Introduction to Derivatives

Read Hull, Chapters 1, 2, and 9

Outline

• 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 asset
  • “derive” - take value from another asset
• Examples
  • Futures contract
  • Forward contract
  • Swaps
  • Options
• Why are derivatives important?
  • Derivatives 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 - buy 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 spot contract is an agreement to buy or sell the asset immediately or within a very short period of time
• 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
• 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

• Trading
  • Traditionally, traders of 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
      • The asset in the denominator is what we buy or sell in derivative
      • The currency in numerator is what we use to do the buying and selling
    • Sell 1,000 barrels of oil @ US$85/barrel 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 (OTC) 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 jnvestors may post collateral
  • 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

• Example
  • On August 8, 2018 the treasurer of a corporation enters 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
  • Governments 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 underlying assets
  • 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 exchange adjusts the balance in the margin account for daily settlement
  • Margin minimizes loss by preventing a default on a contract
• 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 US$10,000 with exchange to buy contract
    • Maintenance margin is US$4,000/contract (US$8,000 in total)
      • Buyer must deposit enough money to bring account balance up to US$10,000 if account falls below maintenance margin
  • Below show the daily changes in the futures price

• 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 are 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

• 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

• Delivery
  • If a futures contract is not closed out before maturity, it is usually settled by delivering the assets specified in 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 F ₀ = S ₀ e ^rt
  • Contango - The futures price is normal because F > S
  • Backwardation - The futures price is not normal because F<S
    • Root is backward in backwardation

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

• Payoff from a Short Forward or Futures Position
  • payoff = (F ₀ - S _T)
  • Buy at the low price, S _T, and sell at the higher price, F ₀

• Forward Contracts vs Futures Contracts

• 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

Options

• 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 (right)
  • The issuer (or writer) must buy or sell (obligated) 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 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

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
• profit = (S _T - K) - c
• Profit includes premium or call price denoted by c
• Payout excludes premium

Short Call - Writer

• Option price $2
• Strike price $50
• profit = (K - S _T) + c
• Profit includes premium

Profit from buying a European put option

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

Profit from writing a European put option

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

What is the Option Position in Each Case?

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

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)

Terminology

• 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 ₀-K>0
  • Put option – buy at S and sell at K
    • K-S ₀<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

• 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

• A company offers employee stock options are a form of remuneration 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