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

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at-the-money option approaches its expiration closer and closer, its gammabecomes bigger and bigger for every unit change of the underlying.An article written by John Braddock and Benjamin Krause has an excellentdescription about the relation between gamma and the option's remainingtime to expiration:Suppose there is a basketball game. Team A and Team B are of equalstrength. At the time when the game starts, the score is 0 and 0 andboth team's chance of winning the game is 50 percent. This is analogousto purchasing an at-the-money call option with a delta of 0.5.During the game, there are times when Team A is in front by a fewpoints and it has a higher probability of winning the game. This isequivalent to the price of the underlying stock goes up and so does thedelta of the call option.How much should the delta go up? This is the same question as the onewe will ask regarding how big a chance it is for Team A to win the gameat this time when it is leading by a few points.It all depends on how much time remains in the game if both teams arestill of (approximately) equal strength. If Team A is leading by 3 pointsat half-time, its winning chance is surely higher than 50 percent, butprobably not by much, say, 55 percent. However, if Team A is leading by3 points with only 30 seconds left in the game, its chance of winning isprobably very high, say, 95 percent. Although the margin of the lead forTeam A is the same, the chance of winning is different.It is the same for options. Assume that for an at-the-money option withthree months to the expiration date, the delta is 0.5 and the gamma is 0.02.After one day, the price of the underlying changes by one point. At thistime, the delta may change from 0.50 to 0.52 - a relatively small changebecause there is plenty of time for the price of the underlying to go eitherThe Gamma of an Option
way. However, if the time is now one day before the expiration date, andthe price of the underlying changes from at-the-money to one point in-themoney,the delta of the option may change from 0.50 to 0.95 because itsurely looks good for the option to be in-the-money before it expires.Gamma estimates the rate of change.For options which are far in-the-money (or far out-of-the-money), gammaprobably does not matter much because the delta is already close to I (orclose to zero for far out-of-the-money options). Just like a basketball game,if one team is leading by 30 points at the half, its chance of winning is veryhigh. Whether it gains a couple of points or loses a couple of points in thesecond half shall not affect the result very much.The Gamma of an Option
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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-
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denominator, value at risk, which c
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the kind of information that superv
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This book is a team effort of the H
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While most market participants defi
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of this investment is 6.32 percent
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Mathematically, the relation betwee
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$10,000. (For simplification of pre
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Hong Kong does go up and the HSI ri
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3OF ATHEPRICING OF A FORWARD CONTRA
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COST OF CARRYIn the above example,
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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
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 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
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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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