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

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If the stock price of A continues to increase to $120, and assuming that thedelta is now 0.15, the option writer should buy back 15 more shares in orderto remain delta neutral. This is the so-called delta-neutral hedge.100 110 120Since stock price does not usually jump from $100 to $110, how often shouldthe option writer hedge his position? Should he hedge every time when deltachanges?In theory, if the option writer remains perfectly hedged at all times and theactual option volatility is the same as implied volatility, the aggregate hedgingcost equals approximately the amount of the option premium of the mirroroption (here we refer to the option premium in the professional market),assuming there is no transaction cost. This leaves the option writer witha 0.5 percent profit for this transaction in our example. He will surely askhimself, "why do I have to go through all the troubles to hedge? I'd betterjust buy a mirror option and earn the 0.5 percent spread." The key forthis strategy to make more money depends on the option trader's professionaljudgement on the volatility. If the volatility indeed decreases from 50 percentto 20 percent after six months as the option trader expected, he can buya mirror option with a premium lower than that he has collected. (Here wefocus only on the volatility factor for easy explanation. In reality, the optiontrader has to consider other factors, such as the change of the intrinsicvalue of the option, etc.) Now he has accomplished all the things he issupposed to do: (I) he remains delta neutral at all times (or at least mostof the time) during this period; (2) he has squared off his option positions;and (3) he has made a profit - the difference between the amount ofpremium he collects and that he pays, plus the 0.5 percent spread.Trading Options is Trading Volatility
Besides that, option traders are normally given a certain degree of freedomfor not maintaining a perfectly hedged position. Every time an option traderdecides not to have a perfectly hedged position, he is running an openposition. Management usually controls option traders' freedom by imposingoption trading limits, such as delta and gamma limits. They are usuallyexpressed in dollar amount. An option trader can make his professionaljudgements by holding long or short positions, or by over-hedging or underhedgingthe positions he holds, as long as he acts within his limits.How much freedom an option trader should be given is a managementdecision. It is determined by a lot of things, such as the institution's risktolerance level, market outlook, product nature and characteristics, trader'sexpertise and past performance, existing trading systems, projected revenue,risk management and internal control systems, etc.The basic mechanism of trading options has been discussed above. It isobvious that for prudent risk control, management should stipulate theoptions trading strategies and establish options trading limits. In the policystatement, management should clearly answer the following questions: whatare the purposes of trading options? Is it mainly a customer-driven businessor mainly a proprietary trading business? What is the planned revenueallocation between customer business and proprietary trading business?Should traders be allowed to buy options simply to participate in the stockmarket? How much freedom should traders have when using the deltaneutralstrategy? What are the delta limits? What are the gross positionlimits for both the options and the underlying assets? All these should bedocumented in the institution's options trading policy and limits structure.Without them, it is very questionable how management can adequatelymanage, control and monitor the institution's options trading activities.Trading Options is Trading Volatility
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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
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 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 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
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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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