10.1

Trading StrategiesInvolving Options

Chapter 10

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)

10.3

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

10.4

Payoff for Put Option

X

x

buy

sell

ST

-X

Cost = p

Cost = -p

10.5

Payoff for Call Option

X

x

buy

sell

ST

Cost = c

Cost = -c

10.6

Payoff for Stock

buy

ST

sell

Cost = S

Cost = -S

10.7Payoff for Investing or Borrowing PV(X) in

Risk-Free Bond

buy

sell

ST

X

-X

Cost = Xe-rT

Cost = -Xe-rT

10.8

Method

• Determine cost of portfolio

• Draw payoff pattern for each position

• Add patterns together to obtain payout pattern

• Subtract cost of portfolio to obtain profit pattern

10.9

Write a Covered Call

X

sellcall

ST

buy stock

X Cost = S - c

10.10

Profit Pattern for Covered Call

X ST

X Cost = S - c

X-S+c

X-S+c-S+c

10.11

Payoff for Protective Put

X

x

ST

Cost = S + p

10.12

Profit Pattern Protective Put

x

ST

Cost = S + p

X-S-p

S+p

X

10.13

Bull Spread

• Buy 1 call and sell 1 call at higher strike

buy

sell

STX1

Cost = c1 - c2 > 0

X2-X1

X2

10.14

Profit Pattern for Bull Spread

ST

X2-X1 -c1+c2

-c1+c2

10.15

Bear Spread

• Sell 1 call and buy 1 call at higher strike

buy

sell

STX1

Cost = c1 - c2 < 0

X2-X1

X2

10.16

Profit Pattern for Bear Spread

STX1

Cost = c1 - c2 < 0

X2

10.17

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

10.18

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

10.19

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

Cost = c1 - 2c2 + c3

X2-X1 payoff

profitcost

10.20

Bull Spread Using Calls• Figure 10.2

X1 X2

Profit

ST

10.21

Bull Spread Using Puts• Figure 10.3

X1 X2

Profit

ST

10.22

Bear Spread Using Calls• Figure 10.4

X1 X2

Profit

ST

10.23

Bear Spread Using Puts• Figure 10.5

X1 X2

Profit

ST

10.24

Butterfly Spread Using Calls• Figure 10.6

X1 X3

Profit

STX2

10.25

Butterfly Spread Using Puts• Figure 10.7

X1 X3

Profit

STX2

10.26

A Straddle Combination• Figure 10.10

Profit

STX

10.27

Strip & Strap• Figure 10.11

Profit

X ST

Profit

X ST

Strip Strap

10.28

A Strangle Combination• Figure 10.12

X1 X2

Profit

ST

10.29

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

10.30

Payoff Table

• Identify critical price ranges

• For each position determine payoff in each critical range

• Sum payoffs across each critical range

10.31

Example: Straddle

Payoff

Action: ST < X ST ≥ X

Buy Call 0 ST - X

Buy Put X - ST 0

Portfolio X - ST ST - X