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

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ates, the forward rate for the period 24/7/97 to 24/10/97 can be calculatedas follows:The discounting factors are:DF/ = - = 0 9773, DF2 = — = 0.9601(I + 6.239% x I36 /365) (I + 6.645% x 228 /3 6 s)The forward rate is calculated usingL(228-365JDF 2which gives r = 7.1 I %.MOVEMENTS OF THE YIELD CURVEBefore we move on to other types of derivatives, there is one final conceptto be introduced here. We often hear from the news that "central banksare cutting the interest rates". Have you ever wondered what exactly thismeans? It does not imply that the central bank has cut the interest ratesacross all maturities by the same margin. If so, the curve would always movein a parallel fashion. In reality only one reference rate (usually an overnightrate) is changed. The effect on the rates with long maturities is usuallydifferent from that of the short maturities. There are three important waysthat the yield curve can move:1) Parallel shift - the whole curve moves up or down by the same margin.2) Change of slope - the curve moves in opposite direction around a pivotpoint. (The curve "steepens" or "flattens".)3) Change of convexity - rates of different maturities move by differentmagnitudes. (The curve "twists".)Forwards and Futures
Rate(1) (2)RateRate(3)TimeTimeTimeIn the first part of this chapter, it is shown that the price of an interest rateforward can be obtained using today's market data. That is what the rateis expected to be given today's information. However, for some morecomplicated derivatives, we need to know what the yield curve wouldpossibly look like in the future. For example, we are asked to price anoption today of the 3-month forward given in the above example. In thatcase, although we know that the expected forward rate given by today'sdata is 6.34%, it is also very likely that the yield curve will move in the next6 months. In order to price the option we need to know how this curvewill move. This is considerably more difficult than the pricing of derivativeson other assets, because here we have to model the movement of thewhole curve, whereas for other asset classes only the spot variable (e.g. theexchange rate or the stock price) needs to be modelled.People have carried out research as to how these yield curves move overtime in practice. Empirical results using US data show that a combinationof parallel shift and change of slope can explain over 90% of the movementsof the curves. This is an important piece of information because by knowingthat two kinds of movements can account for most of the changes in theyield curves, we can simplify the modelling process and approximate themovements by summarising these using one or two "factors", which makesthe life of the "rocket scientist" 2 much easier.2 A nickname for those people who used to study Astrophysics and similar subjects and then apply thisknowledge to design exotic financial derivative products.Forwards and Futures
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 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 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
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)
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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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