1

Trading StrategiesInvolving Options

Chapter 10

2

Positions in an Option & the Underlying

• Buy or sell call

• Buy or sell put

• buy or short sell stock

• buy (lend at) or sell (borrow at) risk-free bond (rate)

3

Trading Strategies Involving Options

• Take a position in the option & the underlying

• Spread: Position in 2 or more options of the same type

• Combination: Position in a mixture of calls & puts

4

Payoff for Put Option

X

x

buy

sell

ST

-X

Cost = p

Cost = -p

5

Payoff for Call Option

X

x

buy

sell

ST

Cost = c

Cost = -c

6

Payoff for Stock

buy

ST

sell

Cost = S

Cost = -S

7Payoff for Investing or Borrowing PV(X) in

Risk-Free Bond

buy

sell

ST

X

-X

Cost = Xe-rT

Cost = -Xe-rT

8

Method

• Draw payoff pattern for each position

• Add patterns together to obtain payout pattern

• Determine cost of portfolio

• Subtract cost of portfolio to obtain profit pattern

9

Write a Covered Call

X

sellcall

ST

buy stock

X Cost = S - c

10

Profit Pattern for Covered Call

X ST

X Cost = S - c

X-S+c

X-S+c-S+c

11

Payoff for Protective Put

X

x

ST

Cost = S + p

12

Profit Pattern Protective Put

x

ST

Cost = S + p

X-S-p

S+p

X

13

Bull Spread

• Buy 1 call and sell 1 call at higher strike

buy

sell

STX1

Cost = c1 - c2 > 0

X2-X1

X2

14

Profit Pattern for Bull Spread

ST

X2-X1 -c1+c2

-c1+c2

15

Bear Spread

• Sell 1 call and buy 1 call at higher strike

buy

sell

STX1

Cost = c1 - c2 < 0

X2-X1

X2

16

Profit Pattern for Bear Spread

STX1

Cost = c1 - c2 < 0

X2

17

Buy a Straddle

• Buy 1 call and 1 put at same strike

X

Cost = c + pX

-p-c

X-p-c X+p+c

profit

payout

18

Butterfly Spread• Buy 1 call at X1, sell 2 calls at X2, buy 1 call

at X3

m = +1

m = - 2

m = -1

Cost = c1 - 2c2 + c3

X1

X2

X3

m = 0

19

Butterfly Spread• Buy 1 call, sell 2 calls, buy 1 call

Cost = c1 - 2c2 + c3

X2-X1 payoff

profitcost

20

Bull Spread Using Calls• Figure 10.2

X1 X2

Profit

ST

21

Bull Spread Using Puts• Figure 10.3

X1 X2

Profit

ST

22

Bear Spread Using Calls• Figure 10.4

X1 X2

Profit

ST

23

Bear Spread Using Puts• Figure 10.5

X1 X2

Profit

ST

24

Butterfly Spread Using Calls• Figure 10.6

X1 X3

Profit

STX2

25

Butterfly Spread Using Puts• Figure 10.7

X1 X3

Profit

STX2

26

A Straddle Combination• Figure 10.10

Profit

STX

27

Strip & Strap• Figure 10.11

Profit

X ST

Profit

X ST

Strip Strap

28

A Strangle Combination• Figure 10.12

X1 X2

Profit

ST

29

Summary• Write covered call: buy stock sell call

• Protective put: buy stock and buy put

• Bull spread: buy X1 call and sell X2 call

• Bear spread: opposite of bull

• Buy Straddle: buy X call and buy X put

• Sell Straddle: opposite of buy straddle

• Strangle: buy X1 put and buy X2 call

• Butterfly spread: buy 1 X1 call, sell 2 X2 calls, and buy 1 X3 call