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

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Percentage change in price due to duration = -4.0555 x (+0.01) x 100= -4.0555%Percentage change in price due to convexity = l/2x20.I886x(+O.OI)(+O.OI)x 100= 0.1009%Total percentage change in price = -4.0555% + 0.1009%= -3.9546%When rate increases, the convexity actually decelerates the pricedepreciation. As shown on the graph on page 44, the tangent line liesbelow the theoretical price line.underestimates the true security price.This implies that duration alwaysAll we are doing here is to figure out what the true theoretical prices are.In reality, observed market prices may be different from the theoreticalprices because of bid-ask spread, demand and supply, market liquidity,market sentiment, etc. Asset pricing is more an art than an exact scienceand all mathematical models are just tools to facilitate the pricing analysis.I had once tried to confirm the market value of a multi-billion dollar, illiquidand below-investment-grade bond (or junk bond) portfolio in order todetermine the viability of the institution who held these bonds. A worldfamousjunk bond consultant group was called in to do the evaluation. Afterdays of hard work, the consultants delivered their final analysis. The marketvalues of most of these bonds given by the consultants ranged between 55and 85 percent of par. The consultants said that if everything (including theeconomy, market sentiment of the company, market sentiment of junkbonds, interest rates, management's ability, etc.) went well, the price couldbe 85, and if everything did not go well, the price could be 55. In otherwords, the user of the analysis had to make a lot of subjective assumptionsin order to come to a definitive conclusion.tDuration and convexity are very useful in bond pricing analysis. They arealso useful tools in trading and derivatives activities. Traders often usesomething called price value basis point (PVBP) to measure the sensitivityof risk of their positions. PVBP uses the duration concept to measure theDuration and Convexity
change in price of a security if rates move one basis point. This is a veryuseful tool for traders to measure their position sensitivity. However, theshortcoming of this measure (and all other duration measures) is that itassumes a parallel shift of the yield curve which usually does not happen inthe real world. Therefore, PVBP is more useful for traders who trade shortterminstruments.Dr Sam Srinivasulu of Michigan University has drawn an excellent analogyregarding duration, convexity, delta and gamma. He said, "duration (ordelta) is the speed, and convexity (or gamma) is the acceleration." It isamazing to see how those bright people connect science and finance together.So we should not be surprised to see that more and more rocket scientistsare now invading our finance territories.Duration and Convexity
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THE UNIVERSITY OF HONG KONGLIBRARIE
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VI- . .7 « i8^p ! ««^^OOSHSlVCJ
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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 54 and 55: This measure of duration is referre
Page 56 and 57: analysis, it also has its shortcomi
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
Page 104 and 105: Daily profit and loss ranked in asc
Page 106 and 107: 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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