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

More documents

Recommendations

Info

analysis, it also has its shortcomings. As we mentioned earlier, duration isquite accurate in calculating changes in price for small changes in yields. Forlarge changes in yields, duration only provides an approximation, and wehave to rely on the concept of convexity for more accurate estimations.CONVEXITYThe true relationship between a change in price and a change in interestrate for option-free securities is not linear. The following graph demonstratesthis relationship:Error not measured by durationPriceActual priceA'Error not measuredby durationB' Tangent linerepresenting durationYi ¥2 Y Y3 Y 4YieldThe actual price of the security is the curve AA', and the straight line BB'which is tangent to the AA' curve represents the duration of the security.Therefore, as the graph shows, the straight line approximation createserrors that grow with the magnitude of the interest rate changes. For smallchanges in yield, e.g. from Y to Ys or Ys, duration does a good job inestimating the actual price. But for larger changes, e.g. from Y to Yi or Y«,duration becomes less accurate and the errors become larger. Convexityis what we use to correct this problem.Duration and Convexity
Mathematically, modified duration is the first derivative of bond price whileconvexity is the second derivative. Convexity measures the rate of changeof duration:C XJt = t[ X ( ll + ' ) X PVCF ' + t2 X (t2 + I ) X PVCF2 + ....... + tn X (tn + i ) X PVCFt0nV6XI y( I + yield/k) 2 x (k 2 x PVTCF) * 'The convexity of the security in our previous illustration is 20.1886 (followingthe calculation format illustrated on page 41.)The price change that is due to the curvature is shown in the followingformula:Percentage change in price due to convexity =1/2 x convexity x (yield change) 2 x 100 (7)Now we can put things together. For a 100 basis point change in yield from8.00 percent to 7.00 percent, the true theoretical price, taking intoconsideration both duration and convexity, is:Percentage change in price due to duration = -4.0555 x (-0.01) x 100 = 4.0555%Percentage change in price due to convexity = 1/2 x 20.1886 x (-0.0 1) (-0.0 1) x 100= 0.1009%Total percentage change in price = 4.0555% + 0.1009%= 4.1564%As you can see, when the interest rate decreases, the convexity actuallyaccelerates the price appreciation. Further, the change in price due toconvexity is largely determined by the change in interest rate. If the yieldchange is small, the square of yield change is negligible. If the yield changeis large, this term can be significant and thus affects the outcome of equation(7).Similarly, the true theoretical price change if the interest rate increases from8.00 percent to 9.00 percent can be calculated as follows:Duration and Convexity
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 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 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
Page 104 and 105: Daily profit and loss ranked in asc
Page 106 and 107:
of the market factor. Through this
Page 108 and 109:
3. Most value at risk models use hi
Page 110 and 111:
16ANDIn Chapter 5, we talked about
Page 112 and 113:
price) of 9,000. For this transacti
Page 114 and 115:
and the June 3-month futures rate i
Page 116 and 117:
needs to take the necessary busines
Page 118 and 119:
ief, the policies and procedures sh
Page 120 and 121:
The derivatives industry can be com
Page 122 and 123:
ANDONOFINTRODUCTION1. The Monetary
Page 124 and 125:
MANAGEMENT AND CORPORATE5. As the B
Page 126 and 127:
ensure that there is sufficient awa
Page 128 and 129:
15. Branches of foreign banks which
Page 130 and 131:
20. Where the institution considers
Page 132 and 133:
RISK MEASUREMENT25. Having identifi
Page 134 and 135:
) the tendency of the relevant mark
Page 136 and 137:
38. The measurement of the market r
Page 138 and 139:
market, credit and liquidity risk o
Page 140 and 141:
Consideration must be given to the
Page 142 and 143:
55. As noted earlier, the market or
Page 144 and 145:
changes in portfolio value;d) the r
Page 146 and 147:
66. A basic and essential safeguard
Page 148 and 149:
73. It is essential that the intern
Page 150 and 151:
Market liquidity risk is the risk t
Page 152 and 153:
Furthermore, contracts with the sam
Page 154 and 155:
There are three main VAR approaches
Page 156 and 157:
Options risk should be captured; ri
Page 158 and 159:
Annex D1. NOTIONAL OR VOLUME LIMITS
Page 160 and 161:
assumptions on which they are based
Page 162 and 163:
* There should be a unit independen
Page 164 and 165:
- the customer had specifically req
Page 166 and 167:
addition and deletion of operators,
Page 168 and 169:
• Profits and losses resulting fr
Page 170 and 171:
This book is due for return or rene
show all

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

Create successful ePaper yourself

Delete template?

Save as template?