Introduction to Derivatives

Read Hull, Chapters 1, 2, and 9


  • The Nature of Derivatives
  • Futures Contracts
  • Forward Contracts
  • Mechanics of Futures Markets
  • Options
  • Reasons to Trade Options
  • Mechanics of Options Markets

The Nature of Derivatives

  • A derivative is a financial instrument whose value depends on the value of another underlying variables
    • “derive” - take value from another asset
  • Examples
    • Futures contract
    • Forward contract
    • Swaps
    • Options
  • Why are derivatives important?
    • Derivatives can transfer risks in the economy
    • Underlying assets include stocks, currencies, interest rates, commodities, debt instruments, electricity, insurance payouts, etc.
    • Many financial transactions may embed derivatives
    • Investors have widely accepted derivatives theory
  • Why do investors use derivatives?
    • To hedge risks - protect against a price or interest rate change
    • To speculate - deliberately gamble by buying low and selling high
    • To earn arbitrage profit - pay in low price market and sell in high price market at same time
    • To change the nature of a liability, such as converting a variable-rate loan to a fixed-rate loan, or vice versa
    • To change the nature of an investment without incurring the costs of selling one portfolio and buying another

Futures Contracts

  • A futures contract is an agreement to buy or sell an asset at a certain time in the future for a certain price
  • All futures contracts require:
    • A future maturity date when tranaction takes place
    • Contract fixes the price
    • Contract sets the quantity
  • A spot contract is an agreement to buy or sell the asset immediately or within a very short period of time
  • Examples of Futures Exchanges
    • Chicago Mercantile Exchange (CME)
    • Group Intercontinental Exchange
    • New York Stock Exchange (NYSE)
    • Euronext Eurex
    • BM & FBovespa (Sao Paulo, Brazil)
    • Kuala Lumpur Stock Exchange - Bursa Malaysia
    • And many more
  • Futures price
    • The futures prices for a particular contract is the price at which you agree to buy or sell at a future time
    • Futures have their own supply and demand while a spot market has their own supply and demand
  • Over-the Counter Markets
    • The over-the counter (OTC) market is an important alternative to exchanges
    • Financial institutions, corporate treasurers, and fund managers participate in the OTC
    • Transactions are much larger than in the exchange-traded market
    • The graph below shows the size of OTC and Exchange-Traded Markets

Size of the OTC annd Exchange Traded Markets

  • Trading
    • Traditionally, traders dealing with futures contracts trade them using the open outcry system.
      • Traders physically meet on the floor of the exchange
    • Electronic trading and high frequency algorithmic trading have replaced the outcry system and have become an increasingly important market component
      • Algorithmic trading – computers use instructions to buy and sell trades
  • Futures contract examples
    • Agree to
      • Buy 100 ounces (oz.) of gold @ US$1,750/oz. in December
      • Sell £62,500 @ 1.5500 US$/£ in March
        • Notice pounds is in the denominator
        • The contract is to sell pounds
      • Sell 1,000 barrels (bbl.) of oil @ US$85/bbl. in April
  • Terminology
    • The buying party takes a long position
      • Buy → Long
    • The selling party takes a short position
      • Sell → short
  • Example
    • In January, an investor enters into a long futures contract to buy 500 ounces (oz) of gold @ $1,950 per oz in April
    • In April, the spot price of gold is $2,025 per oz
    • What is the investor's profit or loss?
    • Hint – The investor buys from the futures and sell on the spot market
      • profit = (2,025 - 1,950) x 500 = 37,500

Forward Contracts

  • Forward contracts are similar to futures except that traders buy and sell them in the over-the-counter market
    • Forward contracts are popular on currencies and interest rates
  • Forward price
    • Foward contract is an OTC agreement to buy or sell an asset at a certain time in the future for a certain price
    • Forwards have no daily settlement but collateral may have to be posted.
    • At the end of the life of the contract one party buys the asset for the agreed price from the other party
    • The forward price for a contract is the delivery price that applies to the contract today
      • The forward price equals the delivery price to make the contract worth exactly zero
      • When a writer creates a forward contract, the contract is worth zero
    • The forward price may differ for contracts of different maturities as shown by the table
    • Foreign Exchange Quotes for USD/Euro exchange rate on August 8, 2018
      • Bid is to buy while offer is to sell
Bid Offer
Spot 1.1685 1.1689
1-month forward 1.1682 1.1687
3-month forward 1.1679 1.1685
6-month forward 1.1673 1.1680
  • Example
    • On August 8, 2018 the treasurer of a corporation might enter into a forward contract to sell € 100 million in six months at an exchange rate of $1.1680/ €
      • Treasurer is writing or selling or shorting
    • The corporation is obligated to pay €100 million and receive $1.1680 million on January 8, 2018
    • What are the possible outcomes?
      • If spot exchange rate equals 1.1500 USD / Euro
      • Profit = (1.1680 – 1.1500) x 100 million = 1.8 million USD
      • Treasurer sells a 100 million euros for 1.168 and can buy from spot at 1.1500.
  • The Lehman Bankruptcy
    • Lehman's filed for bankruptcy on September 15, 2008.
      • The biggest bankruptcy in U.S. history
      • A loss of $3.9 billion on September 10, 2008
      • Lehman actively participated in the OTC derivatives markets and encountered financial difficulties because it took high risks and could not roll over its short-term funding (probably debt)
      • It had hundreds of thousands of transactions outstanding with about 8,000 counterparties
      • Lehman liquidators and their counterparties experienced difficulties to unwind these transactions.
  • New Regulations for OTC Market
    • Regulation of Futures Regulation is designed to protect the public interest
    • Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups
    • The OTC market is becoming more like the exchange-traded market.
    • Gov introduced new regulations since the crisis
      • Standard OTC products must be traded on swap execution facilities
      • Traders must use a central clearing party as an intermediary for standard products
      • Traders must report trades to a central registry

Mechanics of Futures Markets

  • Futures Contracts
    • Available on a wide range of underlyings
    • Exchange traded - standardized contracts
      • What can be delivered
      • Where it can be delivered
      • When it can be delivered
    • Settled daily
  • Margin
    • A margin is an investor deposits cash or marketable securities with his or her broker
    • The balance in the margin account is adjusted to reflect daily settlement
    • Margin minimizes the possibility of a loss through a contract default
  • Margin Example
    • An investor takes a long position in 2 December gold futures contracts on June 5
      • Contract size is 100 oz.
      • Futures price is US$1,750
      • Initial margin requirement is US$5,000/contract (US$10,000 in total)
        • Buyer must deposit money with exchange to buy contract
      • Maintenance margin is US$4,000/contract (US$8,000 in total)
        • Buyer must deposit extra money if value falls below maintenance margin
    • Below show the daily changes in the futures price
Day Trade Price ($) Settle Price ($) Daily Gain ($) Cumul. Gain ($) Margin Balance ($) Margin Call ($)
1 1,750.00 10,000
1 1,725.00 −5,000 − 5,000 5,000 +5,000
2 1,722.00 −600 −5,600 9,400
….. ….. ….. ….. ……
6 1,735.00 2,600 −3,000 12,000
7 1,730.00 −1,000 −4,000 11,000  
8 1,721.00 -1,800 −5,800 9,200
….. ….. ….. ….. ……
16 1.765.00   3,000 18,000
  • Key Points About Futures
    • Futures are settled daily
    • A person closes out a futures position by entering into an offsetting trade
      • For example, if you enter a long position, then the offsetting trade is a short
      • If you enter a short, then the offsetting trade is a long position
    • Most contracts are closed out before maturity
    • Investors do not want to take possession of hogs, crude oil, etc.
  • Clearing Houses and OTC Markets
    • Traditionally transactions have been cleared bilaterally in OTC markets
    • Bilaterally – between two parties
    • Following the 2007-2009 crisis, investors clear most standardized OTC derivatives transactions though clearing houses.
    • Bilateral Clearing vs Central Clearing House
      • The clearing house lies between each buyer and seller

Clearing house

  • Some terminology
    • Open interest: the total number of contracts outstanding
      • Equal to number of long positions or number of short positions
    • Settlement price: the price just before the final bell each day
      • Used for the daily settlement process
    • Volume of trading: the number of trades in one day
  • Crude Oil Trading on July 13, 2012
Open High Low Prior settle Last trade Change Volume
Aug 2012 85.86 87.61 85.58 86.08 87.28 +1.20 223,698
Sept 2012 86.33 88.00 85.95 86.46 87.68 +1.22 87,931
Dec 2012 87.45 89.21 87.39 87.73 88.94 +1.21 31,701
Dec 2013 88.85 90.15 88.78 88.92 89.95 +1.03 11,128
Dec 2014 87.20 87.74 87.20 86.98 87.74 +0.76 2,388
  • Delivery
    • If a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract.
      • The party with the short position chooses the alternatives about what is delivered, where it is delivered, and when it is delivered,.
    • A few contracts such as derivatives for stock indices and Eurodollars are settled in cash
      • Investors cannot trade assets with no physical existence
    • When there is cash settlement contracts are traded until a predetermined time.
      • All are then declared to be closed out.
  • Futures Price Patterns
    • Futures prices can be
      • An increasing function of maturity: normal market
        • Assumed the spot price grew at a risk free interest rate
        • Graph (a)
      • A decreasing function of maturity: inverted market
        • Graph (b)
      • Partly normal, partly inverted
  • Convergence of Futures to Spot
    • We will learn that F > S because F0 = S0 ert
    • Contango - The futures price is normal because F > S
    • Backwardation - The futures price is not normal because F<S
      • Root is backward in backwardation

futures price convergence to spot

  • Payoff from a Long Forward or Futures Position
    • payoff = (ST - F0)
    • Notice: Buy low and sell high
    • Sell at the higher spot price and buy from the lower futures price
    • ST is the spot price at maturity
    • F0 is the futures or forward price entered at time 0

Profit from long forward

  • Payoff from a Short Forward or Futures Position
    • payoff = (F0 - ST)
    • Buy at the low price, ST, and sell at the higher price, F0

Profit from long forward

  • Forward Contracts vs Futures Contracts
Forward Futures
Private contract between two parties Traded on an exchange
Not standardized Standardized
Usually one specified delivery date Range of delivery dates
Settled at end of contract Settled daily
Delivery or final settlement usual Usually closed out prior to maturity
Some credit risk Virtually no credit risk
  • Foreign Exchange Quotes
    • Futures exchange rates are quoted as the number of USD per unit of the foreign currency
    • Forward exchange rates are quoted in the same way as spot exchange rates.
      • GBP, EUR, AUD, and NZD are quoted as USD per unit of foreign currency.
      • Currencies like CAD and JPY are quoted as units of the foreign currency per USD.


  • Call option is an option to buy a certain asset by a certain date for a certain price called the strike or exercise price
    • Holder can choose to exercise or not
  • Put option is an option to sell a certain asset by a certain date for a certain price called the strike or exercise price
    • Holder can choose to exercise or not

American vs European Options

  • Holders can exercise an American option at any time during its life
    • Difficult to value
    • Binominal tree
  • Holders can only exercise a European option at maturity
    • Easy to value
    • Black-Scholes

Exchanges Trading Options

  • Chicago Board Options Exchange (CBOE)
  • International Securities Exchange
  • NYSE
  • Euronext Eurex (Europe)
  • And many more

Options vs Futures/Forwards

  • A futures/forward contract gives the holder the obligation to buy or sell at a certain price
    • Holder must buy at the contract price
    • The issuer (or writer) must sell at the contract price
  • An option gives the holder the right to buy or sell at a certain price
    • Holder can choose to exercise
    • The issuer (or writer) must buy or sell if the holder exercises the option

Reasons to Trade Options

Reasons to trade derivatives

  • Hedging
  • Speculation
  • Arbitrage

Hedge funds trade derivatives for all three reasons

  • Hedge funds are not subject to the same rules as mutual funds and cannot offer their securities publicly.
    • Definition - an offshore investment fund that speculates using credit or borrowed capital.
    • Companies take advantage of international markets to escape regulations
  • Mutual funds must
    • Definition – shareholders fund an investment programme that trades in diversified holdings and is professionally managed
    • Disclose investment policies
    • Makes shares redeemable at any time
    • Limit use of leverage
    • Hedge funds are not subject to these constraints

Hedging examples

  • A US company will pay €10 million for imports from Germany in 3 months and decides to hedge using a long position in a forward contract
    • U.S. company buys Euros
    • The exchange rate is 1.2 USD / Euro
    • Answer – company buys Euros at a fixed exchange rate Company pays $12 million
  • An investor owns 1,000 shares currently worth $40 per share.
    • A two-month put with a strike price of $38.50 costs $1.50 with a quantity of 100 shares
    • The investor decides to hedge by buying 10 contracts
    • Value of shares with and without hedging
    • Answer
      • Investor "insures" $38,500 10 contracts 100 shares per contract
      • Strike price is $38.50
      • If the value of the fund drops below $38,500 on maturity date, investor exercises put and sells shares at $38.50

Heding example for a put

Speculation Example

  • An investor with $2,000 to invest feels that a stock price will increase over the next 2 months.
  • The current stock price is $20 and the price of a 2-month call option with a strike of $22.50 is $1
  • What are the alternative strategies?
    • Investor buys the call option
      • Investor exercises the call option when spot price equal or exceeds strike price
      • Profit = (S – K)* quantity – option cost
      • Profit = (S – $22.50)*100 – 100*$1
      • Investor does not exercise call when spot price is below K
    • Investor buys 100 shares of stock for $2,000
      • Profit = ( S - 20 ) x 100
      • Profit could be negative if stock price drops below 20

Arbitrage Example

  • A stock price is quoted as €100 in Germany and $120 in New York
  • The current exchange rate is: $1.1600 / €
  • What is the arbitrage opportunity?
    • Buy low and sell high
    • USD value of stock in Germany €100 * $1.1600 / € = $116 per share
    • Thus, buy in Germany and sell in the United States
    • Profit = $120 - $116 = $4 per share
    • 100 shares is $400 in profits

Mechanics of Options Markets

Option Type

  • A call is an option to buy
  • A put is an option to sell
  • Holder can only exercise a European option at the end of its life
  • Holder can exercise an American option any time until maturity

Option Positions

  • Long call – buy a call option
    • Pay a premium
  • Long put – buy a put option
    • Pay a premium
  • Short call – write or sell a call
    • Earn a premium
    • Obligated to pay out if holder exercises
  • Short put – write or sell a put
    • Earn a premium
    • Obligated to pay out if holder exercises

Long Call - Holder

  • Profit from buying one European call option
  • Option price = $2, strike price = $50
  • payout = (ST - K) - c
  • Profit includes premium or call price denoted by c

Profit long call

Short Call - Writer

  • Option price $2
  • Strike price $50
  • payout = (K - ST) + c
  • Profit includes premium

Profit long call

Profit from buying a European put option

  • Option price = $4, strike price = $120
  • profit = ( K - ST) - p
  • Profit includes premium or put price denoted by p

Profit from put option

Profit from writing a European put option

  • Option price = $7, strike price = $70
  • Profit includes premium

Profit short call

What is the Option Position in Each Case?

  • K = Strike price
  • ST = Price of asset at maturity
  • Payoff excludes premium, whereas profit includes premium

Profit short call

Option types

  • Stocks
  • Foreign Currency
  • Stock Indices
  • Options on Futures

Specification of Exchange-Traded Options

  • Expiration date
  • Strike price
  • European or American Call or Put (option class)


  • Intrinsic value – option is in the money but you cannot exercise it
  • Time value
  • Moneyness :
  • At-the-money option
    • S = K
  • In-the-money option
    • Call option – buy at K and sell at S
      • S-K>0
    • Put option – buy at S and sell at K
      • K-S<0
  • Out-of-the-money option - exact opposite

Dividends & Stock Splits

  • Suppose you own options with a strike price of K to buy (or sell) N shares:
  • No adjustments are made to the option terms for cash dividends
  • When there is an n-for-m stock split
    • The strike price is reduced to mK/n
    • The number of shares that can be bought (or sold) is increased to nN/m
    • Stock dividends are handled in a manner similar to stock splits
  • Consider a call option to buy 100 shares for $20 per share
  • How should terms be adjusted:
    • For a 2-for-1 stock split?
    • For a 5% stock dividend?
  • Answer
    • Hint – value has to remain the same
      • 2 for 1 stock split
        • Number of shares = nN/m = 2(100)/1 = 200 shares
        • Exercise price = mK/n = 1($20)/2 = $10
        • Value = 200(10)=100(20)=$2,000
      • For 5% dividend
        • Number of shares = 100(1.05) = 105
        • Ratio 105 / 100 = 21 / 20
        • Exercise price = $20(20)/21 = $19.05
        • Value = 100(20)=105(19.05)=$2,000

Market Makers

  • Most exchanges use market makers to facilitate options trading
  • A market maker quotes both bid and ask prices when requested
  • The market maker does not know whether the individual requesting the quotes wants to buy or sell

Margin is required when options are sold

  • For example, when a naked call option is written in the US, the margin is the greater of:
    • Naked – issuer does not own the underlying assets in option
    • A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount (if any) by which the option is out of the money
    • A total of 100% of the proceeds of the sale plus 10% of the underlying share price


  • Warrants - a corporation or a financial institution issues options
  • Holder can buy the underlying stock of the issuing company at the exercise price until the expiry date.
  • The number of warrants outstanding is determined by the size of the original issue and changes only when holder exercises them or warrants expire
  • Warrants are traded in the same way as stocks
  • The issuer settles with the holder when holder exercises a warrant
  • When a corporation issues a call warrants on its own stock, exercising the call usually leads to new treasury stock being issued

Employee Stock Options

  • Employee stock options are a form of remuneration issued by a company to its executives
    • Remuneration – compensation, like a bonus in additional to the salary
  • They are usually at the money when issued
  • When holder exercises options, the company issues more stock and sells it to the option holder for the strike price
  • Expense item on the income statement

Executive Stock Options

  • Company issues options to executives
  • Executives can influence corporate decisions
  • When executives exercise the option, the company issues more stock
  • Usually at-the-money when issued

Convertible bonds - holder can convert a bond into a specified number of shares of common stock in the issuing company or cash of equal value

  • Predetermined exchange ratio
  • Usually a convertible is callable
    • Callable bond – company has the option to buy its bond by a specific date
    • The call provision – the issuer can convert a bond earlier than the holder might otherwise choose