1. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.1 FUTURES MARKETS

2. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.2 The Nature of Derivatives A derivative is an instrument whose value depends (is derived from) on the values of other more basic underlying variables Futures Contracts Forward Contracts Swaps Options

3. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.3 Ways Derivatives are Used To hedge risks To speculate (take a view on the future direction of the market) To lock in an arbitrage profit To change the nature of a liability To change the nature of an investment without incurring the costs of selling one portfolio and buying another

4. 1.4 Positions Every transaction involves two positions Long position (agreement to buy in the future) Short position (agreement to sell in the future) Zero – sum game

5. What is the benefit of derivative markets ? Efficiency Liquidity Ability to forecast trends Transparency Risk management Portfolio diversification Investment opportunities

6. Forward contracts A Forward contract is a contract where an investor A (buyer) agrees with another investor B (seller) That A will buy from B An underlying asset (underlying instrument) At a pre-specified price (forward price/rate) At a pre-specified future date (delivery date) E.g. agree to sell 10 million barrels of oil (underlying asset) at $100 per barrel (forward price) in 9 months (delivery date)

7. Over The Counter (OTC) Forward contracts are between two parties (usually between financial institutions and/or their clients) and NOT via organized exchanges Over The Counter (OTC) →Investors determine the terms of the contract →Confidentiality

9. Disadvantages OTC Limited transparency Limited regulations No official body for approving new products Limited clearance procedures

10. Neutralize Position There is no secondary market As a result, the contract cannot be liquidated However, an investor can neutralize it by taking an exact opposite position (same duration, same size) Short in 10 million barrels of oil at $100 per in 9 months Long in 10 million barrels of oil at $100 per in 9 months

11. Profit and Losses (P&L) Long position on a forward contract –Profit (loss) when the price of the underling asset at delivery is higher (lower) than the delivery price Short position on a forward contract –Profit (loss) when the price of the underling asset at delivery is lower (higher) than the delivery price

13. Example On the 8 th of March we agree with our bank to buy 1,000,000 Pound Sterling at the exchange rate $1.55 in 90 days On the 6 th of August the rate is rate $/BP is at $1.60 Profit or loss?

14. On the 6 th of August we pay $1,550,000 to the bank We take 1,000,000 BP We sell them in the market for $1,600,000 Profit : $50,000 The bank losses the same amount (zero-sum game) We ignore transaction costs

15. Returns S τ =the spot price of the underlying at delivery date Κ = The delivery (forward) price Profit from a long position on a FC:(S τ – Κ) Profit from a short position on a FC: (Κ – Σ τ )

16. In the example: S τ = 1.60 Κ = 1.55 Long Position Profit (S τ – Κ) = $1.60 – $1.55 = $0.05 For 1,000,000 BP = 1.000.000 x $0,05 = $50,000

17. Graphical representation

18. Introduction to hedging A simple example Consider a company that has 1000 units of a product that has a current price of 500 E/unit If the price goes up in 1 month e.g. at 540 E/unit Profit 40 Ε If the price goes down in 1 month e.g. at 460 E/unit Loss 40 Ε

19. Graph

20. Uncertainty What can the Company do ? Assume a forward contract on the product exists short forward for 1000 units at 500 E

21. Graph

22. Forward contracts Forward contracts are similar to futures except that they trade in the over-the-counter market Forward contracts are popular on currencies and interest rates A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract

23. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.23 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 the asset immediately (or within a very short period of time)

24. Organized markets In contrast to forward contracts, futures contracts are traded in organized exchanges The contracts are between the member and the exchange and have the “guarantee” of the exchange Every contract has the same characteristics and this standardization allows easy trading, liquidity, and easy clearing

28. Most important Derivative Exchanges in the US

29. Most important Derivative Exchanges except US

30. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.30 Futures Price The futures prices 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

31. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.31 Electronic Trading Traditionally futures contracts have been traded using the open outcry system where traders physically meet on the floor of the exchange Increasingly this is being replaced by electronic trading where a computer matches buyers and sellers

32. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.32 Examples of Futures Contracts Agreement to: –buy 100 oz. of gold @ US$600/oz. in December (NYMEX) –sell £62,500 @ 1.9800 US$/£ in March (CME) –sell 1,000 bbl. of oil @ US$65/bbl. in April (NYMEX)

33. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.33 Terminology The party that has agreed to buy has a long position The party that has agreed to sell has a short position

34. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 1.34 Example January: an investor enters into a long futures contract on COMEX to buy 100 oz of gold @ $600 in April April: the price of gold $615 per oz What is the investor’s profit?

35. Futures markets 5 parties involved (1) Derivatives Exchange (2) Clearing House (3) Regulator (4)Members (5)Investors (speculators, hedgers,arbitrageurs)

36. Derivatives Exchange →Usually belongs to company that not only offers the physical place where transactions take place but also provides security and sets the rules →In many countries it works with electronic order matching while in other it works with a pit Pit: the traders and brokers transact in the form of an auction-style open-outcry

38. The clearing house →clears all transactions → guarantees all trades → stands between the two parties Once a transaction takes place the clearer: (α) records the transaction (β) clears the transaction (γ) estimate the margins (δ) clear the obligations of the parties

39. Regulator →Securities and Exchange Commission (US) →Capital Market Committee (Greece) For example in Greece the CMC may take regulatory decisions that are equal to state laws It regulates, the Athens Exchange, the clearing organization, brokers, dealers, mutual funds, investment trusts, etc

40. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.40 Futures Contracts Available on a wide range of underlying Exchange traded Specifications need to be defined: –What can be delivered, –Where it can be delivered, & –When it can be delivered Settled daily

41. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.41 Delivery If a futures contract is not closed out before maturity, it is 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 and Eurodollars) are settled in cash

42. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.42 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 1 day

43. Differences Futures - Forwards Futures are standardized (when, where, what) Standardization is necessary for the efficient running of the market (α) since everybody transacts in the same contract the market is liquid and the trade is easy (β) there is a possibility for large trades since the mechanics of buying/selling are easy to manage (γ) transaction costs are lower since the traders do not need to negotiate the terms in every trade

49. Other differences Futures are available for a large number of underlying assets: Weather derivatives Pork bellies Orange juice Coffee

50. Weather derivatives Farmers, theme parks, airliners, gas and power companies Heating degree days (HDD) or cooling degree days (CDD) contractseating degree dayscooling degree days Heating degree days are one of the most common types of weather derivative.

51. daily settlement, mark to market Futures are settled daily i.e. at the end of the day the investors with losses pay the loss to the investors with gains

52. Margins Futures: when a contract is initiated no money change hands However, every party has to pay a “good faith” deposit or “Margin” to the clearing organization They are used as insurance A margin is cash or marketable securities deposited by an investor with his or her broker The balance in the margin account is adjusted to reflect daily settlement Margins minimize the possibility of a loss through a default on a contract Initial margin requirement and maintenance margin

53. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.53 Example of a Futures Trade An investor takes a long position in 4 December gold futures contracts on June 5 –contract size is 100 oz. –futures price is US$380 –margin requirement is US$2,000/contract (US$8,000 in total) –maintenance margin is US$1,500/contract (US$6,000 in total)

54. Example of a Futures Trade Position: 4 December Gold Futures Every Futures is for 100 oz. Price: $380 / oz Thus: 4 x 100 x $380 = $152,000 What dowe deposit: $2,000 x 4 = $8,000 Leverage

55. Example of a Futures Trade Assume that at the end of the day the price drops at $377 We loose $3 x 400 oz ($1,200) Our margin account will reduce by $1,200 (down to $6,800)

56. Example of a Futures Trade Assume that at the end of next day the price drops a further $3 at $374 We loose another $1,200 and the margin account now stands at $5,600 Margin Call

57. Margins for stock futures in Greece

58. Example Trading with Margin

59. Example Leverage

62. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.62 Convergence of Futures to Spot Time (a)(b) Futures Price Futures Price Spot Price

63. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 2.63 Forward Contracts A forward contract is an OTC agreement to buy or sell an asset at a certain time in the future for a certain price There is no daily settlement (unless a collateralization agreement requires it). At the end of the life of the contract one party buys the asset for the agreed price from the other party

66. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.66 Long & Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

67. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.67 Arguments in Favor of Hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables

68. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.68 Arguments against Hedging Shareholders are usually well diversified and can make their own hedging decisions It may increase risk to hedge when competitors do not Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult

69. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.69 Basis Risk Basis is the difference between spot & futures Basis risk arises because of the uncertainty about the basis when the hedge is closed out

70. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.70 Long Hedge Suppose that F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price You hedge the future purchase of an asset by entering into a long futures contract Cost of Asset= S 2 – ( F 2 – F 1 ) = F 1 + Basis

71. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.71 Short Hedge Suppose that F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price You hedge the future sale of an asset by entering into a short futures contract Price Realized= S 2 + ( F 1 – F 2 ) = F 1 + Basis

72. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.72 Choice of Contract Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price.

73. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.73 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is where  S is the standard deviation of  S, the change in the spot price during the hedging period,  F is the standard deviation of  F, the change in the futures price during the hedging period  is the coefficient of correlation between  S and  F.

74. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.74 Rolling The Hedge Forward We can use a series of futures contracts to increase the life of a hedge Each time we switch from 1 futures contract to another we incur a type of basis risk

75. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.75 The Futures/Forward Price In order top find the right future/forward price for an asset we employ the same methodology as for every investment Present Value approach

76. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.76 Notation S0:S0:Spot price today F0:F0:Futures or forward price today T:T:Time until delivery date r:r:Risk-free interest rate for maturity T

77. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.77 1. Gold: An Arbitrage Opportunity? Suppose that: –The spot price of gold is US$600 –The quoted 1-year futures price of gold is US$650 –The 1-year US$ interest rate is 5% per annum –No income or storage costs for gold Is there an arbitrage opportunity?

78. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.78 2. Gold: Another Arbitrage Opportunity? Suppose that: –The spot price of gold is US$600 –The quoted 1-year futures price of gold is US$590 –The 1-year US$ interest rate is 5% per annum –No income or storage costs for gold Is there an arbitrage opportunity?

79. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.79 The Futures Price of Gold If the spot price of gold is S & the futures price for a contract deliverable in T years is F, then F = S (1+r ) T where r is the 1-year (domestic currency) risk- free rate of interest. In our examples, S =600, T =1, and r =0.05 so that F = 600(1+0.05) = 630

80. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.80 When Interest Rates are Measured with Continuous Compounding F 0 = S 0 e rT This equation relates the forward price and the spot price for any investment asset that provides no income and has no storage costs

81. Another example 7-month forward on a zero coupon bind that matures in a year Spot price = $965, interest rate 5.5% βάση S 0 = $965, e = 2.71828, r = 0.055, Τ = (7/12) F 0 = S 0 e r Τ = 965 e 0.055 (7/12) = $996.46

82. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.82 When an Investment Asset Provides a Known Dollar Income F 0 = (S 0 – I )e rT where I is the present value of the income during life of forward contract

83. Example 10-month forward on a stock that has a current price of $20 and will pay a dividend per share of $0.25 in 3, 6, 9 months from today What is the forward price if the dicopunt rate is 6%?

84. Ι =0.25 e -0.06 (3/12) +0.25 e -0.06 (6/12) +0.25 e -0.06 (9/12) = 0.72791 F 0 = (S 0 – Ι) e r Τ = (20-0.72791) e 0.06 (10/12) =$20.2

85. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.85 When an Investment Asset Provides a Known Yield F 0 = S 0 e (r–q )T where q is the average yield during the life of the contract (expressed with continuous compounding)

86. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.86 Valuing a Forward Contract Suppose that K is delivery price in a forward contract & F 0 is forward price that would apply to the contract today The value of a long forward contract, ƒ, is ƒ = (F 0 – K )e –rT Similarly, the value of a short forward contract is (K – F 0 )e –rT

87. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.87 Forward vs Futures Prices Forward and futures prices are usually assumed to be the same. When interest rates are uncertain they are, in theory, slightly different: A strong positive correlation between interest rates and the asset price implies the futures price is slightly higher than the forward price A strong negative correlation implies the reverse

88. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.88 Stock Index Can be viewed as an investment asset paying a dividend yield The futures price and spot price relationship is therefore F 0 = S 0 e (r–q )T where q is the dividend yield on the portfolio represented by the index during life of contract

89. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.89 Stock Index For the formula to be true it is important that the index represent an investment asset In other words, changes in the index must correspond to changes in the value of a tradable portfolio The Nikkei index viewed as a dollar number does not represent an investment asset

90. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.90 Index Arbitrage When F 0 > S 0 e (r-q)T an arbitrageur buys the stocks underlying the index and sells futures When F 0 < S 0 e (r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index

91. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.91 Index Arbitrage Index arbitrage involves simultaneous trades in futures and many different stocks Very often a computer is used to generate the trades Occasionally (e.g., on Black Monday) simultaneous trades are not possible and the theoretical no-arbitrage relationship between F 0 and S 0 does not hold

92. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.92 A foreign currency is analogous to a security providing a dividend yield The continuous dividend yield is the foreign risk-free interest rate It follows that if r f is the foreign risk-free interest rate Futures and Forwards on Currencies

93. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 5.93 Futures on Consumption Assets F 0  S 0 e (r+u )T where u is the storage cost per unit time as a percent of the asset value. Alternatively, F 0  (S 0 +U )e rT where U is the present value of the storage costs.