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

sellSTX1

Cost = c1 - c2 > 0X2-X1

X2

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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

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Profit Pattern for Bear Spread

STX1

Cost = c1 - c2 < 0

X2

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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

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Bull Spread Using Calls• Figure 10.2

X1 X2

Profit

ST

21

Bull Spread Using Puts• Figure 10.3

X1 X2

Profit

ST

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Bear Spread Using Calls• Figure 10.4

X1 X2

Profit

ST

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Bear Spread Using Puts• Figure 10.5

X1 X2

Profit

ST

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Butterfly Spread Using Calls• Figure 10.6

X1 X3

Profit

STX2

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Butterfly Spread Using Puts• Figure 10.7

X1 X3

Profit

STX2

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A Straddle Combination• Figure 10.10

Profit

STX

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Strip & Strap• Figure 10.11

Profit

X ST

Profit

X ST

Strip Strap

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A Strangle Combination• Figure 10.12

X1 X2

Profit

ST

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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