Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries

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$10,000. (For simplification of presentation, we assume a parallel shift of theyield curve and no convexity.) The symmetric payoff pattern in this exampleis apparent.Option derivatives include options, caps, floors and all financial instrumentswith embedded options such as warrants, callable bonds, MBS and CMO.The payoff pattern of these instruments is non-linear and asymmetric. Itmeans that the change in value of the derivative is not in the same proportionand may not be in the same direction as the change in value of the underlying.For options transactions, an option buyer's risk exposure is known andlimited. This option buyer pays a premium for purchasing a call option. Themaximum amount he would lose is the premium he pays. The upsidepotential for him is unlimited, because the price of the underlying couldtheoretically go up by 10 times, 20 times or even 100 times. The optionwriter's situation is just the opposite. He receives a premium for selling theoption. The maximum gain for him is the premium he receives. If the priceof the underlying soars, his loss could be tremendous. Therefore, an optionwriter's risk exposure is unknown and unlimited.In the above discussion, you can also see how leverage comes into play inoption transactions. The option buyer pays a relatively small premium toparticipate in the market. On the one hand, he could lose all the premiumhe pays. On the other hand, he could gain 10 or even 100 times of thepremium he pays if the market soars.SOME HISTORY ABOUT DERIVATIVESThe history of derivatives goes back as far as the Middle Ages. In those days,farmers and merchants used futures and forwards to hedge their risks.For instance, a farmer harvested grain in July. But in April, he was uncertainabout what price of grain he would get in July. During the years of oversupply,the farmer bore tremendous price risk as the price of grain would be lowerthan he expected, and he might not recover the cost of production.A grain merchant also bore tremendous price risk during the years ofSome Fundamentals of Derivatives
scarcity when the price of grain was higher than expected. Therefore, itmade sense for the farmer and the merchant to get together in April toagree upon a price in July for grain. This was how the futures andforwards market developed in grain hundreds of years ago; and then porkbellies, cotton, coffee, petroleum, soya bean, sugar, currencies, interest rates... and even garbage. The Chicago Board of Trade started trading threekinds of garbage — plastics, glasses and paper in October 1995.PARTICIPANTS IN DERIVATIVES MARKETSThree kinds of people participate in derivatives markets: the hedgers, thespeculators and the arbitrageurs.Hedgers are risk-averse. Like the farmer and the merchant in the aboveexample, they want the future sales price of the merchandise to be knownin advance and the transaction be consummated at this known sales price.In doing so, they may give up some upside potential. In the example, if theprice of grain rose substantially in July, the farmer would not benefit fromit because he had already sold the merchandise at a price determined inApril. Hedgers do not care much about the future potential. All they wantis to reduce their price risk. However, now that both the merchant and thefarmer had hedged their risks, this does not mean that they had nothing toworry about. The farmer still worried that the price of grain in July wouldfall drastically and the merchant would not fulfil his promise to buy the grainat the agreed upon price. Or the merchant simply did not have the moneyto pay for the grain in July. This is what we call credit risk. Hedgers canhedge away their price risk, but they cannot eliminate credit risk.Contrary to hedgers who want to avoid uncertainty in price movements,speculators want to take advantage of price movements. For example, if aspeculator thinks that the stock market in Hong Kong will go up in the nextseveral months, he can buy a three-month Hang Seng Index (HS1) futurescontract at the current index level of 14,500. If the stock market inSome Fundamentals of Derivatives
Page 2 and 3: THE UNIVERSITY OF HONG KONGLIBRARIE
Page 4 and 5: VI- . .7 « i8^p ! ««^^OOSHSlVCJ
Page 6 and 7: Ever since derivatives took centre-
Page 8 and 9: denominator, value at risk, which c
Page 10 and 11: the kind of information that superv
Page 12 and 13: This book is a team effort of the H
Page 14 and 15: While most market participants defi
Page 16 and 17: of this investment is 6.32 percent
Page 18 and 19: Mathematically, the relation betwee
Page 22 and 23: Hong Kong does go up and the HSI ri
Page 24 and 25: 3OF ATHEPRICING OF A FORWARD CONTRA
Page 26 and 27: COST OF CARRYIn the above example,
Page 28 and 29: interest rate swap rates. From thes
Page 30 and 31: Borrowers, on the other hand, usual
Page 32 and 33: Again we use our method of having t
Page 34 and 35: ates, the forward rate for the peri
Page 36 and 37: 5In this chapter, we will discuss w
Page 38 and 39: often complain that there is too mu
Page 40 and 41: ABC also has three cash flows:1. It
Page 42 and 43: Assuming that there is no transacti
Page 44 and 45: simulation techniques and mathemati
Page 46 and 47: The calculation of credit risk proc
Page 48 and 49: The payments are exchanged every th
Page 50 and 51: the reference rate. When this type
Page 52 and 53: Effectively this is just a 2-year s
Page 54 and 55: This measure of duration is referre
Page 56 and 57: analysis, it also has its shortcomi
Page 58 and 59: Percentage change in price due to d
Page 60 and 61: 8OFOptions are generally perceived
Page 62 and 63: OPTION'S PAYOFF PATTERNWhat about a
Page 64 and 65: Volatility is the most important fa
Page 66 and 67: fANDTrading options becomes more po
Page 68 and 69: You need to hold 7 shares of stock
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di = [ln(IOO/IOO) + (0.06 + O.P/2)
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is10In the previous chapter, we dis
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stock will go up in the near future
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If the stock price of A continues t
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OF AN11In the previous two chapters
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at-the-money option approaches its
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12Mortgage-backed securities (MBS)
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NEGATIVE CONVEXITYFor MBS, there is
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MULTI-CLASSIn 1983, Freddie Mac int
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13What is a hedge? According to the
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management to enter into swap and o
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transaction. For this criterion to
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CREDIT DEFAULT SWAPThe simplest for
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APPLICATION OF CREDIT DERIVATIVESYo
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in the US. Equally innovative, cred
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THE VARIANCE-COVARIANCE METHODThe t
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"cell" would have a cash flow expos
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Daily profit and loss ranked in asc
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of the market factor. Through this
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3. Most value at risk models use hi
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16ANDIn Chapter 5, we talked about
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price) of 9,000. For this transacti
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and the June 3-month futures rate i
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needs to take the necessary busines
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ief, the policies and procedures sh
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The derivatives industry can be com
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ANDONOFINTRODUCTION1. The Monetary
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MANAGEMENT AND CORPORATE5. As the B
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ensure that there is sufficient awa
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15. Branches of foreign banks which
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20. Where the institution considers
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RISK MEASUREMENT25. Having identifi
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) the tendency of the relevant mark
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38. The measurement of the market r
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market, credit and liquidity risk o
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Consideration must be given to the
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55. As noted earlier, the market or
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changes in portfolio value;d) the r
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66. A basic and essential safeguard
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73. It is essential that the intern
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Market liquidity risk is the risk t
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Furthermore, contracts with the sam
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There are three main VAR approaches
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Options risk should be captured; ri
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Annex D1. NOTIONAL OR VOLUME LIMITS
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assumptions on which they are based
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* There should be a unit independen
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- the customer had specifically req
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addition and deletion of operators,
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• Profits and losses resulting fr
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This book is due for return or rene
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