Options: the basics

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Options the basics
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Content

• What is option?
• Terminology
• No arbitrage
• Pricing Options
• The Binomial Option Pricing Model
• The Black-Scholes Model

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Why do we study options?
The underlying concern Happiness
U(Cnow,Cfuture) We are happier with more Cfuture,
but we are worried about the fluctuation of
Cfuture. As you will see later, options provide
a special payoff structure. In words Our
happiness is derived not only from current
consumption but also from future consumptions
which inherently involves uncertainty. This
ultimately constitutes our risk concern over the
future payoffs of assets that we own. Because of
the special payoff structure of options, holding
options enables us to adjust our risk exposure,
and ultimately change our happiness level.
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Who trade options?

• A quote from Chicago Board Options Exchange
  (CBOE)
• The single greatest population of CBOE users
  are not huge financial institutions, but public
  investors, just like you. Over 65 of the
  Exchange's business comes from them. However,
  other participants in the financial marketplace
  also use options to enhance their performance,
  including
• Mutual Funds
• Pension Plans
• Hedge Funds
• Endowments
• Corporate Treasurers

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How big is option trading?
Figure 6.1 Total number of option contracts
traded in a year in all exchange 1973 1999
(Source CBOE)
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How big is option trading?
Figure 6.1 CBOE average daily trading volume
1973 1999 (Source CBOE)
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How big is option trading?
Figure 6.2 CBOE year-end options open-interest
dollar amount (in thousands)1973 1999 (Source
CBOE)
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Where do we trade options?

• Trading of standardized options contracts on a
  national exchange started in 1973 when the
  Chicago Board Options Exchange (CBOE), the
  world's first listed options exchange, began
  listing call options.
• Options also trade now on several smaller
  exchanges, including
• New York - the American Stock Exchange (AMEX)
• - the International Securities Exchange (ISE)
• Philadelphia - the Philadelphia Stock Exchange
  (PHLX)
• San Francisco - the Pacific Stock Exchange (PCX)

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Where do we trade options?

• Trading of non-standardized (tailor-made) options
  contracts occurs on the Over-the-counter (OTC)
  market. And it is in fact bigger than the
  exchange-traded market for option trading.
• The OTC market is a secondary market that trades
  securities (stocks or options or other financial
  assets) which are not traded on an exchange due
  to various reasons (e.g., an inability to meet
  listing requirements).
• For such securities, broker/dealers negotiate
  directly with one another over computer networks
  and by phone, and their activities are monitored
  by the National Association of Securities
  Dealers.
• One advantage of options traded in OTC is that
  they can be tailored to meet particular needs of
  a corporate treasurer or fund manager.

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Standardized VS Non-Standardized

• Standardized Options
• The terms of the option contract is standardized.
  
• Terms include
• The exercise price (also called the strike price)
• The maturity date (also called the expiration
  date)
• For stock options, this is the third Saturday of
  the month in which the contract expires, or the
  third Thursday of the month if the third Friday
  is a holiday.
• Number of shares committed on the underlying
  stocks
• In US, usually 1 contract 100 shares of stock
• Non-standardized options also involves these
  terms, but they can be anything. For example, 1
  contract underlies 95 shares instead of 100
  shares of stock. Terms being more flexible for
  non-standardized options and are traded in OTC
  market are the two distinct features.

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Option Quotation (standardized)

• You will see how standardized options trading
  would be with a quick look of option quotation
  system.
• Option quotes follow a pattern that enables you
  to easily construct and interpret symbols once
  that formula is understood.
• The basic parts of an option symbol are
• Root symbol Month code Strike price code
• A root symbol is not the same as the ticker
  symbol. Please refer to the option chain for that
  ticker to find the corresponding root.
• In conjunction with the option root symbol, you
  can utilize the tables below to assist you in
  creating or deciphering options symbols.

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Option Quotation (standardized)

• Expiration Month codes
• Strike Price codes
• Exercise quoting price for a call option on
  Microsoft (MSQ) at 27.5 expiring December 2006.
  (MSQ LY)

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What is an option contract?

• There are 2 basic types of options CALLs PUTs
• A CALL option gives the holder the right, but not
  the obligation
• To buy an asset
• By a certain date
• For a certain price
• A PUT option gives the holder the right, but not
  the obligation
• To sell an asset
• By a certain date
• For a certain price
• an asset underlying asset
• Certain date Maturity date/Expiration date
• Certain price strike price/exercise price

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What is an option contract?

• For example, as of Nov 1, 2005 at around 5pm,
  Intel was selling at 22.65 per share.
• A call option that allows the holder to buy a
  share of Intel at the third Saturday of November
  2005 for a price of 20 has a market price of
  2.80
• ONE stock option contract is a contract to buy or
  sell 100 shares. Thus, you need 280 to buy ONE
  such call option contract in the market.

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Call Options payoff

• Assuming you hold ONE contract of that Calls,
  i.e., the call contract allows you to buy 100
  shares of Intel on the third Saturday of December
  at an exercise price of 20/share.
• What is your payoff if Intel at that date is
• (a) Selling _at_ 25
• You will be very happy. To cash in, you do two
  things simultaneously
• 1 exercise your right, and buy 100 Intel at
  20. Total amount you use is 2,000.
• 2 sell 100 shares of Intel at the market price
  (i.e., 25/share). Total amount you get is
  2,500.
• Your payoff is 2,500 - 2,000 500.
• (b) Selling _at_ 19
• You will be very sad. You would not exercise the
  rights. The contract is thus expired without
  exercising.
• Your payoff is 0.

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Call Options payoff

• Exercise Price 20/share.
• If at maturity, market Price 25 gt 20 (You
  exercise and get profit, the option you hold is
  said to be in-the-money because exercising it
  would produce profit)
• If at maturity, market price 19 lt 20(You do
  not exercise, the option you hold is said to be
  out-of-the-money because exercising would be
  unprofitable)
• In general, if you hold a call option contract,
  you want Intels stock price to skyrocket. If
  Intel is selling at 100, you will be really
  happier.
• That means, the value of a call option is higher
  if the underlying assets price is higher than
  the exercise price.
• That also means, the value of a call option is
  zero if the underlying assets price is lower
  than the exercise price. Whether it is 18, 19
  or 2.50, it does not matter, the call option
  will still worth zero.

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Put Options payoff

• Assuming you hold ONE contract of that Puts,
  i.e., the put contract allows you to sell 100
  shares of Intel on the third Saturday of December
  at an exercise price of 22.50/share. (current
  price of this option 0.65)
• What is your payoff if Intel at that date is
• (a) Selling _at_ 25
• You will be very sad. You would not exercise the
  rights. The contract is thus expired without
  exercising.
• Your payoff is 0
• (b) Selling _at_ 19
• You will be very happy. To cash in, you do two
  things simultaneously
• 1 you buy 100 shares of Intel at 19, total
  purchase 1,900
• 2 exercise your right, and sell 100 Intel at
  22.5. Total amount you get is 2,250.
• Your payoff is 2,250 - 1,900 350.

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Put Options payoff

• Exercise Price 22.50/share.
• If at maturity, market Price 25 gt 22.50 (You
  do not exercise, and the option you hold is said
  to be out-of-the-money because exercising would
  be unproductive)
• If at maturity, market price 19 lt 22.50(You
  exercise, and the option you hold is said to be
  in-the-money because exercising would be
  profitable)
• In general, if you hold a put option contract,
  you want Intel to go broke. If Intel is selling
  at a penny, you will be even happier.
• That means, the value of a put option is higher
  if the underlying assets price is lower than the
  exercise price.
• That also means, the value of a put option is
  zero if the underlying assets price is higher
  than the exercise price. Whether it is 23, 24
  or 1000, it does not matter, the put option will
  still worth zero.

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Bunch of Jargons

• Option is a derivative since the value of an
  option depends on the price of its underlying
  asset, its value is derived.
• In the Money - exercise of the option would be
  profitable
• Call market pricegtexercise price
• Put exercise pricegtmarket price
• Out of the Money - exercise of the option would
  not be profitable
• Call market pricegtexercise price
• Put exercise pricegtmarket price
• At the Money - exercise price and asset price are
  equal
• Long buy
• Short sell
• e.g., Long a put on company x buy a put
  contract of company x.
• Short a call on company y sell a call contract
  of company y

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Bunch of Jargons
American VS European Options An American option
allows its holder to exercise the right to
purchase (if a call) or sell (if a put) the
underlying asset on or before the expiration
date. A European option allows its holder to
exercise the option only on the expiration
date.
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Bunch of Jargons

• If the underlying asset of an option is
• A stock then the option is a stock option
• An index the option is an index option
• A future contract the option is a futures
  option
• Foreign currency the option is a foreign
  currency option
• Interest rate the option is an interest rate
  option
• ECMC49F will only focus on stock option. But you
  should know that there are other options trading
  in the market. You should definitely know them
  when you do interview with a firm or an i-bank
  for financial position. You will fail your CFA
  exam if you dont know them.

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Stock options VS stocks

• Lets say you hold a option contract for GE. How
  does that differ from holding GEs stock?
• Similarities
• GEs options are securities, so does GEs stocks.
• Trading GEs options is just like trading stocks,
  with buyers making bids and sellers making
  offers.
• Can easily trade them, say in an exchange.
• Differences
• GEs options are derivatives, but GEs stocks
  arent
• GEs options will expire, while stocks do not.
• There is not a fixed number of options. But there
  is fixed number of stock shares available at any
  point in time.
• Holding stocks of GE entitles voting rights, but
  holding GEs option does not
• GE has control over its number of stocks. But it
  has no control over its number of options.

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Notations
Strike price X Stock price at present
S0 Stock price at expiration ST Price of a call
option C Price of a put option P Risk-free
interest rate Rf Expiration time T Present
time 0 Time to maturity T 0 T
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Payoff of Long Call
If you buy (long) a call option, what is your
payoff at expiration?
Payoff to Call Holder at expiration (ST - X)
if ST gtX 0 if ST lt X Profit to Call
Holder at expiration Payoff Purchase Price
Strike price X Stock price at present
S0 Stock price at expiration ST Price of a call
option C Price of a put option P Risk-free
interest rate Rf Expiration time T Present
time 0 Time to maturity T 0 T

Payoff
Profit
ST
x
Purchase price
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Payoff of Short Call
If you sell (short) a call option, what is your
payoff at expiration?
Payoff to Call seller at expiration -(ST -
X) if ST gtX 0 if ST lt X Profit to Call
seller at expiration Payoff Selling Price
Strike price X Stock price at present
S0 Stock price at expiration ST Price of a call
option C Price of a put option P Risk-free
interest rate Rf Expiration time T Present
time 0 Time to maturity T 0 T

Selling price
ST
x
Profit
Payoff
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Payoff of Long Put
If you buy (long) a put option, what is your
payoff at expiration?
Payoff to Put Holder at expiration 0 if
ST gtX (X ST) if ST lt X Profit to Put Holder
at expiration Payoff - Purchasing Price
Strike price X Stock price at present
S0 Stock price at expiration ST Price of a call
option C Price of a put option P Risk-free
interest rate Rf Expiration time T Present
time 0 Time to maturity T 0 T

Payoff
ST
x
Purchasing price
Profit
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Payoff of Short Put
If you sell (short) a put option, what is your
payoff at expiration?
Payoff to Put seller at expiration 0
if ST gtX -(X ST) if ST lt X Profit to Put
seller at expiration Payoff Selling Price
Strike price X Stock price at present
S0 Stock price at expiration ST Price of a call
option C Price of a put option P Risk-free
interest rate Rf Expiration time T Present
time 0 Time to maturity T 0 T

Profit
Selling price
Payoff
ST
x
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Payoff of Long Put Short Call
If you buy (long) a put option and sell (short) a
call, assuming their exercise prices are the
same, what is your payoff at expiration?
Payoff to Call seller at expiration -(ST -
X) if ST gtX 0 if ST lt X
Payoff to Put Holder at expiration 0 if
ST gtX (X ST) if ST lt X



Payoff
ST
ST
x
x
Payoff
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Payoff of Long Put Short Call
If you buy (long) a put option and sell (short) a
call, assuming their exercise prices are the
same, what is your payoff at expiration?
Payoff to Call seller at expiration -(ST -
X) if ST gtX 0 if ST lt X
Payoff to Put Holder at expiration 0 if
ST gtX (X ST) if ST lt X
-(ST X) (X - ST)


ST
x
Payoff
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Long Put Short Call Long stock
If you buy (long) a put option and sell (short) a
call, as well as holding 1 stock. Assuming the
options exercise prices are the same, what is
your payoff at expiration?
if ST gtX if ST lt X
X if ST gtX X if ST lt X
-(ST X) (X - ST)
Stock price (ST) at time T
Payoff (long the stock)

Total Payoff (risk-free)
x
ST
x
Payoff (short call long put)
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Put-Call Parity
What we just do introduces a very important
concept for pricing options. Holding a portfolio
with (a) 1 stock (which costs S0) (b)
selling one call (which earns C) (c) buying
one put (which costs P) Total value of
constructing portfolio S0 P - C
The payoff at maturity/expiration is always X !!!
Payoff (long the stock)

Total Payoff (risk-free)
x
ST
x
Payoff (short call long put)
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Put-Call Parity
Total value of constructing portfolio S0 P
C Get back X at maturity for sure. Thus X
discounted at the risk-free rate should equal to
the portfolio value now. Thus, S0 P C
X/(1Rf)T In words Current stock price plus
price of a corresponding put option at exercise
price X minus the price of a corresponding call
option with exercise price X is equal to the
present value of X at maturity discounted at
risk-free rate.
Payoff (long the stock)

Total Payoff (risk-free)
x
ST
x
Payoff (short call long put)
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Put-Call Parity
S0 P C X/(1Rf)T Lets do an exercise.
What is the risk-free interest rate? From the
data below, S0 22.65, 05 DEC 22.50 Call sells
at 0.90, C 0.90, X 22.50 05 DEC 22.50 Put
sells at 0.65, P 0.65, X 22.50 Time to
maturity is roughly 6 weeks. Thus, T 6/52 We
have 22.65 0.65 0.90 22.50/(1Rf)6/52
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Readings for next class on pricing options

• Forget about the textbook. Read online free
  sources and the lecture notes.
• Many of the course materials are drawn from CBOE
  learning center Online tutorials
• Click on Options Basics and read
• 1 Options Overview
• 2 Introduction to Options Strategies
• 3 Expiration, Exercise and Assignment
• 4 Options Pricing 1
• There are some other online sources you may find
  useful. For example, optionscentral.com.
• Check out the websites for US exchanges.