Introduction

• There are important differences between options and forwards/futures.
• With forwards and futures, a trader is obligated to buy or sell the
  underlying asset at a certain price. As a result, it costs nothing to take
  a long or short forward/futures position.
• By contrast, an option involves paying a certain amount (called the
  premium) to obtain the right to buy (or sell) an asset at a certain price
  in the future. However, this right does not have to be exercised.
• In the US, tens of millions of options are traded daily on exchanges such as
  the CBOE, NASDAQ, the New York Stock Exchange, and the International
  Securities Exchange.
• Exchanges trading options outside of the United States include
• the Eurex,
• the National Stock Exchange of India, and
• BM&FBOVESPA.

• Options are also traded globally in the over-the-counter market.

Calls And Puts

• A European call (or put) option gives the buyer the right to buy (or sell)
  an asset at a certain price on a specific date.
• An American call (or put) option gives the buyer the right to buy (or sell)
  an asset at a certain price at any time before and during the specified
  date.
• The date specified in the option is known as the expiration date (also
  called the maturity date).
• Most (though not all) exchange-traded options are American. By contrast,
  many of the options traded in the over-the-counter market are European.
• The price at which an asset can be bought or sold using an option is
  referred to as the strike price (also called the exercise price).

• American options are more difficult to analyze than European options because
  they can be exercised at any time before maturity.

Moneyness

• Options can be in-the-money, at-the-money, or out-of-the-money. This is
  referred to as their moneyness.
• An option that would give a positive payoff if exercised today is referred
  to as in-the-money.
• If it would give a negative payoff, the option is referred to as
  out-of-the-money.
• An option that is at-the-money would give a payoff of zero.
• A call (put) option is in-the-money when the asset price is greater (less)
  than the strike price.
• A call (put) option is out-of-the-money when the asset price is less
  (greater) than the strike price.
• An option is referred to as at-the-money when the strike price equals the
  asset price.

Profits From Call Option – Example

• Suppose a trader buys an out-of-the-money European call option with a strike
  price of USD 60 for an asset currently worth USD 55. The option premium is
  USD 4 and the expiration date is six months from the day of transaction
• Let
  
  be the asset price on the expiration date.
• Profit as a function of asset price on the expiration date for the buyer of
  a European call option is shown in this figure.

• Now consider the situation of the call option’s seller. Selling (or
  shorting) an option is also referred to as writing the option.
• Profit as a function of asset price on the expiration date for the seller of
  a European call option is shown in this figure.

• Options (like other derivatives) are zero-sum games in the sense that one
  side’s gain always equals the other side’s loss.

Profits From Put Option

• Now suppose a trader buys an out-of-the-money European put option with a
  strike price of USD 60 for an asset currently worth USD 62. The option
  premium is USD 5, and the expiration date is three months from the date of
  transaction.
• Profit as a function of asset price on the expiration date for the buyer of
  a European put option is shown in this figure.

• The profit of the corresponding put option seller is the mirror image of the
  profit of the option buyer.
• Profit as a function of asset price on the expiration date for the seller of
  a European put option is shown in this figure.

Payoffs

• Instead of characterizing a European option by its profit, ONLY the payoff
  can be plotted as a function of the asset price on the expiration date.
  These plots show the value of the option at maturity and do not account for
  how much was paid to purchase the option.

• Denoting the asset price on the expiration date by S and the strike price by
  K, the payoffs from the option positions are as follows:
• Long Call –

max⁡( S – K, 0)

• • Short Call –

– max⁡( S – K, 0)=min⁡( K – S, 0)

• • Long Put –

max⁡( K – S, 0)

• • Short Put –

− max⁡( K – S, 0) = min⁡( S – K, 0)

• Intrinsic value measures the value the option would have if it could only be
  exercised immediately. The intrinsic value of a call is
  and
  the intrinsic value of a put is
  .

Exchange-Traded Options On Stocks

• CBOE is the largest options exchange in the world and trades over a billion
  contracts each year. The options on individual stocks are American-style
  (i.e., they can be exercised at any time before their maturities).
• When a trader with a long position decides to exercise, the Options Clearing
  Corporation uses a random procedure to choose a trader with a short position
  to be exercised against. (This trader is referred to as being assigned.)
• Options that are in the-money at maturity are usually exercised
  automatically.
• A single option contract on the CBOE is the right to buy or sell 100 shares.

Maturity

• Stock options on the CBOE are assigned one of the following maturity cycles:
  • January, April, July, and October (referred to as the January cycle);
  • February, May, August, and November (referred to as the February cycle);
    and
  • March, June, September, and December (referred to as the March cycle).
• Prior to the third Friday of the current month, options trade with
  maturities in the current month, the following month, and the next two
  months in the cycle. Following the third Friday of the current month,
  options trade with maturities in the next month, the month after that, and
  the next two months in the expiration cycle. For example, IBM is on a
  January cycle –
  • This means that at the beginning of April, options trade with maturities
    in April, May, July, and October.
  • After the third Friday in April, they trade with expirations in May,
    June, July, and October.
• The precise maturity date is the third Friday of the month.
• Trading takes place every business day (8:30 p.m. to 3:00 p.m. Chicago time)
  until the maturity date.

• The CBOE also offers short-term options called Weeklys and long-term options
  known as LEAPS (long-term equity anticipation securities).
  • Weeklys mature on Fridays, other than the third Friday of the month, and
    are typically offered on several such Fridays.
  • LEAPS on individual stocks mature on the third Friday of January and
    provide maturities of up to three years.

Strike Prices

• The CBOE sets option strike prices as follows –
  • When the current price of the underlying asset is between USD 5 and USD
    25, strike prices are usually multiples of USD 2.50
  • When the current price is between USD 25 and USD 200, strike prices are
    usually multiples of USD 5.
  • When the current price is greater than USD 200, they are usually
    multiples of USD 10.
• Strike prices are also adjusted for dividends and splits (as will be
  described in the next section).
• Initially, the three strike prices closest to the current price are
  typically listed. As the stock price moves, more strike prices are
  introduced.
  • For example, suppose the stock price is USD 19 when trading for a new
    options contract begins.
    • Initially, strike prices of USD 17.50, USD 20.00, and USD 22.50
      would be traded.
    • If the stock price moved below USD 17.50, options with a strike
      price of USD 15 would start trading.
    • If the price moved above USD 22.50, options with a strike price of
      USD 25 would start trading.

Dividends And Stock Splits

• Cash dividends usually do not affect the terms of a stock option. However,
  exceptions are sometimes made when the cash dividend is unusually large.
• In contrast, stock splits do lead to strike price adjustments. For example,
  if a company announces a 5-to-1 stock split (i.e., each share is replaced by
  five new shares), the strike price will be reduced to one fifth of the
  original price and the number of options is multiplied by five.
• Similarly, stock dividends also lead to strike price adjustments. Note that
  a 10% stock dividend means shareholders receive one new share for each ten
  shares owned (this is identical to an 11-to-10 stock split). Using the stock
  split rule, the strike price will be reduced to ten-elevenths of its
  original level and the number of options is multiplied by 11/10.
• All these adjustments are designed to keep the positions of buyers and
  sellers unchanged by incidents of stock splits or stock dividends.

Index Options

• In addition to options on individual stocks, the CBOE also offers options on
  equity indices. Among these include the S&P 500 Index, the S&P 100
  Index, the Dow Jones Industrial Average, the Russell 1000, the FTSE 100, and
  the FTSE China 50.
• Many of these options are European-style rather than American-style.
• Index Weeklys (maturing on Wednesdays and Fridays) and LEAPS (maturing in
  December and June) are also traded.

ETP Options

• There are also CBOE options on many exchange-traded products (ETPs) such as
  exchange traded funds (ETFs). An ETF can be designed to track an equity
  index, bond index, a commodity, or a currency.
• ETP options are like options on individual stocks in that they are
  American-style and involve physical settlement (i.e., settlement by delivery
  of the underlying asset).

Non-Standard Products

• To compete with the over-the-counter options market, the CBOE also offers
  some nonstandard options. For example, FLEX options are options with
  non-standard terms that sometimes include
  • Non-standard strike prices,
  • Non-standard maturity dates, and
  • Variations in style (American or European).

• Other non-standard options on the CBOE include Asian and Cliquet options on
  indices.
  • Asian options provide a payoff based on the average price of the
    underlying asset during the life of the option.
  • Cliquet options provide a payoff equal to the sum of the monthly capped
    returns provided by the asset (if this sum is positive).

Trading

• Even with electronic matching platforms, exchanges still rely on market
  makers to provide liquidity to the options market. These market makers will
  quote option bid and ask prices when they are asked to do so, while
  exchanges set upper limits on the size of the bid-ask spread.
• To take an option position, a trader customarily places an order through a
  broker, who charges a commission. Commissions vary from broker to broker and
  can be as low as USD 5 per trade.
• Like futures, exchange-traded options can be closed out by taking an
  offsetting position. For example, a trader owning a put with a certain
  strike price and maturity can exit from the position by selling a put with
  the same strike price and maturity. Just like the futures market, the open
  interest in the options market measures the number of outstanding contracts.
• A position limit is defined as the number of contracts an investor can hold
  on the same side of the market (i.e., long calls and short puts are
  considered to be on one side of the market, while short calls and long puts
  are considered to be on the other side of the market). The exercise limit is
  the maximum number of contracts that can be exercised in five business days.
  It is usually the same as the position limit.

Margin Requirements

• Options with maturities less than nine months cannot be bought on margin,
  and the full price must be paid upfront.
• Options with maturities greater than nine months can be bought on margin,
  but no more than 25% of the purchase price can be borrowed.
• If a trader pays cash for an option, there would be no margin requirements
  because the trader has no future liabilities. However, the seller of an
  option does have potential future liabilities. The CBOE margin requirements
  for a short call position include 100% of the sale’s proceeds along
  with the greater of the following two values:
  • 20% of the share price less the amount the option is out of the money,
    and
  • 10% of the share price.
• The CBOE margin requirements for a short put include 100% of the
  sale’s proceeds along with the greater of the following two
  calculations:
  • 20% of the share price less the amount the option is out of the money,
    and
  • 10% of the strike price.

• For options on indices, the 20% in the previous calculation is replaced by
  15%.
• The CBOE Margin Manual has special rules governing traders with portfolios
  consisting of long and short option positions (which are perhaps combined
  with positions in the underlying asset). For example, no margin is required
  on a covered call position (i.e., a written call plus a long position in the
  asset underlying the call).
• As with futures, options margins are handled by the members of the Options
  Clearing Corporation (OCC). All option trades must be cleared through an OCC
  member. Nonmember brokers must arrange to clear their clients’ trades
  with a member. Thus, all brokers maintain margin accounts with OCC members,
  while all end users maintain margin accounts with their respective brokers.
  The margin requirements for these accounts must be at least as great as
  those specified by the OCC for its members.

Over-The-Counter Market

• While options on individual stocks trade primarily on exchanges, options on
  foreign currencies, interest rates, and many other financial variables are
  traded actively in the OTC market.
• The main advantage of the OTC market is that financial institutions can
  tailor options to meet the specific needs of their clients.
• The size of the typical options transaction in the OTC market is large and
  the options often last longer than those traded on exchanges. OTC options
  can also be exotic (i.e., have non-standard structures).

Warrants

• Warrants are options issued by a corporation. They are usually call options
  on the corporation’s own stock, but they can also be options to buy or
  sell another asset (e.g., gold). Once issued, they are often traded on an
  exchange.
• To exercise a warrant, the holder needs to contact the issuer. When a call
  warrant on the issuing company’s stock is exercised, the firm issues
  more of its stock. Once that happens, the warrant holders can then buy the
  stock at the strike price.
• Warrants can be used by firms to make debt issuances more attractive to
  investors. For example, suppose a company’s stock price is currently
  USD 40 and the firm is planning a debt issue. It might choose to add two
  warrants to each USD 1,000 bond; each warrant would give the holder the
  right to buy one share at USD 45 on the expiration date. The bondholders
  would then have a stake in the fortunes of the company beyond the desire to
  see it avoid a default.

Convertibles

• A convertible bond (also referred to as a convertible) is similar to a
  warrant. Specifically, a convertible is a bond that can be converted into
  equity using a pre-determined exchange ratio.

For example, suppose a company’s current share price is USD 40. It might
choose to issue ten-year bonds, each with a USD 1,000 par value, that can be
converted into 20 shares at any time after four years. When an investor
chooses to convert, the company simply issues more of its stock to be
exchanged for the bonds.

• Like warrants, convertible bonds are often traded on exchanges.

Employee Stock Options

• Employee stock options are call options granted by a company to its
  employees. They differ from exchange-traded options in several ways. The
  following are examples.
  • There is usually a vesting period during which options cannot be
    exercised. These periods can last up to four years.
  • Employees may forfeit their options if they leave their jobs
    (voluntarily or involuntarily) during the vesting period.