Energy & Finance Track Futures and Options Prof. Christophe Pérignon (HEC) perignon@hec.fr www.hec.fr/perignon Spr

1. Energy & Finance TrackFutures and OptionsProf. Christophe Pérignon (HEC)perignon@hec.frwww.hec.fr/perignonSpring 2011 - May 3, 2011

2. Futures and OptionsProf. Christophe Pérignon (HEC)perignon@hec.frPart 1:Introduction and Background

3. The Nature of Derivatives • A derivative is a financial asset whose value depends on the value of another asset, called underlying asset • Examples of derivatives include Futures, Forwards, Options, Swaps, Credit Derivatives (CDS)

4. Historical Facts • Derivatives, while seemingly new, have been used for thousands years * Aristotle, 350 BC (Olive) * Netherlands, 1600s (Tulips) * USA, 1800s (Grains, Cotton) * Spectacular growth since 1970’s • Increase in volatility (Liberalization, International trade, End of Bretton Woods, Oil price shocks) • Black-Scholes model • Derivatives Exchanges + Over The Counter (OTC)

5. Examples of Underlying Assets • Stocks • Bonds • Exchange rates • Interest rates • Commodities/metals • Energy • Number of bankruptcies among a group of companies • Pool of mortgages • Temperature, quantity of rain/snow • Real-estate price index • Loss caused by an earthquake/hurricane • Dividends • Volatility • Derivatives • etc

6. Ways Derivatives are Used • Hedge risks: reducing the risk • Speculate: betting on the future direction of the market • Lock in an arbitrage profit: taking advantage of a mispricing Net effect for society?

7. 1. Interest Rate Swap • Consider a 3-year swap initiated on 5 March 2008 between Microsoft and Intel. • Microsoft agrees to pay to Intel an interest rate of 5% per annum on a notional principal of $100 million. • In return, Intel agrees to pay Microsoft the 6-month LIBOR on the same notional principal. • Payments are to be exchanged every 6 months, and the 5% interest rate is quoted with semi-annual compounding. 5% Intel MSFT LIBOR

8. ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar. 5, 2008 4.2% Sep. 5, 2008 4.8% +2.10 –2.50 –0.40 Mar. 5, 2009 5.3% +2.40 –2.50 –0.10 Sep. 5, 2009 5.5% +2.65 –2.50 +0.15 Mar. 5, 2010 5.6% +2.75 –2.50 +0.25 Sep. 5, 2010 5.9% +2.80 –2.50 +0.30 Mar. 5, 2011 6.4% +2.95 –2.50 +0.45 Microsoft Cash Flows

9. 2. 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 • By contrast in a SPOT contract there is an agreement to buy or sell an asset immediately • The party that has agreed to buy has a LONG position (initial cash-flow = 0) • The party that has agreed to sell has a SHORT position (initial cash-flow = 0)

10. 2. Futures Contracts (II) • The FUTURES PRICE (F0) for a particular contract is the price at which you agree to buy or sell • It is determined by supply and demand in the same way as a spot price • Terminal cash flow for LONG position: ST - F0 • Terminal cash flow for SHORT position: F0 - ST Futures are traded on organized exchanges: • Chicago Board of Trade, Chicago Mercantile Exch. (USA) • Montreal Exchange (Canada) • EURONEXT.LIFFE (Europe) • Eurex (Europe) • TIFFE (Japan)

11. Example: Gold S0 = $1,250.4 F0(Nov 2010) = $1,251.3 Source: www.kitco.com Source: www.cmegroup.com

12. Sources: www.onechicago.com and yahoo finance

13. Quotes retrieved on September 7, 2010

14. 3. Forward Contracts • Forward contracts are similar to futures except that they trade on the over-the-counter market (not on exchanges) • Forward contracts are popular on currencies and interest rates

15. 4. Options • A call option is an option to buy a certain asset by a certain date for a certain price (the strike price K) • A put option is an option to sell a certain asset by a certain date for a certain price (the strike price K) American vs. European Options • An American option can be exercised at any time during its life. Early exercise is possible. • A European option can be exercised only at maturity

16. Example: Cisco Options (CBOE quotes) From NASDAQ : Option Cash Flows on the Expiration Date • Cash flow at time T of a long call : Max(0, ST - K) • Cash flow at time T of a long put : Max(0, K - ST)

18. Size of the Global Derivative Market Total outstanding notional amount : $688 trillion (OTC = $615 ; Exchanges = $73, BIS, December 2009) Annual U.S. Growth National Product : $14 trillion(US Department of Commerce,Year 2010) Total Value of global stocks: $48 trillion(World Federation of Exchange Members, December 2009) Total Value of global bonds : $26 trillion(BIS, June 2010) 1-18

19. Trading Activity for Derivatives Contracts outstanding, Table 23B, BIS June 2010: Futures: Interest Rates 68%, Currency 7%, Equity 25% Options: Interest Rates 40%, Currency 2%, Equity 58% 1-19

20. International Evidence on Financial Derivatives Usage” by Bartram, Brown and Fehle (2008) 7,319 non-financial firms from 50 countries, 2000-2001 60% of the firms use derivatives in general 45% use currency derivatives 33% use interest rate derivatives 10% use commodity price derivatives Factors Determining Derivatives Usage: Size of the local derivatives market Level of risk and financial sophistication 1-20

21. Derivatives and Risk In today’s derivatives markets, any type of financial payoff one can think of can be obtained at a price For instance, if a corporation wants to receive a payment that is a function of the square of the yen/dollar exchange rate if the volatility of the S&P 500 index exceeds 35% during a month, it can do so When anything is possible, but one does not have the required knowledge or experience, it is easy to make mistakes 1-21

22. Losses Attributed to Derivatives: 1993-2008 1-22

23. Banks' SubprimeWritedowns & Losses Top 20 Source: Bloomberg, http://www.bloomberg.com/apps/news?pid=20601087&sid=aSKLfqh2qd9o&refer=worldwide 1-23

24. 5. Credit Derivatives: (1) Credit Default Swap Payment if default by reference entity Default protection buyer Default protection seller CDS spread • Provides insurance against the risk of default by a particular company • The buyer has the right to sell bonds issued by the company for their face value when a credit event occurs. • The buyer of the CDS makes periodic payments to the seller until the end of the life of the CDS or a credit event occurs 1-24

25. 5. Credit Derivatives: (2) Collateralized Debt Obligations (CDO) AAA15% Pool of Loans AA 8% B 3% 1-25

26. 6. Toxic Loans of Local Authorities It's a joke that we are in markets like this. We are playing the dollar against the Swiss franc until 2042.” Cedric Grail, City of Saint Etienne CEO, quoted by Business Week (2010) • Loan features: • Notional: EUR20m • Maturity: 15 years • coupon rate: • Y1-2: 3.80% • Y3-15: 3.80% + Max(1.9700 – GBPCHF) • Capped at 24% • Market evolution: • GBPCHF at time of trade inception: 2.0700 • => expected coupon of 3.80% per year • GBPCHF today: 1.5215 • => current coupon level of 24% per year (it would be 45% without the cap…) 1-26

27. Delivery Most contracts are closed out before maturity : long 5 contracts at t1 + short 5 contracts at t2 > t1 If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. A few contracts (for example, those on stock indices) are settled in cash 1-27

28. Contract Specifications: Futures on CAC40 Index 1-28

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30. Default Risk with Futures Two investors agree to trade an asset in the future One investor may: regret and leave not have the financial resources Margins and Daily Settlement 1-30

31. Margins A margin is cash (or liquid securities) deposited by an investor with his broker The balance in the margin account is adjusted to reflect daily gains or losses: “Daily Settlement” or “Marking to Market” If the balance on the margin account falls below a pre-specified level called maintenance margin, the investor receives a margin call If the investor is unable to meet a margin call, the position is closed Margins minimize the possibility of a loss through a default on a contract 1-31

32. Derivatives and Risk In today’s derivatives markets, any type of financial payoff one can think of can be obtained at a price For instance, if a corporation wants to receive a payment that is a function of the square of the yen/dollar exchange rate if the volatility of the S&P 500 index exceeds 35% during a month, it can do so When anything is possible, but one does not have the required knowledge or experience, it is easy to make mistakes 1-32

33. Losses Attributed to Derivatives: 1993-2008 1-33

34. Banks' Subprime Writedowns & Losses Top 20 (Aug 2008) Source: Bloomberg, http://www.bloomberg.com/apps/news?pid=20601087&sid=aSKLfqh2qd9o&refer=worldwide 1-34

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36. Are Derivatives “Financial Weapons of Mass Destruction” ? • “Derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.” Warren Buffet • Numerous losses caused by (mis)using derivatives • Credit derivative losses

37. Should We Fear Derivatives? • “The answer is no. We should have a healthy respect for them. We do not fear planes because they may crash and do not refuse to board them because of that risk. Instead, we make sure that planes are as safe as it makes economic sense for them to be. The same applies to derivatives. Typically, the losses from derivatives are localized, but the whole economy gains from the existence of derivatives markets.” Rene Stulz (Ohio State University)

38. Regulation of Derivatives Markets • Exchange-based trades are transparent and cleared • OTC trades are less transparent and less frequently cleared • Most OTC derivatives are arranged with a dealer (below) • Systemic risk concerns • Current derivatives reform proposals: • Migration of OTC trading to exchanges • Centralized clearing for OTC products • Improved price/position transparency • Speculation position limits • Improved corporate governance in financial risk management

39. Futures and OptionsProf. Christophe Pérignon (HEC)perignon@hec.frPart 2:Pricing

40. 1. Corn: An Arbitrage Opportunity? • Suppose that: • The spot price of corn is US$390 (for 1,000 bushels) • The quoted 1-year futures price of corn is US$425 • The 1-year US$ interest rate is 5% per annum • No income or storage costs for corn • Is there an arbitrage opportunity?

41. NOW • Borrow $390 from the bank • Buy corn at $390 • Short position in a futures contract • IN ONE YEAR • Sell corn at $425 (the futures price) • reimburse 390  exp(0.05) = $410 ARBITRAGE PROFIT = $15  NOTE THAT ARBITRAGE PROFIT AS LONG AS S0 exp(r T) < F0

42. 2. Corn: Another Arbitrage Opportunity? • Suppose that: • The spot price of corn is US$390 • The quoted 1-year futures price of corn is US$390 • The 1-year US$ interest rate is 5% per annum • No income or storage costs for corn • Is there an arbitrage opportunity?

43. NOW • Short sell corn and receive $390 • Make a $390 deposit at the bank • Long position in a futures contract • IN ONE YEAR • Buy corn at $390 (the futures price) • Terminal value on the bank account 390  exp(0.05) = $410 ARBITRAGE PROFIT = $20  NOTE THAT ARBITRAGE PROFIT AS LONG AS S0 exp(r T) > F0 Therefore F0 has to be equal to S0exp(r T) = $410

44. Futures Price for an Investment Asset For any investment asset that provides no income and has no storage costs F0 = S0erT Immediate arbitrage opportunity if: F0 > S0erT  short the Futures, long the asset F0 < S0erT  long the Futures, short sell the asset

45. The Cost of Carry • The cost of carry, c, is the storage cost plus the interest costs less the income earned • For an investment asset F0 = S0ecT • For a consumption asset F0S0ecT • The convenience yield, y, is the benefit provided when owning a physical commodity. • It is defined as: F0 = S0 e(c–y )T

46. Examples Source: www.theoildrum.com Source: Quarterly Bulletin, Bank of England, 2006

47. Relation Between European Call and Put Prices (c and p) • Consider the following portfolios: • Portfolio A : European call on a stock + present value of the strike price in cash (Ke -rT) • Portfolio B : European put on the stock + the stock • Both are worth Max(ST, K ) at the maturity of the options • They must therefore be worth the same today:c + Ke -rT= p + S0

48. Su ƒu S ƒ S d ƒd The Binomial Model of Cox, Ross and Rubinstein • An option maturing in T years written on a stock that is currently worth S where u is a constant > 1 : option price in the upper state where d is a constant < 1 : option price in the lower state

49. S u D – ƒu • Consider the portfolio that is D shares and short one option • The portfolio is riskless when S u D –ƒu = S d D –ƒd or S d D – ƒd

50. Value of the portfolio at time Tis: S uD – ƒu or S dD – ƒd • Value of the portfolio today is: (S uD – ƒu )e–rT • Another expression for the portfolio value today is SD – f • Hence the option price today is: f = S D – (S uD – ƒu)e–rT • Substituting for D we obtain: f = [ p ƒu + (1 – p )ƒd ]e–rT where