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世聯(lián)翻譯公司完成基本的期權(quán)頭寸英文翻譯
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世聯(lián)翻譯公司完成基本的期權(quán)頭寸英文翻譯
Position Risk ProfilesBASIC OPTION POSITIONS
To evaluate option position risks comprehensively, one first must have some working classifications of the universe of possible types of option positions. The basic option positions may be considered to be composed of the 22 core positions listed in Table 4.1.These positions may be defined briefly as follows (see the Ap¬pendix to this chapter for some illustrated examples):Straddle. Long (short) same strike put and call; for example, long the 100 call and the 100 put.Strangle. Long (short) different strike put and call; for example, long the 110 call and the 90 put.Vertical spread. Long (short) and short (long) different strike options; for example long the 100 call, short the 110 call. Vertical spreads may be either bull or bear spreads depending on the directional expectation of price.Fence. Long (short) put/call and short (long) a different strike call/put; for example, long the 100 call, short the 90 put.Ratio spread. Long (short) one strike option, and short (long) a greater number of other strike options; for example, long one 100 call, short two 110 calls. There are four possible ratio spreads: long call, short call, long put, and short put. A ratio spread is long or short in the direction of the net options held. For instance, a long call ratio spread is short one 100 call, long two 110 calls. Long ratio spreads are also known as backspreads.Table 4.1 Basic option positions1 Long call2 Short call3 Long put4 Short put5 Long straddle/strangle6 Short straddle/strangle7 Bull spread8 Bear spread9 Bull fence10 Bear fence11 Ratio spread long calls (call backspread)12 Ratio spread long puts (put backspread)13 Ratio spread short calls14 Ratio spread short puts15 Long cartwheel16 Short cartwheel17 Long wrangle18 Short wrangle19 Long butterfly/condor20 Short butterfly/condor21 Conversion/reversal/box22 Time spreadsNote: See Chapter Appendix for payoff and risk profiles of single-month positions.Cartwheel. Long one ratio spread and short another ratio spread; for example, short one 100 call, long two 110 calls, long one 100 put, short two 90 puts.Wrangle. Long (short) both the put and call ratio spreads; for instance, short one 100 call, long two 110 calls, and short one 100 put and Iong two 90 put.Butterfly. Long (short) the middle strike options and short (long) an equal number of outer strike options on both sides of the middle; for example, long one 90 call, short two 100 calls, and long one 110 call. A condor means selling (buying) the middle strikes as a strangle rather than as a combination of a straddle. A butterfly or condor is always both a bull and bear spread combined.Synthetics. A conversion, reversal or box. Synthetics are generally risk-free option positions composed of some combination of underlying instrument and same-strike puts and calls. These terms are defined and discussed in Chapter 5.Time Spreads. A time spread is an option position composed of two or more different option calendar cycles (the “legs”). For further details see Chapter 6.For a simpler classification, this text groups straddles and strangles as one position type, and butterflies and condors as another single type. Straddles/ strangles and butterflies/condors are grouped together because members of each pair are essentially similar to each other except for the distance of the strike spread. This study considers the standard vertical ratio spreads as separate positions, and examines several position types less frequently discussed: fences, cartwheels, and wrangles. Conversions, reversals, and boxes may be treated as one position type from the standpoint of risk and are, therefore, one synthetic type.All time spreads are considered as belonging to one category in Table 4.1. Actually, any time spread may be created in any of the other basic position types, as either a two-legged or three- legged (butterfly) time spread. When time spreads are considered, the number of basic possible positions increases by a factor of 21 for each leg added, since this is the number of the basic singlemonth positions possible. Because of the complex possibilities of time spreads, this topic will be taken up separately in Chapter 6. This chapter will only discuss single-month option position risks.There are other option positions, not listed in Table 4.1, that are irregular in one way or another. Irregular option positions are usually some combination of one of the basic option positions, executed separately over a very wide strike/futures range. For example, the payoff schedule of an irregular option position might look like Figure 4.1.Figure 4.1 Irregular option position expiration payoff.Irregular option positions are quirky and display unstable risk profiles over extremely wide strike or futures price ranges. Essentially any irregular position may be built up with some combination of the 20 basic single-month positions spread across wide strike ranges. Quirkiness results from a tendency for a spread to take on the risk characteristics of the nearest strike option to fu¬tures near expiration as the absolute standard deviation shrinks as expiration nears. For example, a butterfly position in the back month may take on the risk characteristics of a straddle in the front month as the standard deviation shrinks over time. Almost any extremely large option position that is composed of almost all the strikes traded will have some quirky characteristics very near to expiration. This topic will be reserved until expiration risks are discussed in Chapters 5 and 7.Dealer positions are rarely composed of only single options or simple spreads. In practice, a market maker’s total carryover position over the course of an option cycle is likely to grow quite large and may easily total thousands of contracts in complex spreads, even if few contracts are traded every day. There are several reasons for this inevitable growth.First, a trader making markets in active months will be faced with a market that potentially has up to 50 or more option instruments differing by strike, month, and option type. One reason a large inventory of options accumulates over the course of an options cycle is simply that if a market maker can make a market in all option series, he or she will probably do so with enough capital to maximize profits. Over time, an active market maker’s total carryover position will probably cover every strike that has an open interest. Second, an option carryover position is likely to grow larger with time because the market maker usually makes necessary continual small adjustments to correct for risk changes and drift.But no matter how large or complex any option carryover position becomes, it will always resemble (on a single-month basis) one of the basic option positions in Table 4.1, irregular option positions not withstanding. An option trader should always know the exact type of the carryover option position, no matter how large or complex.POSITION RISK PROFILESOptions differ from underlying assets in their exposure to risk. Financial assets or futures generally are only subject to positive or negative price change risk. Options also are subject to this risk as delta risk; in addition single-month options are exposed to gamma, theta, and kappa/vega risks. Options that include calendar spreads are exposed to all of these and to time delta and kappa/vega risk as well. The payoff at expiration and at 30 days and the delta, gamma, theta, and kappa/vega risk at 30 days are shown for selected single-month option positions in the Appendix to this chapter.In Chapter 3 option risk was characterized by sign and dollar size for any small increment in instrument price, gamma, implied volatility, or time. But the sign and size of this risk may, and usually do, change as assets or futures price change. For example, a long call position may have a large negative theta in dollar terms at-the-money but a small negative theta either deep in- or out-of- the-money. A vertical spread may have positive theta at the short option strike but negative theta at the long option strike.That option risks change as asset or futures prices change is termed the risk modality of the option. Each option position has its own risk modality for delta, gamma, theta, and kappa/vega. To quantify risk modality, one must measure risk over the extended range of futures prices over which options may continue to change value. This range must be at least six standard deviations wide to be able to capture extreme change.The change in sign of risk in the basic single-month positions is reflected in the number of peaks (statistical modes) of gamma, kappa/vega, and theta risk (see Figure 4.2). No change in sign corresponds to one peak or mode, characteristic of single-option positions or straddles. A change in risk sign will be reflected in a twin-peaked risk (one positive and one negative) and is bimodal. A second change in risk sign results in a triple-peaked distribution and is trimodal.These risk sign modes show that any spread risk is not equally proportional to the distribution of risk over a range of futures prices. Risk tends to gravitate to that strike option in a spread nearest to the futures price. The different modal peaks, then, just reflect the number of underlying spreads with different risk characteristics within a total position.A single nonspread option or straddle position has unimodal kappa/vega, gamma, and theta risk profiles. Bi- or trimodality is introduced to risk any time any vertical spreads other than straddles are traded. Consider a simple bull spread in the figure on page 76, where gamma, kappa/vega, and theta risks have become bimodal. On the upside, a bull spread is positive theta and negative gamma and kappa/vega. On the downside, it is negative theta and positive gamma and kappa/vega. The two modes are positive or negative at the downside and upside strikes of the spread. Bimodality of gamma, kappa/vega and theta risk is also characteris¬tic of other spreads, including fences, ratio spreads, and cartwheel positions.Figure 4.2 Risk sign modalities.Butterfly and wrangle spread positions display trimodality of gamma, kappa/vega, and theta risk (figures on pages 82-83). The trimodality of the butterfly and wrangle strategies is an important feature in considering the optimal strategy to fit real market conditions (Chapter 7).An option position’s risk profile is composed of the simultaneous modalities of all risks-the delta, gamma, kappa/vega, and theta risk modalities and, if a calendar spread, the time delta and kappa/vega risk modalities as well. An option position’s risk profile will uniquely identify that option position from all others, and will be critical in evaluating option strategies as trading vehicles.For single-month option positions, several risk relationships are characteristic for gamma, kappa/vega, and theta. First, as with single option positions, gamma and theta are always of opposite sign but identical modality. Indeed, except for sign and an adjustment constant, gamma and theta are remarkably similar.Second, for all single-month option positions, gamma and kappa/vega are always of the same sign, and each is opposite in sign to theta over all futures price ranges (Table 4.2). A trader is either long (positive) gamma and kappa/vega and short (negative) theta, or short (negative) gamma and kappa/vega and long (positive) theta. A trader who is long volatility, therefore, is also always negative theta in all single-month positions.Third, gamma, kappa/vega, and theta risk have identical modalities in each single-month option position. If one knows any one risk sign and modality, one knows the signs and modalities of the other two risks. For example, if gamma is positive and unimodal, then kappa/vega is unimodally positive and theta is unimodally negative. If gamma is trimodal, then kappa/vega is trimodal and of the same sign; and theta is trimodal and opposite in sign to gamma and kappa/vega.Table 4.2 Sign of risk factorsCase I Case IIPositive gamma Negative gammaPositive kappa/vega Negative kappa/vegaNegative thetn Positive thetaThus, if the sign and mode of any one of the non-delta risks are known, then the sign and mode of the other risks are known as well. In effect, there is really only one gamma/kappa/theta risk cluster (by sign and modality) in single-month positions, with gamma/kappa collapsing into one dummy (by sign) risk factor. For the statistically minded, there is only one degree of freedom.The passage of time affects risk in single-month positions identically with single-option positions. In back-month positions kappa/vega is large while gamma and theta are low and wide. In front-month positions theta and gamma become larger although narrower while kappa/vega grows smaller and narrower in range. All long single-month positions grow more expensive to carry owing to time decay but are less affected by implied volatility change as time passes to expiration.The interrelation of delta, gamma/theta, kappa/vega, and time risk modalities enormously simplifies option risk analysis of single-month option positions. Option positions now become strategic in which risk may be evaluated and not just measured, which is the topic of the next section.LIMITED- AND UNLIMITED-RISK ANALYSISTheoretical consideration of option risks is validated only if it provides some practical guide to the relative risk exposure of the different option positions for trading purposes. Risk analysis must be both descriptive and evaluative. Previous sections have formally defined and quantitatively measured option risk profiles. In this section we begin to evaluate them.For trading evaluation option positions must be divided between those that have limited- and those that have unlimited-risk exposure. A limited-risk option (LRO) position is one in which potential dollar loss is always finite and fixed in the worst-case risk scenario. Limited-risk exposure does not mean that dollar losses may not be large or severe, hut only that they are fixed and finite no matter how large. The simplest LRO position is a long call or put.An unlimited-risk option (URO) position has no fixed limit on the potential dollar loss in the worst-case risk outcome. Without a fixed limit on the amount of dollar loss that an option position may sustain in the worst-case scenario, risk is catastrophic. The potential dollar loss from an option position is unlimited and, therefore, could potentially be greater than the trader’s entire capital, no matter how large. Unlimited risk is potentially catastrophic be-cause it exposes the trader in the long run to bankruptcy. The simplest URO position is a short call or put.Option risks such as rho, skew, or risks connected with expiration are almost always limited and will be considered in other chapters. But what are the limits on delta, gamma, theta, and kappa/vega risk? Which option risks are limited, and which are unlimited?The delta risk is limited (or neutral) when delta converges asymptotically to zero change, or is positive on the upside and negative on the downside of the asset or futures price movement. The delta risk is unlimited when negative on the upside and positive on the downside, that is, the position loses unlimited money on either the upside or the downside.The gamma and theta risks are limited whether they are positive or negative; they are always finite risks, no matter how large the loss. The same is not true for kappa/vega, however. There is no limit on the amount of profit/loss due to kappa/vega, and it is a potentially unlimited or catastrophic risk. In particular, it is usually a negative kappa/vega that is associated with unlimited-risk exposure in the case of an implied volatility blowout on the upside. Option positions which are negative kappa/vega, therefore, are unlimited-risk positions and generally poor strategy.In normal markets, a positive kappa/vega risk exposure often is limited, although possibly large. In the event of a high implied volatility market, being positive with respect to kappa/vega might possibly represent an unlimited-risk situation should implied levels drop dramatically and fast. However, in normal markets, this risk should be limited. A market situation of high implied levels and positive kappa/vega will be taken up in Chapter 7.A risk profile with a negative gamma, negative kappa/ voga, and positive theta represents an unlimited-risk position. A positive gamma, positive kappa/vega, and negative theta risk profile constitutes a limitod-risk exposure for single-month positions in normal markets, resulting primarily from the positive kappa/ vega risk stance. Of course, each of these asset-based risks also has a modality over a range of asset or futures prices. It is possible for an option position to be both limited and unlimited in delta or kappa/vega risk, depending upon the direction of asset prices. A short call, for example, has only a limited delta risk on the downside of asset prices but an unlimited risk on the upside. Its kappa/vega risk, however, is unlimited on both the upside and downside, reflecting the unimodal nature of single-option kappa/vega risk.For most multi-option positions, however, kappa/vega risk is bi-or trimodal and may be both positive and negative over a range of futures prices. Kappa/vega risk, therefore, may be potentially both limited and unlimited. For purposes of initial risk evaluation, however, bi- or trimodal risk positions will be considered limited in kappa/vega risk (with normal volatility markets) if the number of options long in the total position is even with or greater than the number of short. As long as there is at least one long option to cover the risk of a short option, even negative kappa/vega risk in bi- or trimodal risk positions may be considered limited. The only single-month position in which this equal balance in long and short options may not limit risk is a fence, which will be the topic of a separate section in Chapter 7.Table 4.3 summarizes the level of risk for the basic non- calendar-option positions. A URO position is subject to unlimited risk (U) in at least one direction of one risk in a risk profile. A LRO position only has limited risk (L) in both directions for all risks, or is a net even option spread.Unlimited-risk option (URO) positions include the short call or put, short straddle/strangle and short ratio spreads, fences, and cartwheels. Some may be surprised to see a covered call position classified as a URO position, but a short call, long asset or future position is just a synthetic short put. A URO position may experience loss either as a result of an unlimited move in asset or futures prices or as a result of sudden increases in the implied volatility of option prices. A short straddle position may experience unlimited loss due to a delta extreme range move on limit days, and option prices may trade at extremely high implied volatility levels. In either case, the potential dollar loss is unlimited and catastrophic for those negative kappa/vage risks.Table 4.3 Single-month option position risk summary (* = unlimited risk)Option Position Delta Gamma/Theta Kappa/VegaUnlimited risk positionShort call or put * *Short straddle/strangle * *Bull and bear fence * *Short ratio spread, calls, * *or putsShort ratio spread, calls, * *and puts (short wrangle)Bull or bear cartwheel * *Limited risk positionLong call or putLong straddle/strangleBull or bear spreadLong ratio spread, calls,or putsLong ratio spread, calls,and puts (long wrangle)Long or short butterfly/condorSyntheticsLimited-risk option (LRO) positions include all the remaining positions except time spreads. These include the long options, long straddle/strangle, spreads and long ratio spreads, butterflies, long wrangles, and synthetics. All of these risks are limited bidirection- ally in both delta and kappa/vega. Likewise, if one is in a spread position, risks are limited in either direction as long as the num¬ber of long options is equal to or greater than the number of short options in the total position. Some LROs are delta neutral and some are not.The first prudent principle and strategic goal of every finan¬cial business is to avoid the risks of bankruptcy, even before consideration of profitability. It makes no sense to earn high profits if the likelihood of bankruptcy is still higher. This perspective toward risk will be referred to as the prudent market-maker strategy and represents the safe bet in the long run.The strategies recommended in this text are of the limited-risk type. A prudently rational trader knows that any option strategy that is exposed to unlimited risk, no matter how small the probability, will eventually suffer catastrophe under the law of large numbers. As a Wall Street maxim notes, “There are bold traders and old traders but no bold, old traders.”Limited risk does not necessarily mean limited profits. Limited- risk option strategies may be highly profitable in several market situations—that is, those that are unprofitable to unlimited-risk traders! It is possible to have limited option risks yet unlimited profit potential. Prudent and informed market makers will strive to follow strategies that have these limited-riskAinlimited-reward characteristics.A URO position resembles the risk exposure of a martingale gambling strategy, which increases the amount of the bet every time a loss occurs. In a series of losses, one could bet $1, $2, $4,... in a double-up martingale. If a gambler has sufficient capital and is content with modest profit, he or she may consistently earn money for long but limited periods of time with martingale strategies.However, there eventually comes a series of consecutive-run losses that ultimately bankrupts the gambler. At that point, the gambler will no longer be able to play. For example, betting only a single dollar to start in a double martingale will bankrupt a gambler with a stake of less than $255 within 1000 plays or so. Starting with only a dollar bet, a stake of $1000 may expect to be wiped out in the course of over 4000 plays. There is no way in the long run to beat the odds consistently if they are against you. The improbable should never be assumed to be the impossible.A naive option trader employing martingale strategies may make money for long periods before losing the entire stake in a rare or freak futures price run. This is the risk of the unlimited- risk option trader.One could argue, of course, that the dollar loss on the short put is limited to ii complete collapHe of futures or asset prices, which is unlikely, and that it would sill be a fixed loss. Indeed, the loss on a short put, at least in terms of intrinsic (delta) value, is limited. However, the value of the potential loss is catastrophically huge with most futures margins. Premium expansion for at-the-money options can easily reach $5000 per option in high implied volatility situations, and the margin required may increase exponentially.Of course, at some level of capital (for example, $1 million or more) it may be possible to sell some small number of options net short and be exposed to negligible catastrophic risk. However, using $1 million of capital to short two or three options is probably not the optimum trading strategy, or use of margin or capital.If the option speculator’s profits are akin to gambling returns, then profits of limited-risk market makers may be considered sim¬ilar to the returns to the house, that is, returns that take the opposite side of the bet from the gambler but that ultimately offset or hedge this bet with the bet of another gambler. The returns of the house (or market maker) come as a percentage of total wagers, whatever the side of the bet or the event outcome. (See Reichen- stein and Davidson, 1987, for a gambling interpretation of option trading from the perspective of horse racing.)RISK DETERMINATIONThis section introduces a quick way to determine approximately the general limit of delta and kappa/vega risk of any single-month option position. (Time spread risk determination is taken up in Chapter 6). An option trader will always want to know what the exact risk profile is for each single-month carryover position at all times. Market-maker positions, however, have a tendency to grow larger during a complete cycle and include spreads covering every strike, with total carryover positions rising into the thousands. As we have already observed, any carryover position, no matter how large or complex, can be represented in one of the basic position types (Table 4.1); but identifying which one may require the use of option software (see Appendix).Usually, a trader will have such option software available to perform this risk analysis on each cycle position. Nevertheless, a trader should be able to determine by hand calculation, with¬out computer assistance, an approximate catastrophic risk profile for his or her carryover position. A trader may never have to do such manual calculations, but he or she should know how they are dono.Approximate single-month position, catastrophic risk exposure may be quickly estimated with some simple position numbers and calculations. There are three primary risk calculations: upside delta risk, downside delta risk, and kappa/vega risk. Consider futures options for illustration.To calculate the potential upside delta risk, add the net total delta of the futures position and net call position, where each call carries the equivalent of one whole delta point.△ upside risk = Net total futures + Net callsIf the result is positive, then the trader appears to have some limited upside delta risk, which is good. A negative delta would indicate potential unlimited risk.To calculate the potential downside delta risk, add the net total of the futures position and the net put position, where each put carries the equivalent of one whole delta point.△ downside risk = Net total futures + Net putsIf the result is negative, then the trader has a negative potential delta on the downside and is exposed only to limited risk. A positive downside delta exposure is an unlimited risk.These risk calculations estimate upside and downside delta risk exposure but do not indicate a position’s exposure to volatility risk. To approximate the position kappa/vega risk, add the net to¬tals of calls and puts (long-positive), which gives net total options.Kappa/vega risk = Total net puts + Net calls= Net total optionsA positive total indicates that a position potentially has only limited kappa/vega risk in the event of a volatility explosion. A negative total indicates a position with unlimited-risk expo-sure. Consider the example of a single-month position shown in Table 4.4.In this position, the delta upside risk is short 5, (short 10 futures and net long 5 calls). This result represents unlimited delta risk on the upside. Downside delta risk is short 30 (short 10 futures and net long 20 puls). The knppn/vega risk is long 25 options (net long 5 calls and net long 20 puts), which is a positive kappa/vega exposure.Table 4.4 Hypothetical single-month positionPosition SubtotalLong 10 130 callsShort 5 100 calls(Net long 5 calls)Short 20 100 putsLong 40 90 puts(Net long 20 puts)Short 10 futures(Net short 10 futures)Summarizing this example, the upside delta risk is negative (unlimited), the downside delta risk is negative (limited), and the kappa/vega risk is positive (limited). This position risk profile resembles a bear cartwheel (see also the figure on page 81 in the Appendix to this chapter). Note that what is of importance is the number of options, in full delta points, rather than the dollar value of the net option position or its delta neutrality.A trader must always know what the effect would be on the profit/loss of a position if futures prices were to experience a series of limit price moves on the upside or downside, or if implied volatility levels went from normal to high ranges (or from high to normal in high-volatility periods). If any of these trading events, no matter how unlikely, were to happen, would the position experience an unlimited loss? If the answer is yes, the position is catastrophically risk exposed.These risk determinations are only approximate and may sometimes be deceptive, and of course they do not include time spread risks. What is often critical to the risk of a carryover position is the futures standard deviation between the constituent strike spreads. Obviously, a long 110 call may be a good delta hedge against a short 100 call if the standard deviation is 15 points, but not if it is only 2 points.The risk determinations above also do not indicate the absolute dollar risk exposure by delta or kappa/vega, or the risk modalities, which are very important for position adjustment. For these reasons, option software analysis of position risk is almost indispensable. Nevertheless, a prudent trader should know how to do quick catastrophic risk determinations without such assistance.APPENDIX: Position Risk Profiles—Selected Single-Month PositionsPositions Positions1 Long Call Buy 1 100 call 10 Long Call Short 1 100 call2 Short Cal Sell 1 100 put Long 2 105 calls3 Long Put Buy 1 100 put 11 Short Call Long 1 100 call4 Short Put Sell 1 100 put Ratio Spread Short 2 105 calls5 Long Straddle Buy 1 100 call 12 Bear Cartwheel Long 1 100 callBuy 1 100 put Short 2 105 calls6 Short Straddle Sell 1 100 call Short 1 100 putSell 1 100 put Long 2 95 puts7 Bull Spread Buy 1 95 call 13 Long Butterfly Short 1 100 callSell 1 105 call Long 1 105 call8 Bear Spread Buy 1 105 put Short 1 100 putSell 1 95 put Long 1 95 put9 Bull Fence Buy 1 105 call 14 Long Wrangle Short 1 100 callSell 1 95 put Long 2 105 callsShort 1 100 putLong 2 95 putsWhere Futures price= 100Day to Expiration= 30Implied Volatility= 15Interest Rate= 101 Standard Deviation= 5.72 SD=11.4Scale Key:A. $ = Dollar payoff at expiration (solid line) and at 30 days (light line).B. A = DeltaC. = GammaC. = ThetaC. K = Kappa/Vega世聯(lián)翻譯-讓世界自由溝通！專業(yè)的全球語言翻譯供應(yīng)商，上海翻譯公司專業(yè)品牌。絲路沿線56種語言一站式翻譯與技術(shù)解決方案，專業(yè)英語翻譯、日語翻譯等文檔翻譯、同傳口譯、視頻翻譯、出國外派服務(wù)，加速您的全球交付。 世聯(lián)翻譯公司在北京、上海、深圳等國際交往城市設(shè)有翻譯基地，業(yè)務(wù)覆蓋全國城市。每天有近百萬字節(jié)的信息和貿(mào)易通過世聯(lián)走向全球！積累了大量政商用戶數(shù)據(jù)，翻譯人才庫數(shù)據(jù)，多語種語料庫大數(shù)據(jù)。世聯(lián)品牌和服務(wù)品質(zhì)已得到政務(wù)防務(wù)和國際組織、跨國公司和大中型企業(yè)等近萬用戶的認(rèn)可。
