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

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of the market factor. Through this method, the simulation can be donemany times and the results of each of the simulation processes are unrelatedto each other. That is, they follow the independence condition.The theoretical foundation for stochastic process is that if "we sum oraverage a group of independent random variables, which themselves are notnormally distributed, the sum or average will be normally distributed if thegroup is sufficiently large." 2In layman's term, a researcher simulates many times through a randomprocess to obtain a series of values from changes in market factors in astochastic process. Although we use the term random, the process actuallygoes through certain precise mathematical processes. To simplify ourdiscussion, we could think that the researcher simulates the behaviour ofthe current market price through a random process. In this random process,the current market price goes through many random paths independent ofeach other under certain defined parameters. By the end, the researcherobtains a distribution of values.How many times a researcher should repeat the simulation process or howmany paths he should use depends on how accurate he wants the outcometo be and how powerful his computer is. Researchers usually use at leastone thousand paths in a Monte Carlo simulation process.But this is just the value at risk of one instrument in the portfolio. If thereare 10,000 instruments in the portfolio, the researcher has to repeat theabove process 10,000 times. If 1,000 paths are being used for each instrument,the researcher has to run the simulation 10,000,000 times. Therefore, runninga Monte Carlo simulation for value at risk purpose is quite time-consumingand is seldom run on a full portfolio basis. It is usually run on option relatedinstruments and on a less frequent basis for management information purpose.2 Mark Kritzman, "About Monte Carlo Simulation", Financial Analysts Journal, November/December / 993.Value at Risk
ABOUT VALUE ATThe financial world is moving towards a direction of increasingly relying onquantitative methodology to manage risk. The value at risk method is based onsound mathematical foundation. Its result can be explained by statistical theoriesand is more accurate than other traditional risk measurement methodologies.The most significant benefit of using value at risk to measure a portfolio'srisk exposure is that all the exposures in the portfolio can be summarisedinto one single meaningful number and this number is tied directly to theP/L Value at risk expresses the risk exposure of a portfolio in terms of howfrequent a specific level of potential loss will be exceeded. Managementonly needs to review the bank's daily value at risk number to understandthe risk exposure of the portfolio.Nevertheless, there are some shortcomings in the various approaches ofthe implementation of value at risk. Here are some of them:1. The variance-covariance models assume portfolio values are normallydistributed, but usually they are not. Therefore, using standard deviationto measure potential loss would likely provide an inaccurate result.2. The variance-covariance method usually applies the delta-gamma methodto calculate the value at risk for portfolios which contain options. Deltais a linear measurement and is good only for a small change in the priceof the underlying (or market factors). For large changes, delta is notaccurate. Ironically, measuring large changes is what value at risk attemptsto do. Even with enhanced models which incorporate gamma, "since thechange in slope or curvature of the option value curve is not constant fordifferent prices of the underlying, the risk measure including gamma willagain provide an inaccurate measure of market risk for larger changes inthe price of the underlying" 3 Therefore, if a portfolio has a lot of options,it is more suitable to use Monte Carlo method.3 Charles Smithson, "Va/ue-at-r/s/c" Risk, February 1996.Value at Risk
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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
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Borrowers, on the other hand, usual
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Again we use our method of having t
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ates, the forward rate for the peri
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5In this chapter, we will discuss w
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often complain that there is too mu
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ABC also has three cash flows:1. It
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Assuming that there is no transacti
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simulation techniques and mathemati
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The calculation of credit risk proc
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The payments are exchanged every th
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the reference rate. When this type
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Effectively this is just a 2-year s
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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)
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 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
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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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