Mechanics of Options Markets

Presented by:

Akhil Jain

00811403909

1

Types of Options

A call is an option to buy A put is an option to sell A European option can be exercised only

at the end of its life An American option can be exercised at

any time

2

  Call Option Put Option

Option Buyer Buys the right to buy the underlying asset at the Strike Price

Buys the right to sell the underlying asset at the Strike Price

Option Seller Has the obligation to sell the underlying asset to the option holder at the Strike Price

Has the obligation to buy the underlying asset from the option holder at the Strike Price

Option Positions

Long callLong putShort callShort put

4

Long Call

Profit from buying one European call option: option price = $5, strike price = $100.

30

20

10

0-5

70 80 90 100

110 120 130

Profit ($)

Terminalstock price ($)

5

Short Call

Profit from writing one European call option: option price = $5, strike price = $100

-30

-20

-10

05

70 80 90 100

110 120 130

Profit ($)

Terminalstock price ($)

6

Long Put

Profit from buying a European put option: option price = $7, strike price = $70

30

20

10

0

-770605040 80 90 100

Profit ($)

Terminalstock price ($)

7

Short Put

Profit from writing a European put option: option price = $7, strike price = $70

-30

-20

-10

7

070

605040

80 90 100

Profit ($)Terminal

stock price ($)

8

Payoffs from OptionsWhat is the Option Position in Each Case? K = Strike price, ST = Price of asset at maturity

Payoff Payoff

ST STK

K

Payoff Payoff

ST STK

K

9

Illustration on Call Option

Let’s say that you entered into a call option on IBM stock: Today IBM is selling for roughly $78.80/share, so let’s say you

entered into a call option that would let you buy IBM stock in December at a price of $80/share.

If in December the market price of IBM were greater than $80, you would exercise your option, and purchase the IBM share for $80.

If, in December IBM stock were selling for less than $80/share, you could buy the stock for less by buying it in the open market, so you would not exercise your option.

Thus your payoff to the option is $0 if the IBM stock is less than $80 It is (ST-K) if IBM stock is worth more than $80

Thus, your payoff diagram is:

Long Call on IBMwith Strike Price (K) = $80

-20

0

20

40

60

80

0 20 40 60 80 100 120 140 160

IBM Terminal Stock Price

Pay

off

K =

What if you had the short position? Well, after you enter into the contract, you have granted the

option to the long-party. If they want to exercise the option, you have to do so. Of course, they will only exercise the option when it is in there

best interest to do so – that is, when the strike price is lower than the market price of the stock. So if the stock price is less than the strike price (ST<K), then the long

party will just buy the stock in the market, and so the option will expire, and you will receive $0 at maturity.

If the stock price is more than the strike price (ST>K), however, then the long party will exercise their option and you will have to sell them an asset that is worth ST for $K.

We can thus write your payoff as: payoff = min(0,ST-K),

which has a graph that looks like:

Short Call Position on IBM Stockwith Strike Price (K) = $80

-85

-63.75

-42.5

-21.25

0

21.25

0 20 40 60 80 100 120 140 160

Ending Stock Price

Pay

off t

o S

hort

Pos

ition

Illustration on Put Option

Recall that a put option grants the long party the right to sell the underlying at price K.

Returning to our IBM example, if K=80, the long party will only elect to exercise the option if the price of the stock in the market is less than $80, otherwise they would just sell it in the market.

The payoff to the holder of the long put position, therefore is simply

payoff = max(0, K-ST)

Payoff to Long Put Option on IBMwith Strike Price of $80

-10

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120 140 160

Ending Stock Price

Pay

off

The short position again has granted the option to the long position. The short has to buy the stock at price K, when the long party wants them to do so. Of course the long party will only do this when the stock price is less than the strike price.

Thus, the payoff function for the short put position is:

payoff = min(0, ST-K)

And the payoff diagram looks like:

Options Trading

At-the-money optionIn-the-money optionOut-of-the-money option

18

Long Call on IBMwith Strike Price (K) = $80

-20

0

20

40

60

80

0 20 40 60 80 100 120 140 160

IBM Terminal Stock Price

Pay

off

K =

T

Out of the money In the money

At the money

Intrinsic valueTime value

20

Illustration

Suppose market price of share is Rs. 260, the exercise price of a call option on the share is Rs. 250, and the market price of the call option is Rs. 15.

Thus the intrinsic value of the option is Rs. 10 and the time value of the option is Rs. 5.

Thank You !