options basics and trading strategies for frm/cfa level 1

Options: Basics and Trading

Strategies

Session Agenda

• Part I- Introduction to Options

– What are Options?

– Intrinsic Value of Options

– Returns to Option buyers and sellers

– Put Call Parity

– Bounds and Option Values

– Determinants of Option Values

– Some special cases

3

• Trading Strategies

– Covered Call

– Protective Put

– Spread Strategies

– Combination Strategies

Part II- Options Trading Strategies

Part-I: Introduction to

Options

• Options are contracts that give its buyer the right to buy or sell a particular asset

– In future

– At a pre-decided price (i.e. exercise or strike price)

– Without any obligations

• The seller of the option collects a payment (Option Premium) from the buyer for providing the

option

• Types of options:

– Call or Put Options

• Call Option: gives option holder the right to buy the asset at an agreed price

• Put Options: gives option holder the right to sell the asset at an agreed price

– European or American Options

• European options are those that can only be exercised on expiration.

• American options may be exercised on any trading day on or before expiration

• Positions:

• Long position: An option buyer is said to be in a long position

• Short Position: An option writer (or seller) is said to be in a short position

5

What are Options?

6

Factors that affect Options value

1. Assuming the stock price and all other variables remain the same what will be the impact of an

increase in the risk-free interest rate on the price of an American put option?

A. No impact.

B. Negative.

C. Positive.

D. Cannot be determined.

Solution: B

7

Example Question

8

Intrinsic Value of Options

• Intrinsic value: is the maximum of zero and the value of the option if the option were exercised

immediately.

– At the money:

• When the price of the underlying is the same as the strike price of the option, the option is termed at the

money and exercising it carries a nil pay-off.

– In the money:

• When the price of the underlying is greater than the strike price carried by a call option, the call option is

termed in the money, as exercising it results in a positive pay off.

• When the price of the underlying is less than the strike price carried by a put option, the put option is termed in

the money, as exercising it results in a positive pay off.

– Out of the money:

• When the price of the underlying is less than the strike price carried by a call option, the call option is termed

out of the money, as exercising it will result in a nil pay off.

• When the price of the underlying is greater than the strike price carried by a put option, the put option is termed

out of the money, as exercising it will result in a nil pay off.

9


• Illustration: Pay-offs from buying a Call

– Call option is written on the stock of XYZ Corporation with a strike price of 5. Consider options on a stock

whose price is expected to range from 0 - 10 at the time of expiration.

– If share price is less than 5, then the pay off to the option buyer is nil.

– If the price is more than 5, the pay-off moves upward linearly with the share price.

0

1

2

3

4

5

6

0 2 4 6 8 10 12C

all

-Pa

yo

ff

Stock Price

Call Value

Stock

Price

Call

Value

Put Value Strike

Price

0 0 5 5

1 0 4 5

2 0 3 5

3 0 2 5

4 0 1 5

5 0 0 5

6 1 0 5

7 2 0 5

8 3 0 5

9 4 0 5

10 5 0 5

10


• Illustration: Pay-offs from buying a Put

– Put option is written on the stock of XYZ Corporation with a strike price of 5. Consider options on a

stock whose price is expected to range from 0 - 10 at the time of expiration.

– If share price is more than 5, then the pay off to the option buyer is nil.

– If the price is less than 5, the pay-off moves linearly with the share price.

0

1

2

3

4

5

6

0 2 4 6 8 10 12P

ut-

Pa

yo

ff

Stock Price

Put Value

Stock

Price

Call

Value

Put Value Strike

Price

0 0 5 5

1 0 4 5

2 0 3 5

3 0 2 5

4 0 1 5

5 0 0 5

6 1 0 5

7 2 0 5

8 3 0 5

9 4 0 5

10 5 0 5

11

Payoffs from Options

12

Returns to Option Sellers

• Returns to Option sellers:

– The price that the option writer gets for underwriting the contract is called premium.

– If the option is not exercised, the option writer makes profit from the premium.

– If the option is exercised, the option writer may make profit or loss depending on the spot price of the

underlying asset at the time.

• Example: A Call option writer gets premium of 1 for an option with strike price of 5.

– He makes a profit if:

• The option is not exercised when spot price is less than 5. The profit is 1 (i.e. premium);

• The option is exercised and spot price is more than 5 but less than 6.

• The profit to the call writer is less than 1.

• If the spot price is 6, the writer has no profit and no loss.

• For all spot prices more than 6, the call writer makes losses, which increase linearly with increase in spot

prices.

13

-5

-4

-3

-2

-1

0

1

2

0 2 4 6 8 10 12

Sho

rt-P

ut

Pay

off

Stock Price

Short-Put Payoff with Premium

-5

-4

-3

-2

-1

0

1

2

0 2 4 6 8 10 12

Sho

rt C

all P

ayo

ff

Stock Price

Short-Call Payoff with Premium

Returns to Option Sellers

Stock

Price

Option

Premium

Short-Call

Value

Put Value Strike

Price

0 1 1 -4 5

1 1 1 -3 5

2 1 1 -2 5

3 1 1 -1 5

4 1 1 0 5

5 1 1 1 5

6 1 0 1 5

7 1 -1 1 5

8 1 -2 1 5

9 1 -3 1 5

10 1 -4 1 5

14

Returns to Option Buyers

• Profit to Option buyers:

– The pay-off are distinct from the profit (or loss) to the option holder.

– To estimate the profit, the premium (price of option) is to be subtracted from the pay-off.

• Illustration: In continuation to above, further consider options which carries a premium of 1.

-2

-1

0

1

2

3

4

5

0 2 4 6 8 10 12Long

Cal

l Pay

off

Stock Price

Long-Call Payoff with Premium

-2

-1

0

1

2

3

4

5

0 2 4 6 8 10 12Lon

g-P

ut P

ayo

ffStock Price

Long-Put Payoff with Premium

Stock

Price

Option

Premium

Call Value Put Value Strike

Price

0 1 -1 4 5

1 1 -1 3 5

2 1 -1 2 5

3 1 -1 1 5

4 1 -1 0 5

5 1 -1 -1 5

6 1 0 -1 5

7 1 1 -1 5

8 1 2 -1 5

9 1 3 -1 5

10 1 4 -1 5

15

Put Call parity

• Consider the Pay-off of a trader who has the following position:

– A Call Option with a Strike Price of 5 and,

– A Bond with a maturity value of 5.

Share Price at

Expiration

Call

Pay-Off Strike Price

Bond Value at

Maturity Bond + Call

0 - 5 0 5 5 5

6 1 5 5 6

7 2 5 5 7

8 3 5 5 8

9 4 5 5 9

10 5 5 5 10

16

Put Call parity

• Consider, now, the Pay-off of a trader who has :

– A Put Option with a Strike Price of 5 and,

– An equivalent unit of the underlying asset

Share Price at

Expiration

Put Pay-Off (Exercise

Price 5)

Stock

Pay-off

Stock+

Put

0 5 0 5

1 4 1 5

2 3 2 5

3 2 3 5

4 1 4 5

5-10 0 5-10 5-10

17

Put Call parity

• The Pay-offs are exactly the same

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Share Price

To

talP

ay

-off

18

Put Call parity

• Put Call parity provides an equivalence relationship between the Put and Call options of a

common underlying and carrying the same strike price:

• It can be expressed as:

– Value of call + Present value of strike price = value of put + share price.

• If value of put is not available, it can be derived as:

– Value of put = Value of call + present value of strike price - share price.

• Put-call parity relationship, assumes that the options are not exercised before expiration day, i.e. it

follows European options.

• This holds true for American options only if they are not exercised early.

• In case of dividend-paying stocks, either the amount of dividend paid should be known in advance or it

is assumed that the strike price factors the future dividend payment.

• The mathematical representation of Put Call Parity is:

= Initial stock price (S) + Put premium (P)

Put Call Parity is valid only for European options, for American Options this

relationship turns into an inequality

tt r

ddividendsofPV

r

XpricestrikeofPVCemium

11)(Pr

19

Question: Put Call parity

1. According to Put Call parity for European options, purchasing a put option on ABC stock will be

equivalent to

A. Buying a call, buying ABC stock and buying a Zero Coupon bond.

B. Buying a call, selling ABC stock and buying a Zero Coupon bond.

C. Selling a call, selling ABC stock and buying a Zero Coupon bond.

D. Buying a call, selling ABC stock and selling a Zero Coupon bond

Solution: B: p + S0 = c + Ke-rT

20

Question: Put Call parity

1. Consider a 1-year European call option with a strike price of $27.50 that is currently valued at $4.10

on a $25 stock. The 1-year risk-free rate is 6%.What is the value of the corresponding put option?

A. 4.1

B. 5

C. 6

D. 25

Solution: p + S0 = c + D + Xe -rt

21

Bounds and Option Values

• The value of an option changes over its life.

• Consider the earlier illustration of the call.

– If the share price of is below 5 on the exercise date, the call will be worthless.

– If the stock price is above 5, the call will be worth 5 less than the value of the stock.

– Even before maturity of the option, its value can never remain below this lower-bound line.

– For options that still have some time to run, the heavy lower line is thus the lower-bound limit on the

market price of the option.

– The diagonal line in the plot is the upper bound limit to the option price, because the stock gives a higher

ultimate pay-off than the option.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11

Call

Pay-

off

Share Price

22


• The value of an option changes over its life.

• Consider the earlier illustration of the call.

– If at the option’s expiration, stock price > exercise price, the option is worth the stock price minus the

exercise price.

– If the stock price < exercise price, the option is worthless. But the share owners still have a valuable

financial asset in the form of stock of ABC Corporation.

– The value of the option would lie between these two bounds throughout the option’s life.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11

Call

Pay-

off

Share Price

23

Option Minimum Value Maximum

Value

European call (c) ct ≥ Max(0,St-(X/(1+RFR)t) St

American Call

(C)

Ct ≥ Max(0, St-(X/(1+RFR)t) St

European put (p) pt ≥Max(0,(X/(1+RFR)t)-St) X/(1+RFR)t

American put (P) Pt ≥ Max(0, (X-St)) X

Where t is the time to expiration


Part-II: Options Trading

Strategies

25

Trading Strategies

• Traders may create positions using different kinds of strategies depending on the:

– Expectations regarding the movement of the price of the underlying

– Risk appetite

– Availability of contracts

26

Covered Call

• Involves selling call options of stocks already owned or simultaneously bought

• Motivation

– Earning a return from the underlying that is already owned

– Lowering the cost of acquisition of the underlying asset

• Expectation`

– Moderate rise in the price of the underlying

• Profit Potential

– Maximum Profits when the options are exercised by the buyer

• Premium received + Strike Price – Spot Price

– If the options are not exercised the trader gets to keep the premium, thus lowering the cost of acquiring the

asset

• More conservative than buying the stock only Stock price

at expiration

Net

profit/loss

Comparison to

simple stock

purchase

$30 (200) (300)

$32 0 (100)

$33 100 0

$35 300 200

$37 300 400

If MyCompany (MC) trades at Rs33 and Rs35 calls are priced at Rs1, then

an investor can purchase 100 shares of MC for Rs3300 and sell one (100-

share) call option for Rs100, for a net cost of only Rs3200. The Rs100

premium received for the call will cover a Rs1 decline in stock price. The

break-even point of the transaction is Rs32/share. Upside potential is

limited to $300, but this amounts to a return of almost 10%. (If the stock

price rises to Rs35 or more, the call option holder will exercise his option

and the investor's profit will be Rs35-Rs32 = Rs3). If the stock price at

expiry is below Rs35 but above Rs32, the call option will be allowed to

expire, but the investor can still profit by selling his shares. Only if the price

is below Rs32/share will the investor experience a loss.

27

Protective Put

• Involves buying put options of stocks already owned or simultaneously bought

• Motivation

– Protection against loss in the value of stocks owned

• Expectation

– Rise in the price of the underlying

• Advantage

– Trader profits from the rise in price of the underlying albeit the amount of profit is reduced by the premium

paid to purchase the put

– In case the price of the underlying goes down, the trader is still able to sell the underlying at the strike

price, thus insuring her profit

28

Spread Strategies

Bull Call Spread

• Involves purchase of Call options at a particular strike price and selling Call options for the same

underlying and carrying the same maturity but having a higher strike price.

– A vertical spread

• Motivation

– Downside protection by agreeing to a limit to the upside profits

• Expectation

– Moderate rise in the price of the underlying


– Maximum Profits when the trader is able to exercise the option purchased, i.e. the spot price is greater

than the strike price of the option written

• Difference in Strike Prices + Premium Received – Premium Paid

– Loss is limited to

• Premium Paid – Premium Received, when the options expire unexercised

29

Spread Strategies (Cont...)

• Bull Call Spread

-4

-2

0

2

4

6

8

95 100 105 110 115 120 125

Share Price

30

Bear Spread

• Involves purchase of put options at a particular strike price and the sale of the same put options at a

lower strike price.

– A vertical spread

• Motivation

– Downside protection by agreeing to a limit to the upside profits

• Expectation

– Moderate fall in the price of the underlying


– Maximum Profits when the trader is able to exercise the option purchased, i.e. the spot price is lower than

the strike price of the option written

• Difference in Strike Prices + Premium Received – Premium Paid


• Premium Paid – Premium Received, when the options expire unexercised`


31

• Bear Spread

-4

-2

0

2

4

6

8

95 100 105 110 115 120 125

Share Price

Tota

l Pro

fits


32

Butterfly Spread

• Involves sale and purchase of two calls (or puts) of the same underlying carrying the same maturity. A

Long Call Butterfly can be established by selling two at the money calls with strike price say P, buying

one out of money call at price say P+X and buying another in the money call at price say P-X.

• Motivation

– To profit even when the price of the underlying is range bound and limit losses in case it moves beyond the

expected bound

• Expectation

– Not much change in the price of the underlying.


– Profits translate when the stock price remains within the bounds indicated by the purchased calls. Profits

are maximized when the price of the underlying remains unchanged


• Premium Paid – Premium Received, when the options expire unexercised


33

• Butterfly Spread

-4

-2

0

2

4

6

8

10

100 105 110 115 120 125 130

SharePrice

Tota

l Pro

fits


34

Combination Strategies

• Combination Strategy: Positions taken in both the call as well as the put options of the same

underlying stocks.

Straddle

• Involves purchasing same quantity of at the money call and put options carrying the same strike price

and same maturity.

• Motivation

– To profit from wide variations in the price of the underlying, even though the direction of the movement in

price is uncertain.

• Expectation

– Large change in the price of the underlying.


– Profits translate when any one of the options can be exercised and the resultant pay-off is greater than the

premium paid for establishing the position. Profit potential is unlimited.


• Premium Paid

35

• Straddle

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Straddle Profits

SharePrice

Tota

l Pro

fits

Combination Strategies (Cont...)

36

Strap

• Involves purchasing two at the money calls for every one at the money put purchased. Both put and

call options carry the same strike price and same maturity. More bullish version of the straddle

• Motivation


price is uncertain.

• Expectation

– Large change in the price of the underlying, price expected to increase more than decrease



premium paid for establishing the position. Profit potential is unlimited although the rise profit is steeper in

case the underlying price increases more than the call strike price.


• Premium Paid


37

• Strap

-4

-3

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10

Strap Profits

SharePrice

Tota

l Pro

fits


38

Strip

• Involves purchasing two at the money puts for every one at the money call purchased. Both put and

call options carry the same strike price and same maturity. Bearish version of the straddle

• Motivation


price is uncertain.

• Expectation

– Large change in the price of the underlying, price expected to decrease more than increase



premium paid for establishing the position. Profit potential is unlimited although the rise profit is steeper in

case the underlying price decreases more than the put strike price.


• Premium Paid


39

• Strip

-4

-3

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10

Strip Profits

SharePrice

Tota

l Pro

fits


40

Long Strangle

• Involves purchasing slightly out of money calls and puts of the same underlying carrying the same

maturity.

• Motivation


price is uncertain.

• Expectation

– Large change in the price of the underlying



premium paid for establishing the position.


• Premium Paid


41

• Long Strangle

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Strangle ProfitsTo

tal P

rofit

s

SharePrice


42

• Box Spread

• Involves purchasing a Bull Call Spread and one Bear Put Spread. Box Spread yields us Risk-free rate


43

Questions

1. The S&P March 2005 index futures contract is trading at 280. The associated American 260 call

option is at 16 and the associated 260 American put option is at 3. Which of the following strategies

would you select to lock in a profit?

A. No strategy would result in a risk-free profit.

B. Buy the put, sell the call and buy the futures contract.

C. Buy and exercise the put and buy the futures contract.

D. Buy and exercise the call and sell the futures contract.

2. An investor sells a June 2008 call of ABC Limited with a strike price of USD 45 for USD 3 and buys a

June 2008 call of ABC Limited with a strike price of USD 40 for USD 5. What is the name of this

strategy and the maximum profit and loss the investor could incur?

A. Bear Spread, Maximum Loss USD 2, Maximum Profit USD 3

B. Bull Spread, Maximum Loss Unlimited, Maximum Profit USD 3

C. Bear Spread, Maximum Loss USD 2, Maximum Profit Unlimited

D. Bull Spread, Maximum Loss USD 2, Maximum Profit USD 3

44

Solution

1. D

2. D

Five Minute Recap

45

-4

-2

0

2

4

6

8

95 100 105 110 115 120 125

Share Price

-4

-2

0

2

4

6

8

95 100 105 110 115 120 125

Share Price

Tota

l Pro

fits

Bull Call Spread

Bear Spread

-4

-2

0

2

4

6

8

10

100 105 110 115 120 125 130

SharePrice

Tota

l Pro

fits

Butterfly Spread

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Straddle Profits

SharePrice

Tota

l Pro

fits

-4

-3

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10

Strap Profits

SharePrice

Tota

l Pro

fits

-4

-3

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10

Strip Profits

SharePrice

Tota

l Pro

fits

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Strangle Profits

Total

Prof

its

SharePrice

Option Trading Strategies:

•Covered Call

•Protective Put

•Combination Strategy

Other Webinars

Here are the links for the blogs of the other recent webinars on our website to

help you with CFA/FRM preparation

Linear regression analysis (11/04/2013)

Blog: http://www.edupristine.com/blog/demystifying-linear-regression-analysis-

for-frm-level-1-exam/

Understanding Income statement (12/04/2013)

Blog: http://www.edupristine.com/blog/cfa-tutorial-understanding-income-

statement-from-cfa-perspective/

Hedging strategies using futures (13/04/2013)

Blog: http://www.edupristine.com/blog/frm-tutorial-hedging-strategies-using-

futures-for-frm-level-1-exam/

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http://www.edupristine.com/blog/demystifying-linear-regression-analysis-for-frm-level-1-exam/

















http://www.edupristine.com/blog/cfa-tutorial-understanding-income-statement-from-cfa-perspective/















http://www.edupristine.com/blog/frm-tutorial-hedging-strategies-using-futures-for-frm-level-1-exam/





















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options basics and trading strategies for frm/cfa level 1

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