9fOption Terminology

8/13/2019 9fOption Terminology

1/19

How do derivatives minimize risks?

Forwards, futures and swaps involve firm

commitments to exchanges of cash flows in

the futureat prices or rates determined in

the present.

An option provides the right, but not the

obligation,to a future exchange at a price or

rate determined in the present.


2/19

Options

As we have learned, the holder of a forwardcontract is obliged to trade at maturity. Unlessthe position is closed before maturity the holdermust take possession of the asset, regardless of

whether the underlying asset has risen or fallenin price.Wouldnt it be nice if we only had totake possession of the asset if it had risen?

To address this ,derivatives known as optionsare traded. The two most common ones are calloptions and put options.


3/19

Call Vs Put Option

Call Option

A call option gives the

investor the right (not

the obligation!) to buy

an underlying asset atan agreed upon price

(the strike price) at a

date in the future (the

expiration date)

Put Option

A Put Option gives the

holder the right (but not

the obligation!) to sell an

underlying asset at anagreeduponprice (the

strike price) at a date in

the future (the

expiration date T).


4/19

Option Terminology.

Premiumthe amount paid to the seller for buying an option(call orPut) at the time of agreement.

Strike price (K)The price at which the option holder may buy or sell theunderlying as defined in the option contract.Also known as exerciseprice.

ExerciseAction taken by the option holder to exercise his right.

Time to expiration (T)time units (a time unit has the length t) untilexpiration

European Optionthe holder can exercise this option only at expiry American Optionthe holder can exercise this option at any time during

the life of the option

(The right to exercise at any time is clearly valuable. Therefore the valueof an American option cannot be less than an equivalent Europeanoption)

Market Price, or Spot Price (S)the current price you have to pay in themarket for the underlying.


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Premium

Why does the buyer of an option(call or put),

have to pay a premium?

The buyer of an option has potential for

profit without the risk of a loss. For this

situation the buyer of an option has to pay a

premium.

What is the maximum loss ,that a buyer of an

option can incur?


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Call option

If the market price of the underlying is higher

than the strike price, it is profitable to

exercise the option.

If market price is lower, the option holder

(buyer) is not obliged to exercise it since he

would incur a loss. The option would

automatically expire on its last date(expiry

date)


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Important-Selling an option.

The seller of an option has a limited upside,(

ie limited to the premium received), but an

unlimited downside depending on price

movement. Selling an option is risky.


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Call option

A call option gives the investor the right (not

the obligation!) to buy an underlying asset atan agreed upon price (the strike price) at a

date in the future (the expiration date)

The holder of a call option wants theunderlying asset to rise as much as possible

so that he can buy the asset for a relatively

small amount, then sell it and make money.

The value of a purchased call option is given

by the expression max{SK, 0} .The value

cannot be negative


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Value of an option

Option Price = Intrinsic Value + Time Value.

Intrinsic Value: For a call option, it is thegreater of,(a) Spot price minus Strike Price (b)

Zero. : For a put option, it is the greater of,(a)

Strike price minus Spot Price (b) Zero.

Time Value is the value of an option arising

from time left to maturity/expiry.


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Moneyness of an option

In the case of a call option if the spot price is

greater than the strike price it is Inthe-

Money. If strike price is more than the spot

price, it is Out-of-the-Money .

In the case of a put option if the strike price is

greater than the spot price it is In-the-Money

.If spot price is more than strike price, it isOut of the Money


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Determinants of Option Price/Premium

1. Spot/Market Price

2. Strike Price.

3. Risk free Interest rate r4. Time to expiry.

5. Volatality(Standard Deviation)


12/19

Selling a call option

The call option we have discussed so far is a

purchased call option. But we can sell a call

option also. When we sell a call option we

receive a premium. Then we speak of awritten call option.

The payoff and the profit of a written calloption are just the mirror images of the

corresponding purchased option.


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Put Option

A Put Option gives the holder the right (but not

the obligation!) to sell an underlying asset at an

agreeduponprice (the strike price) at a date in thefuture (the expiration date T).

The holder of a put option wants the underlying

asset to fall as much as possible

The payoff function of a Purchased Put Option is

max{ KS, 0},Cannot be negative.


14/19

Call option Payoff for Buyer/Seller

Spo tpri ce 2 5Stri kep rice 2 7Pre miu m 2

Buy ers S elle rsPrice P ro fit P rofit

20 - 2 221 - 2 222 - 2 223 - 2 224 - 2 225 - 2 226 - 2 227 - 2 228 - 1 129 0 030 1 - 131 2 - 232 3 - 333 4 - 434 5 - 535 6 - 6

-8-6-4-2

02468

Pro fit

Price

Bu yersP rofi tSe llers Profi t

Sp o tp rice 2 5St rik ep rice 2 7P re miu m 2

Buye rs S e lle rsPric e P ro fit P ro fit

20 - 2 221 - 2 2

22 - 2 223 - 2 224 - 2 225 - 2 2

26 - 2 227 - 2 228 - 1 129 0 0

30 1 - 131 2 - 232 3 - 333 4 - 4

34 5 - 535 6 - 6

-8

-6

-4

-2

0

2

4

6

8

202 12 2 23 24 25 2 62 72 82 93 03 1 32 33 34 35P rofit

P rice

B uye rsP rofi tSe lle rsP rofi t

Spot price 29

Strike price 27

Premium 2

Buyers Sellers

Price Profit Profit

20 -2 2

21 -2 2

22 -2 2

23 -2 224 -2 2

25 -2 2

26 -2 2

27 -2 2

28 -1 1

29 0 030 1 -1

31 2 -2

32 3 -3

33 4 -4

34 5 -5

35 6 -6

-8

-6

-4

-2

0

2

4

6

8

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Profit

Price

Buyers Profit

Sellers Profit


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Put option Payoff for Buyer/SellerSpot price 25

Strike price 27

Premium 2

Buyers Sellers

Price Profit Profit

20 5 -5

21 4 -4

22 3 -3

23 2 -2

24 1 -1

25 0 0

26 -1 1

27 -2 2

28 -2 2

29 -2 2

30 -2 2

31 -2 2

32 -2 2

33 -2 2

34 -2 2

35 -2 2

-6

-4

-2

0

2

4

6

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Profit

Price

Buyers Profit

Sellers Profit

C ll V P t


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Call Vs Put CALL OPTION

-8

-6

-4

-2

0

2

4

6

8

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Profit

Price

Buyers Profit

Sellers Profit

PUT OPTION

-6

-4

-2

0

2

4

6

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Profit

Price

Buyers Profit

Sellers Profit


17/19

It may not look like much, but it is the mostdangerous equation since E=MC squared.Just as

Albert Einsteins equation eventually led to

Hiroshima and Nagasaki, this one has had the

financial impact of a nuclear bomb. It

contributed to stock market booms and busts,

to a succession of financial crises and to

economic slumps that lost millions of peopletheir livlihood.It is the Black Scholes formula.

-rt

C=S.N(d1)-Ke .N(d2)


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Black Scholes Option Pricing Model-rt

C=S.N(d1)-Ke .N(d2)

C=Call option Price

S=Current price of stock

K=Strike price of the stock

N(d1) /N(d2) = Probabilities(Cumulative Normal Distribution Function)

e=2.71828

t=time to expiry in years

r=risk free annualised interest rate as a decimal


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Black Scholes Option Pricing Model

d1= ln(S/K)+rt + 0.5 t t

d2= ln(S/K)+rt - 0.5 t

t

9fOption Terminology

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