100)(101 11/16 - 85) = $3,375.00 Payoff on one put = 0, expires out of the money
Net gain/loss = $3,375.50 - $3,362.50 = $13.00 gain
9 Long strip: purchase one OCT 85 call and two OCT 85 puts Cost of one call = 16 3/4(100) = $1,675.00
Cost of two puts = 2(1/8)(100) = $25.00
Total cost = $1,700.00
Payoff on one call = 100(101 11/16 - 85) = $1,668.75 Payoff on two puts = 0, expires out of the money Net gain/loss = $1,668.75 - $1,700.00 = $31.25 loss
10 Long straddle: purchase one OCT 90 put and one OCT 90 call Cost of one call = 12(100) = $1,200.00
Cost of one put = 3/8(100) = $37.50
Total cost = $1,237.50
Payoff on one call = 100(101 11/16 - 90) = $1,168.75 Payoff on one put = 0, expires out of the money Net gain/loss = $1,168.75 - $1,237.50 = $68.75 loss
11 Long strap: purchase two OCT 90 calls and one OCT 90 put Cost of 2 calls = 2(12.00(100) = $2,400.00
Cost of one put = 3/8(100) = $37.50
Total cost = $2,437.50
Payoff on 2 calls = 2(100)(101 11/16 - 90) = $2,337.50 Payoff on one put = 0, expires out of the money
Net gain/loss = $2,337.50 - $2,437.50 = $100.00 loss 12 Long strip: purchase one 90 call and two OCT 90 puts
Cost of one call = 12(100) = $1,200.00 Cost of two puts = 2(3/8)(100) = $75.00
Total cost = $1,275.00
Payoff on one call = 100(101 11/16 - 90) = $1,168.75 Payoff on two puts = 0, expires out of the money Net gain/loss = $1,168.75 - $1,275.00 = $106.25 loss
13 Long straddle: purchase one OCT 95 put and one OCT 95 call Cost of one call = 7 5/8(100) = $762.50
Cost of one put = 13/16(100) = $81.25
Total cost = $763.31
Payoff on one call = 100(101 11/16 - 95) = $668.75 Payoff on one put = 0, expires out of the money Net gain/loss = $668.75 - $763.31 = $94.56 loss
14 Long strap: purchase two OCT 95 calls and one OCT 95 put
Cost of 2 calls = 2(7 5/8)(100) = $1,525.00 Cost of one put = 13/16(100) = $81.25
Total cost = $1,606.25
Payoff on 2 calls = 2(100)(101 11/16 - 95) = $1,337.50 Payoff on one put = 0, expires out of the money
Net gain/loss = $1,337.50 - $1,606.25 = $268.75 loss 15 Long strip: purchase one 95 call and two OCT 95 puts
Cost of one call = 7 5/8(100) = $762.50 Cost of two puts = 2(13/16)(100) = $162.50
Total cost = $925.00
Payoff on one call = 100(101 11/16 - 95) = $668.75 Payoff on two puts = 0, expires out of the money Net gain/loss = $668.75 - $925.00 = $256.25 loss
16 Bull money spread = buy the in-the-money call, i.e., OCT 85 and sell the out-of-the-money call, i.e., OCT 95
Cost of buying OCT 85 call = 100(16 3/4) = $1,675.00 Proceeds from selling OCT 95 call = 100(7 5/8) = $762.50
Net cost $912.50
Payoff on OCT 85 call = 100(110 - 85) = $2,500.00 Payoff on OCT 95 call = 100(110 - 95) = ($1,500.00) Net payoff = $2,500.00 - 1,500.00 = $1,000.00 Total gain/loss = $1,000.00 - 912.50 = $87.50 gain 17 Price using the B-S option pricing model
d1 = ln(130/125) + [(.03 + 5(.352))(.0833)]/(.35(.02778.5))
= 0.715807
d2 = 0.715807 - (.35(.02778.5)) = 0.657474 N(d1) = 0.762945
N(d2) = 0.744562
Call price = Pc = 120[0.762945– 125(e-.03(.02778))( 0.744562]
= $6.19
18 Put price = 6.19 + 125(e-.03(.02778)) – 130 = $1.086 19 The effective price is 65 + 6.75 = $71.75
The option expires worthless so your effective price is the current price plus the option premium.
20 The effective price is 70 + 6.75 = $76.75
The option is exercised so your effective price is the strike price plus the option premium.
21 The effective price is 80 – 7.25 = $72.75
The option is exercised so your effective price is the strike price less the option premium.
22 The effective price is 85 – 7.25 = $77.75
The option expires worthless so your effective price is the current price less the option premium.
23 At S = 20
Net value of protective put = (32.5 – 20) – 2.85 + 20 = 29.65 At S = 45
Net value of protective put = – 2.85 + 45 = 42.15
24 This strategy is appropriate if an investor wished to insure against a decline in share values.
25 At S = 20
Net value of covered call = 1.65 + 20 = 21.65 At S = 45
Net value of covered call = -(45 – 32.5) + 1.65 + 45 = 34.15
26 This strategy is appropriate if an investor wished to generate additional income.
27 At S = 20
Net payoff on a long straddle = (32.5 – 20) -1.65 – 2.85 = 8 At S = 45
Net payoff on a long straddle = (45 - 32.5) -1.65 – 2.85 = 8
28 This strategy is appropriate if an investor expected share prices to be volatile.
29 At S = 20
Net payoff on a short straddle = -(32.5 – 20) + 1.65 + 2.85 = -8 At S = 45
Net payoff on a long straddle = -(45 - 32.5) + 1.65 + 2.85 = -8
30 This strategy is appropriate if an investor expected share prices to remain in a trading range.
31 At S = 20
Net payoff on a long strap = (32.5 – 20) – (2)(1.65) – 2.85 = 6.35 At S = 45
Net payoff on a long straddle = (2)(45 - 32.5) – (2)(1.65) – 2.85 = 18.85 32 This strategy is appropriate if an investor expected share prices to be volatile.
33 If the stock rises the price one year for now will be = 50(1 + 0.25) = $62.50 If the stock falls the price one year for now will be = 50(1 - 0.25) = $37.50 34 Current stock price = $50
Exercise price = $45 Risk free rate = 2%
Price in one year if stock rises = 50(1.25) = $62.50 Price in one year if stock declines = 50(1.25) = $37.50
Intrinsic value of call option if stock rises to $62.50 = Max[0, 62.50 – 45] = $17.50 Intrinsic value of call option if stock falls to $37.50 = Max[0, 37.50 – 45] = $0
Estimate the number calls needed by setting:
The hedge portfolio will consist of one share of stock held long plus some number of call options written.
Value of hedge portfolio if stock rises = Value of hedge portfolio if stock falls 62.50 + (17.5)(n) = 37.50 + (0)(n)
n = -1.4286
35 Value of hedge portfolio today = 50 – (1.4286)(C0) = 37.5/(1.02) C0 = $9.26
36 Current stock price = $60
Price in one year if stock rises 15% per six month period= 60(1.15)(1.15) = $$79.35 Price in one year if stock rises 15%, then falls 15% = 60(1.15)(0.85) = $58.65
Price in one year if stock declines 15% per period = 60(0.85)(0.85) = $43.35 37 Current stock price = $60
Exercise price = $65
Risk free rate = 3% or 1.49% per six month period = (1.03)0.5 – 1 = 0.0149 Price in six months if stock rises 15% = 60(1.15) = $69
Price in six month if stock falls 15% = 60(0.85) = $51
Price in one year if stock rises 15% per six month period= 60(1.15)(1.15) = $79.35 Price in one year if stock rises 15%, then falls 15% = 60(1.15)(0.85) = $58.65
Price in one year if stock declines 15% per period = 60(0.85)(0.85) = $43.35
Intrinsic value of call option if stock rises to $79.35 = Max[0, 79.35 – 65] = $14.35
Intrinsic value of call option if stock falls to $58.65= Max[0, 58.65 – 65] = $0 Intrinsic value of call option if stock falls to $43.35 = Max[0, 43.35 – 65] = $0 Estimate the number calls needed by constructing a hedge portfolio.
The hedge portfolio will consist of one share of stock held long plus some number of call options written.
At the end of the first six month period:
Value of hedge portfolio if stock rises = Value of hedge portfolio if stock falls 79.35 + (14.35)(n) = 58.65 + (0)(n)
n = -1.44251
Value of hedge portfolio at the end of first six months = 69 – (1.44251)(Cu) = 58.65/(1.0149)
Cu = $7.7719
38 Cd = 0. Since the ending stock prices of $58.65 and $43.35 are both below the exercise price.
39 To solve for the value of the call today (C0), first determine the number of calls by constructing a hedge portfolio where:
Right now:
Value of hedge portfolio if stock rises = Value of hedge portfolio if stock falls 69 + (7.7719)(n) = 51 + (0)(n)
n = -2.31603
Value of hedge portfolio now = 60 – (2.31603)(C0) = 51/(1.0149) C0 = $4.2092