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

More documents

Recommendations

Info

fANDTrading options becomes more popular these days. Options traders aresometimes perceived to be some of the smartest traders in dealing roomsbecause they always deal with some complex pricing models and talk inGreek - at least some letters of Greek.In this chapter, we will discuss two very important concepts about optionsand the famous Black-Scholes formula, and hopefully uncover some of themystique about options.THE PAYOFF PATTERN OF OPTIONSIn the previous chapter, we discussed that options have an asymmetricpayoff pattern - the buyer of an option pays a premium to obtain the rightto purchase (for a call option) or sell (for a put option) an asset at a specificprice (the exercise or the strike price) within a specific time period. Hiscost (the premium he has paid) is fixed; however, his potential benefit canbe unlimited. The seller of an option receives a premium to commit anobligation to allow the buyer of the option to purchase or sell an asset ata specific price within a specific time period. The following graphs illustratethe payoff pattern of a call option at maturity:ProfitCall OptionWriterProfitPayoffDelta and Volatility
As shown in the above graph, the down-side risk for writing options ispotentially unlimited. Because writing options is a high risk operation fora bank, the management should stipulate in the policy document the optiontrading strategies such as whether traders are allowed to write nakedoptions, i.e. writing options without holding the underlying asset, or whethertraders are required to hedge (fully or partially) the positions. If writingoptions is allowed, how the management controls this risk should be clearlywritten down in the policy statement.THE DELTA OF AN OPTIONThe payoff line of the above graph for the option buyer kinks at $100 andthen slopes upward. The slope of this line can be anywhere from zero toone for call options (-1 to 0 for put options). How does the slope of thepayoff line relate to options trading? An important point to remember is:a call option (at a specific strike price) with a slope of 0.5 means that whenthe price of the underlying increases by $ I, the price of the option increasesby $0.5. The slope of the payoff line is also called the hedge ratio. Marketparticipants commonly call the hedge ratio the option's delta. IIf the option writer does not want to take the potentially unlimited down- vside risk, he can fully hedge his positions. For every at-the-money calloption written, he needs to purchase 0.5 share of the underlying stock if thedelta is 0.5. For example, you have written 10 at-the-money options, thestock price is currently at $100 and the hedge ratio or the delta is 0.5. Youneed 5 shares of stock to fully hedge the position. This is because if thestock price increases by $1.00, the value of the 10 options increases by $0.5x 10 options = $5.00. The value of the 5 shares of stock also increases by$101 x 5 - $100 x 5 = $5.00.What if the delta is 0.7?If the delta increases from 0.5 to 0.7, you need 2 more shares of stock tofully hedge your position. This is because if the stock price increases by$1.00, the value of the 10 options increases by $0.7 x 10 options = $7.00.Delta and Volatility
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 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 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?