Financial Analysis, Planning and Forecasting Theory and Application

Financial Analysis, Planning and Forecasting

Theory and Application

ByAlice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan ChaseCheng F. Lee

Rutgers University

Chapter 9 Option and Option Strategies

Outline9.1 Introduction9.2 The Option market and related

definition9.3 Index and futures option 9.4 Put-call parity9.5 Risk-return characteristics of options9.6 SummaryAppendix 9A Options and Exchanges

9.2 The Option market and related definition

What is an Option? Types of Options and Their Characteristics Relationship Between the Option Price and

the Underlying Asset Price Additional Definitions and Distinguishing

Features Types of Underlying Asset Institutional Characteristics

9.2 The Option market and related definitionTable 9-1 Options Quotes for Johnson& Johnson at 09/21/2006

Call Options Expiring Fri. Jan.18, 2008Strike Symbol Last Bid Ask Vol Open Int

40 JNJAH.X 24 25.5 25.6 10 5,427

45 JNJAI.X 20 20.5 20.7 3 2,788

50 JNJAJ.X 15.5 15.7 16 11 8,700

55 JNJAK.X 11.1 10.9 11.1 33 10,327

60 JNJAL.X 6.4 6.4 6.5 275 32,782

65 JNJAM.X 2.65 2.65 2.7 1,544 70,426

70 JNJAN.X 0.55 0.55 0.6 845 48,582

75 JNJAO.X 0.1 0.05 0.1 2 13,629

80 JNJAP.X 0.05 N/A 0.05 10 4,497

85 JNJAQ.X 0.05 N/A 0.05 0 3,275

90 JNJAR.X 0.05 N/A 0.05 0 3,626

9.2 The Option market and related definition

Put Options Expiring Fri. Jan.18, 2008

Strike Symbol Last Bid Ask Vol Open Int

40 JNJMH.X 0.05 N/A 0.05 0 1,370

45 JNJMI.X 0.1 0.05 0.1 3 5,002

50 JNJMJ.X 0.12 0.1 0.15 1 14,004

55 JNJMK.X 0.25 0.25 0.3 99 31,122

60 JNJML.X 0.7 0.65 0.7 227 69,168

65 JNJMM.X 1.8 1.85 1.95 30 46,774

70 JNJMN.X 5 4.9 5 20 1,582

75 JNJMO.X 13.3 9.7 9.9 0 20

Table 9-1 Options Quotes for Johnson& Johnson at 09/21/2006 (Cont’d)

9.2 The Option market and related definition

Intrinsic value = Underlying asset price－ Option exercise pric

e (9.1)

Time value = Option premium－ Intrinsic value

(9.2)

9.2 The Option market and related definition

where: C = the value of the call option; S = the current stock price; and E = the exercise price.

Max ( , 0)C S E

9.2 The Option market and related definition

FIGURE 9-1 The Relationship Between an Option’s Exercise Price and Its Time Value

9.2 The Option market and related definition

FIGURE 9-2 The Relationship Between Time Value and Time to Maturity for a Near-to-the-Money Option (Assuming a Constant Price for the Underlying Asset)

9.2 The Option market and related definition

Sample Problem 9.1

9.3 Put-call parity

European Options

American Options

Futures Options

Market Applications

9.3 Put-call parity

(9.3)

where: = value of a European call option at time t that matures at time T (T > f);

= value of a European put option at time t, that matures at time T;

= value of the underlying stock (asset) to both the call and put options at time t;

E = exercise price for both the call and put options;

= price at time t of a default-free bond that pays $1 with certainty at time T (if it is assumed that this risk-free rate of interest is the same for all maturities and equal to r － in essence a flat-term structure － then = , under continuous compounding), or = for discrete compounding.

TttTtTt EBSPC ,,,

TtC ,

TtP ,

tS

TtB ,

TtB , tTre

TtB , tTr 1/1

9.3 Put-call parity

(9.4)

(9.5)

Max 0,T TC S E

Max 0,T TP E S

9.3 Put-call parityTABLE 9-2 Put-Call Parity for a European Option with No Dividends

9.3 Put-call parity

Sample Problem 9.2 A call option with one year to maturity and exercise price of

$110 is selling for $5. Assuming discrete compounding, a risk-free rate of 10 percent, and a current stock price of $100, what is the value of a European put option with a strike price of $110 and one-year maturity?

Solution tTtTtTt SEBCP ,,,

100$

1.11110$5$ 11,0

yrP

5$1,0 yrP

9.3 Put-call parity

(9.6) Sample problem 9.3 A put option with one year to maturity and an exercise price of $90 is

selling for $15; the stock price is $100. Assuming discrete compounding and a risk- free rate of 10 percent, what are the boundaries for the price of an American call option?

Solution

ESPCEBSP tTtTtTtTt ,,,,

ESPCEBSP tTtTtTtTt ,,,,

90$100$15$

1.1190$100$15$ ,1

TtC

25$18.33$ 1, yrtC

9.3 Put-call parity(9.7)

(9.8)TABLE 9-3 Put-Call Parity for a European Futures Option

EFBPC TtTtTtTt ,,,,

EBFBCP TtTtTtTtTt ,,,,,

9.4 Risk-return characteristics of options Long Call Short Call Long Put Short Put Long Straddle Short Straddle Long Vertical (Bull) Spread Short Vertical (Bear) Spread Calendar (Time) Spread

9.4 Risk-return characteristics of optionsFIGURE 9-3 Profit Profile for a Long Call

9.4 Risk-return characteristics of options

FIGURE 9-4 Profit Profile for a Short Call

9.4 Risk-return characteristics of options

FIGURE 9-5 Profit Profile for a Covered Short Call

9.4 Risk-return characteristics of options

FIGURE 9-6 Profit Profile for a Long Put

9.4 Risk-return characteristics of options

FIGURE 9-7 Profit Profile for an Uncovered Short Call

9.4 Risk-return characteristics of options

FIGURE 9-8 Profit Profile for a Long Straddle

9.4 Risk-return characteristics of options Sample problem 9.4 Situation: An investor feels the stock market is going to

break sharply up or down but is not sure which way. However, the investor is confident that market volatility will increase in the near future. To express his position the investor puts on a long straddle using options on the S&P 500 index, buying both at-the-money call and put options on the September contract. The current September S&P 500 futures contract price is 155.00. Assume the position is held to expiration.

9.4 Risk-return characteristics of optionsTransaction: 1. Buy 1 September 155 call at $2.00. ($1,000) 2. Buy 1 September 155 put at $2.00. ($1,000) Net initial investment (position value) ($2,000)

Results: 1. If futures price = 150.00:

(a) 1 September call expires at $0. ($1,000) (b) 1 September put expires at $5.00. $2,500(c) Less initial cost of put ($1,000)Ending position value (net profit) $ 500

9.4 Risk-return characteristics of optionsResults:

2. If futures price = 155.00: (a) 1 September call expires at $0. ($1,000)(b) 1 September put expires at $0. ($1,000)Ending position value (net loss) $2,000

3. If futures price = 160.00: (a) 1 September call expires at $5.00 $2,500(b) 1 September call expires at $0. ($1,000)(c) Less initial cost of put ($1,000)Ending position value (net profit) $ 500

9.4 Risk-return characteristics of optionsSummary:

Maximum profit potential: unlimited. If the market had contributed to move below 150.00 or above 160.00, the position would have continued to increase in value.

Maximum loss potential: $2,000, the initial investment.

Breakeven points: 151.00 and 159.00, for the September S&P 500 futures contract.2

Effect of time decay: negative, as evidenced by the loss incurred, with no change in futures price (result 2)

2 Breakeven points for the straddle are calculated as follows: Upside BEP = Exercise price + Initial net investment (in points) 159.00 = 155.00 + 4.00 Downside BEP = Exercise price - Initial net investment (in points) 159.00 = 155.00 + 4.00 151.00 = 155.00 - 4.00

9.4 Risk-return characteristics of options

FIGURE 9-9 Profit Profile for a Short Straddle

9.4 Risk-return characteristics of options Sample problem 9.5 Situation: An investor feels the market is overestimating price volatility

at the moment and that prices are going to remain stable for some time. To express his opinion, the investor sells a straddle consisting of at-the-money call and put options on the September S&P 500 futures contract, for which the current price is 155.00. Assume the position is held to expiration.

Transaction: 1. Sell 1 September 155 call at $2.00 (x $500 per point).

$1,0002. Sell 1 September 155 put at $2.00.

$1,000Net initial inflow (position value) $2,000

9.4 Risk-return characteristics of optionsResults:

1. If futures price = 150.00: (a) 1 September 155 call expires at 0. $1,000 (b) I September 155 put expires at $5.00. ($2,500)(c) Plus initial inflow from sale of put $1,000Ending position value (net loss) ($ 500)

2. If futures price = 155.00: (a) 1 September 155 call expires at 0. $1,000(b) I September 155 put expires at 0. $1,000Ending position value (net profit) $2,000

9.4 Risk-return characteristics of optionsResults:

3. If futures price = 160.00: (a) 1 September 155 call expires at $5.00. ($2,500)(b) I September put expires at 0. $1,000(c) Plus initial inflow from sale of call $1,000Ending position value (net loss) ($ 500)

Summary:

Maximum profit potential: $2,000, result 2. where futures price does not move. Maximum loss potential: unlimited. If futures price had continued up over 160.00 or

down below 145.00, this position would have kept losing money. Breakeven points: 151.00 and 159.00, an eight-point range for profitability of the

position.3

Effect of time decay: positive, as evidenced by result 2.

3 Breakeven points for the short straddle are calculated in the same manner as for the long straddle: exercise price plus initial prices of options.

9.4 Risk-return characteristics of options

FIGURE 9-10 Profit Profile for a Long Vertical Spread

9.4 Risk-return characteristics of options Sample problem 9.6 Situation: An investor is moderately bullish on the West German mark. He would

like to be long but wants to reduce the cost and risk of this position in case he is wrong. To express his opinion, the investor puts on a long vertical spread by buying a lower-exercise-price call and selling a higher-exercise- price call with the same month to expiration. Assume the position is held to expiration.

Transaction: 1. Buy 1 September 0.37 call at 0.0047 (x 125.000 per point). ($

587.50) 2. Sell 1 September 0.38 call at 0.0013. $ 1 62.50

Net initial investment (position value) ($ 425.00)

9.4 Risk-return characteristics of optionsResults: 1. If futures price = 0.3700:

(a) 1 September 0.37 call expires at 0. ($ 587.50)(b) 1 September 0.38 call expires at 0. $ 162.50Ending position value (net loss) ($ 425.00)

2. If futures price = 0.3800: (a) 1 September 0.37 call expires at 0.0100. $1,250.00(b) I September 0.38 call expires at 0. $ 162.50Less initial cost of 0.37 call ($ 587.50)Ending position value (net profit) $ 825.00

3. If futures price = 0.3900: $2,500.00(a) 1 September 0.38 call expires at 0.0200. $2,500.00(b) 1 September put expires at 0. ($1,250.00)Less initial premium of 0.37 call ($ 587.50)Plus initial premium of 0.38 call $ 162.50Ending position value (net profit) ($ 825.00)

9.4 Risk-return characteristics of options

Summary:

Maximum profit potential: $825.00, result 2. Maximum loss potential: $425.00, result 1. Breakeven point: 0.3734.4

Effect of time decay: mixed. positive if price is at high end of range and negative if at low end.

4 Breakeven point for the long vertical spread is computed as lower exercise price plus price of

long call minus price of short call (0.3734 = 0.3700 + 0.0047 – 0.0013).

9.4 Risk-return characteristics of options

FIGURE 9-11 Profit Profile for a Short vertical Spread

9.4 Risk-return characteristics of options

FIGURE 9-12 Profit Profile for a Neutral Calendar Spread

9.4 Risk-return characteristics of optionsTABLE 9-4 Call and Put Option Quotes for CEG at 07/13/2007

Call Option Expiring close Fri Oct 19, 2007

Strike Symbol Bid Ask

70 CEGJN.X 23.5 25.5

75 CEGJO.X 19 20.9

80 CEGJP.X 14.6 16.4

85 CEGJQ.X 11.4 12.2

90 CEGJR.X 8 8.5

95 CEGJS.X 5 5.4

100 CEGJT.X 2.85 3.2

105 CEGJA.X 1.5 1.75

110 CEGJB.X 0.65 0.9

115 CEGJC.X 0.2 0.45

9.4 Risk-return characteristics of optionsTABLE 9-4 Call and Put Option Quotes for CEG at 07/13/2007 (Cont’d)

Put Option Expiring close Fri Oct 19, 2007

Strike Symbol Bid Ask

70 CEGVN.X 0.15 0.35

75 CEGVO.X 0.4 0.65

80 CEGVP.X 0.9 1.15

85 CEGVQ.X 1.6 1.85

90 CEGVR.X 2.95 3.4

95 CEGVS.X 4.9 5.5

100 CEGVT.X 7.7 8.6

9.4 Risk-return characteristics of optionsTABLE 9-5 Value of Protective Put position at option expiration

Long a Put at strike price $95.00     Premium $5.50

Buy one share of stock       Price $94.21

Stock One Share of Stock   Long Put

(X=$95)   Protective Put Value  

Price Payoff Profit Payoff Profit Payoff Profit

$70.00 $70.00 -$24.21 $25.00 $19.50 $95.00 -$4.71

$75.00 $75.00 -$19.21 $20.00 $14.50 $95.00 -$4.71

$80.00 $80.00 -$14.21 $15.00 $9.50 $95.00 -$4.71

$85.00 $85.00 -$9.21 $10.00 $4.50 $95.00 -$4.71

$90.00 $90.00 -$4.21 $5.00 -$0.50 $95.00 -$4.71

$95.00 $95.00 $0.79 $0.00 -$5.50 $95.00 -$4.71

$100.00 $100.00 $5.79 $0.00 -$5.50 $100.00 $0.29

$105.00 $105.00 $10.79 $0.00 -$5.50 $105.00 $5.29

$110.00 $110.00 $15.79 $0.00 -$5.50 $110.00 $10.29

$115.00 $115.00 $20.79 $0.00 -$5.50 $115.00 $15.29

$120.00 $120.00 $25.79 $0.00 -$5.50 $120.00 $20.29

9.4 Risk-return characteristics of options

Figure 9-12 Profit Profile for Protective Put

Protective Put : Profit

-$30

-$20

-$10

$0

$10

$20

$30

$70 $75 $80 $85 $90 $95 $100 $105 $110 $115 $120

Stock Price

Profi

t

One Shareof Stock

Long Put(X=$95)

ProtectivePut Value

9.4 Risk-return characteristics of optionsTable 9-6 Value of Covered Call position at option expiration

Write a call at strike price $100.00   Premium $2.85

Buy one share of stock       Price $94.21

Stock One Share of Stock   Written Call (X=$100)   Covered Call  

Price Payoff Profit Payoff Profit Payoff Profit

$70.00 $70.00 -$24.21 $0.00 $2.85 $70.00 -$21.36

$75.00 $75.00 -$19.21 $0.00 $2.85 $75.00 -$16.36

$80.00 $80.00 -$14.21 $0.00 $2.85 $80.00 -$11.36

$85.00 $85.00 -$9.21 $0.00 $2.85 $85.00 -$6.36

$90.00 $90.00 -$4.21 $0.00 $2.85 $90.00 -$1.36

$95.00 $95.00 $0.79 $0.00 $2.85 $95.00 $3.64

$100.00 $100.00 $5.79 $0.00 $2.85 $100.00 $8.64

$105.00 $105.00 $10.79 -$5.00 -$2.15 $100.00 $8.64

$110.00 $110.00 $15.79 -$10.00 -$7.15 $100.00 $8.64

$115.00 $115.00 $20.79 -$15.00 -$12.15 $100.00 $8.64

$120.00 $120.00 $25.79 -$20.00 -$17.15 $100.00 $8.64

9.4 Risk-return characteristics of options

Figure 9-13 Profit Profile for Covered Call

Covered Call : Profit

-$30

-$20

-$10

$0

$10

$20

$30

$70 $75 $80 $85 $90 $95 $100 $105 $110 $115 $120Stock Price

Profi

t

One Shareof StockWritten Call(X=$100)Covered Call

9.4 Risk-return characteristics of optionsTable 9-7 Value of Collar position at option expirationLong a Put at strike price  $85.00 Premium $1.85

Write a Call at strike price  $105.00 Premium $1.50

Buy one share of stock  Price $94.21

Stock One Share of Stock  Long put (X=$85) Write Call (X=$105) Collar Value

Price Payoff Profit Payoff Profit Payoff Profit Payoff Profit

$70.00 $70.00 -$24.21 $15.00 $13.15 $0.00 $1.50 $85.00 -$9.56

$75.00 $75.00 -$19.21 $10.00 $8.15 $0.00 $1.50 $85.00 -$9.56

$80.00 $80.00 -$14.21 $5.00 $3.15 $0.00 $1.50 $85.00 -$9.56

$85.00 $85.00 -$9.21 $0.00 -$1.85 $0.00 $1.50 $85.00 -$9.56

$90.00 $90.00 -$4.21 $0.00 -$1.85 $0.00 $1.50 $90.00 -$4.56

$95.00 $95.00 $0.79 $0.00 -$1.85 $0.00 $1.50 $95.00 $0.44

$100.00 $100.00 $5.79 $0.00 -$1.85 $0.00 $1.50 $100.00 $5.44

$105.00 $105.00 $10.79 $0.00 -$1.85 $0.00 $1.50 $105.00 $10.44

$110.00 $110.00 $15.79 $0.00 -$1.85 -$5.00 -$3.50 $105.00 $10.44

$115.00 $115.00 $20.79 $0.00 -$1.85 -$10.00 -$8.50 $105.00 $10.44

$120.00 $120.00 $25.79 $0.00 -$1.85 -$15.00 -$13.50 $105.00 $10.44

9.4 Risk-return characteristics of options

Figure 9-14 Profit Profile for Collar

Collar : Profit

-$30

-$20

-$10

$0

$10

$20

$30

$70 $75 $80 $85 $90 $95 $100 $105 $110 $115 $120

Stock Price

Profi

t

One Share ofStockLong put(X=$85)Write Call(X=$105)Collar Value

9.6 Summary This chapter has introduced some of the essential differences between

the two most basic kinds of option, calls and puts. A delineation was made of the relationship between the option’s price or premium and that of the underlying asset. The option’s value was shown to be composed of intrinsic value, or the underlying asset price less the exercise price, and time value. Moreover, it was demonstrated that the time value decays over time, particularly in the last month to maturity for an option.

Index and futures options were studied to introduce these important financial instruments. Put-call parity theorems were developed for European, American, and futures options in order to show the basic valuation relationship between the underlying asset and its call and put options. Finally, investment application of options and related combinations were discussed, along with relevant risk-return characteristics. A thorough understanding of this chapter is essential as a basic tool to successful study of option-valuation models in the next chapter.