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

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This measure of duration is referred to as Macaulay's duration, which isnamed after Frederick Macaulay, who first computed it in 1 938 in his article,"Some Theoretical Problems Suggested by the Movement of Interest Rates,Bond Yields, and Stock in the US since 1856".Duration is a single number that is measured in units of time, e.g. monthsor years. For securities that make only one payment at maturity, such aszero coupon bonds, duration equals term-to-maturity.USE OF DURATIONDuration is a very useful measure. First, it converts a very complex cashflow structure into a single number that represents the rate sensitivity ofthe financial instrument. Second, it can be used in a formula to calculatethe change in the security's market value that occurs as a result of a changein market rate. Third, it can also be used to measure the overall ratesensitivity of a portfolio of instruments or the entire asset liability structure.The relationship between Macaulay's duration and security price volatility is:Percentage _ |change in price = - x Macaulay's duration x yield change x 100 (I)(I + yield/k)For easy calculation, academics and market practitioners usually combinethe first two expressions on the right-hand side into one term and call it"modified duration":M ,.* , , . Macaulay's duration , xModified duration = — / . - (2)(I + yield/k)v 'The relationship can then be expressed as follows:Percentage change in price = - modified duration x yield change x 100 (3)To illustrate this relationship, consider a change in yield (change in marketrate) from 8.00 percent to 9.00 percent for the bond described earlier:Modified duration = -~~~ 4.0555 (4)Change in price = -4.0555 x (+0.01) x 100 = -4.0555 percent (5)Duration and Convexity
In other words, when the interest rate increases from 8.00 percent to 9.00percent, the bond originally sold for 100, is now priced at 95.9445, adecrease of 4.0555 percent.Equation (3) is quite accurate for small changes in yields, but is only anapproximation for large changes in yields. This will be discussed later in thischapter.From the above example and the previous illustration, we can see howduration applies to bond pricing analysis. (We constrain our discussion tooption-free securities.)First, we see from the illustration that we have converted a 5-year bondwith 10 cash flows into a single number - a modified duration of 4.0555.What does it mean? It means that if the interest rate increases by, say onepercent, the price of the security decreases by 4.0555 percent; or if theinterest rate decreases by one percent, the price of the security increasesby 4.0555 percent. Therefore, this modified duration of 4.0555 representsthe interest rate sensitivity of this 5-year bond.Second, as we can see in equations (3) and (5), the percentage change inbond price due to a change in interest rate can be easily calculated.Third, by using the duration concept, we can perform some forms of asset/liability management. We can match the durations between assets andliabilities portfolios to create a "duration-matched portfolio". Or we canconstruct an "immunised portfolio" that provides assured returns over atarget holding period.In addition, because modified duration is the percentage change in the priceof a security given a change in yields, and a change in yields is a measureof the change in the bond market, modified duration actually plays a similarrole of measuring market risk for bonds that beta plays for stocks.Although the duration concept is simple and easy to apply in bond pricingDuration and Convexity
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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 20 and 21: $10,000. (For simplification of pre
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 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
Page 70 and 71: di = [ln(IOO/IOO) + (0.06 + O.P/2)
Page 72 and 73: is10In the previous chapter, we dis
Page 74 and 75: stock will go up in the near future
Page 76 and 77: If the stock price of A continues t
Page 78 and 79: OF AN11In the previous two chapters
Page 80 and 81: at-the-money option approaches its
Page 82 and 83: 12Mortgage-backed securities (MBS)
Page 84 and 85: NEGATIVE CONVEXITYFor MBS, there is
Page 86 and 87: MULTI-CLASSIn 1983, Freddie Mac int
Page 88 and 89: 13What is a hedge? According to the
Page 90 and 91: management to enter into swap and o
Page 92 and 93: transaction. For this criterion to
Page 94 and 95: CREDIT DEFAULT SWAPThe simplest for
Page 96 and 97: APPLICATION OF CREDIT DERIVATIVESYo
Page 98 and 99: in the US. Equally innovative, cred
Page 100 and 101: THE VARIANCE-COVARIANCE METHODThe t
Page 102 and 103: "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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