
Risk of a Big Move with Short Options, Delta-NeutralCol 1
Col 2
Col 3
Col 4
Col 5
Row
Position
InitialPrices
Prices afterBig Move
Proﬁt/Lossper Share
PositionLoss
123
Short 100 45 CallsLong 3,000 sharesPosition delta*
1.0042.00-0-
4.9049.005,000
(3.90)7.00Total loss:
(39,000)†21,000‡(18,000)
* With stock price 42.00, the delta of the short 45 Call is 0.30.† Option position loss  ($390) per option  100 options  ($39,000).‡ Stock position proﬁt  $7 per share  3,000 shares  $21,000.
Delta-Neutral Trading: Theory and Reality • 275
Option traders who employ delta-neutral trading must be familiarwith the historic volatility and implied volatility of the underlyinginstrument they are trading (see Chapter 7), and they must make judgments about what is low and what is high. Delta-neutral trading is nota quick road to riches for speculators; it is a difﬁcult enterprise involving judgment and discipline. It has its risks and potential rewards, asdoes any trading endeavor.
Trading Delta-Neutral—Opportunities and Risksfor Market MakersMarket makers, in contrast to speculators, attempt to proﬁt by buyingat the bid price and selling at the ask price. Delta-neutral trading formarket makers therefore is the ﬁrst step in a two-step process that hopefully lasts only minutes or no more than a few hours.As will be discussed in Chapter 8 with several examples, step one fora market maker is to buy an option at the bid price (or sell at the askprice) and then to create a delta-neutral position with the underlyingstock. Step two is to sell the option at the ask price (or buy at the bidprice) and then close the stock position. The market maker hopes thatwhen both the stock and option positions are closed, a proﬁt will result.The risk, of course, is that the market maker will instead suffer a loss.When market makers buy at the bid price and immediately createa delta-neutral position by trading stock, the stock trade is known as ahedge. A hedging trade or, simply, a hedge is establishing a positionthat offsets the short-term market risk of another position. Considerthe delta-neutral positions in Tables 8-1 through 8-4. Market makerscould have created each of these positions after buying (or selling) theoptions at the bid (or ask) price.A market maker in XYZ options, call him Market Maker A, mighthave created the position in Table 8-1 as follows: After reviewing thehistoric volatility of XYZ stock and the implied volatility of its options,and after evaluating several bids and offers in XYZ options, themarket maker decides that XYZ options at 28 percent volatility would
276 • Trading Options As a Professional
be a good buy and that at 30 percent volatility those options would bea good sell. Market Maker A also decides that he is willing to buy orsell 50 contracts at these levels. He then programs his computer tomake trades at these levels. When the price of XYZ stock is at $89.05,Market Maker A’s computer automatically bids 2.75 for 50 XYZ 90Calls and offers 50 at 2.85.At this instant, with XYZ trading at $89.05, assume that anothertrader, call her Trader B, decides to sell 20 XYZ 90 Calls at “the market.” A market order is an instruction to a broker to make a trade at thebest price currently available. Trader B could be a nonprofessionalindividual trader or a professional trader at a mutual fund, or she couldbe another market maker. The seller’s identity does not matter. All thatmatters is that Market Maker A, who is bidding for XZY 90 Calls, hasjust purchased 20 of them at a price of 2.75. Trader B is the seller.At this point, with XYZ stock at $89.05, Market Maker A now holds20 calls with a delta of 0.45 each, creating is an exposure of 900deltas that he wants reduced to zero. The quickest and surest way ofbringing the delta to zero is to short 900 shares of XYZ stock, so MarketMaker A’s computer automatically executes this trade. As a result, Market Maker A has the delta-neutral position described in Table 8-1 oflong 20 XYZ 90 Calls at 2.75 and short 900 shares of XYZ stock at 89.05.How Market Maker A decides what to do next is more complicatedand is discussed in Chapter 10. In brief, however, market makers strivenot only to be delta-neutral, but they also try to be volatility-neutral.Consequently, as long as Market Maker A senses that implied volatility is staying the same or rising, he will maintain his long call and shortstock position and hope that still another trader will purchase the callsat the ask price. If, however, it appears that implied volatility is beginning to decline, then Market Maker A will sell another option tohedge the volatility risk of the long 90 Calls.In theory, the risk borne by market makers is the same risk borneby speculators. Buying options delta-neutral poses substantial risk,whereas selling options delta-neutral caries unlimited risk regardlessof the trader. In practice, however, speculators enter delta-neutral
Delta-Neutral Trading: Theory and Reality • 277
positions with the intention of holding them for several days or longer,whereas market makers hope to limit their exposure to much shorterperiods of time, which decreases their risk exposure.Speculators who engage in delta-neutral trading strategies hope toproﬁt from predicted changes in implied and realized volatility. Theyrisk losing money if their forecasts are wrong. For market makers, adelta-neutral position does not involve a forecast. It is a hedge, or riskreducing tactic, until they make “step two” of a trade.
SummaryDelta-neutral trading is a nondirectional trading technique that profits, loses, or breaks even from the relationship between impliedvolatility and realized volatility. A delta-neutral position is one whosedelta is at or near zero. Professional market makers and professionalspeculators have very different motivations for using delta-neutraltrading.Long volatility describes delta-neutral positions in which optionsare owned, such as long calls and short stock or long puts and longstock. Short volatility describes delta-neutral positions with shortoptions, such as short calls and long stock or short puts and short stock.Delta-neutral positions can have more than two components.The process of delta-neutral trading involves, ﬁrst, establishing adelta-neutral position; second, making adjusting stock trades over several days according to predetermined rules; and third, closing theremaining position. The theory behind delta-neutral trading is thatthe proﬁt or loss from option trades will exactly offset the loss or proﬁtfrom stock trades. In the language of options, the theory is that impliedvolatility equals realized volatility.The reality of delta-neutral trading is different from the theory.Implied volatility and realized volatility both change because both aresubject to market forces. Consequently, there is no assurance that theywill be equal. Traders who use delta-neutral trading therefore mustassume some risk.
278 • Trading Options As a Professional
Speculators use a forecast for the direction of implied volatility andrealized volatility and the relationship of the two, and they assume therisk that their forecast is wrong. Market makers use delta-neutral trading as a short-term hedging technique with a goal of closing a positionby buying at the bid price or selling at the ask price in a short periodof time before implied volatility changes adversely.
Chapter 9SETTING BID-ASK PRICESarket makers must feel comfortable with the prices at which theybuy and sell options. They therefore must have a system to establish these prices to their advantage. At a minimum, the prices must beset in such a way that traders believe that they have a slight theoreticaladvantage. This chapter will discuss four important concepts related tohow traders establish bid and ask prices. The ﬁrst concept explained isthe theory of the bid-ask spread, how it works, and why it is so important to market makers. Second, the chapter explores how market makers attempt to earn the bid-ask spread by trading delta-neutral. Settingbid and ask prices based on implied volatility will be discussed next,and ﬁnally, the fourth concept, how market makers use implied volatility to keep track of bid and ask prices as stock prices change, will beexplained. The discussion concludes with four exercises that illustratehow buying options on the bid, selling at the ask, and trading deltaneutral can help to establish butterﬂy spreads, reverse conversions, andbox spreads at proﬁtable prices.This chapter assumes that you are familiar with “the market” beinga combination of a bid price, an ask price, and a quantity for both. Ifyou need a refresher on these concepts, please review Chapter 1before proceeding through the following material.
M
• 279 •
280 • Trading Options As a Professional
The Theory of the Bid-Ask SpreadTables 9-1 and 9-2 illustrate how market makers attempt to makemoney by buying on the bid, selling at the ask, and hedging deltaneutral. Each table has an opening trade, a closing trade, and aproﬁt/loss calculation. The hypothetical market maker engaging inthe trades in these examples is called Alex.Alex makes his ﬁrst trade in Table 9-1 at 10:00 a.m. when the stockhas bid and ask prices of 53.99 and 54.01, respectively, and the 55 Callhas a bid price of 1.80, an ask price of 1.85, and a delta of 0.40. Forsimplicity, this example assumes that the necessary number of sharesand options can be traded at the prices indicated, so the quantities ofshares and options bid for and offered are not mentioned.Trade 1 in Table 9-1 has two parts. Alex sells 10 of the 55 Calls atthe ask price of 1.85 per share and purchases 400 shares of stock atthe ask price of 54.01 to hedge the option position. A hedging stocktrade is the purchase or sale of the speciﬁc number of shares that offsets the total delta of an option position. The calculation of totalposition delta is shown after the trade 1 description. Alex purchasesstock at the ask price because a market maker must act quickly aftermaking an option trade. If he fails to act quickly, the stock pricecould move the wrong way, which would make the hedging stocktrade ineffective.Alex’s next trade in Table 9-1 occurs at 11:00 a.m. after the stockprice rallies $1.00 and the bid and ask prices for the 55 Call increaseby 40 cents. For simplicity, these changes in option prices are exactlyas predicted by the delta. In the real world, gamma or vega or both,as explained in Chapter 4, would cause the option price to change differently than indicated by the delta. Trade 2 closes both parts of theposition established in trade 1. Alex buys the short options at the bidprice of 2.20 and sells the stock at the bid price of 54.99.Proﬁt and loss are calculated at the bottom of Table 9-1. Alex sold10 of the 55 Calls at 1.85 per share and repurchased them for 2.20 fora loss of 35 cents per share, or $35 per option or $350 total for 10options. He bought 400 shares of stock at 54.01 and sold them at 54.99
Setting Bid-Ask Prices • 281
Table 9-1
Theory of the Bid-Ask Spread Part 1
10:00 a.m.
Stock quote:55 Call quote:55 Call delta:
Bid
Ask
53.991.800.40
54.011.85
Trade 1: Sell 10 55 Calls at the ask price and hedge delta-neutral with stockNumberof SharesSell 10 55 CallsBuy 400 shares
11:00 a.m.
1.8554.01
Delta

PositionDelta
1,000 0.40400 1.00Total position delta

4004000

PositionDelta
Stock quote:55 Call quote:

Bid
Ask
54.992.20
55.012.25
Trade 2: Buy 10 55 Calls on the bid, and close the stock positionNumberof SharesBuy 10 55 Calls
2.20
Sell 400 shares
54.99

Delta
(Closes position fromTrade 1)(Closes position fromTrade 1)
Calculation of proﬁt or loss
Sell priceBuy priceP/L per share Number of sharesProﬁt or loss
Stock Trade
Option Trade
Net Proﬁt/Loss
54.9954.01 0.98 400 392
 1.85 2.20 0.35 1,000350
 42
for a proﬁt of 98 cents per share, or $392 total. The net result is a proﬁtof $42, not including transaction costs.The message of Table 9-1 seems to be that buying options on thebid and selling them at the ask yields proﬁts for market makers, evenif they have to give up the bid-ask spread on the underlying stock. But
282 • Trading Options As a Professional
is Table 9-1 conclusive? Suppose that the stock price declines insteadof rallies. What would the result be? Table 9-2 addresses this question.Table 9-2 is similar to Table 9-1 with one major difference: The stockprice declines by $1.00 rather than rises. Alex’s ﬁrst trade in Table 9-2 isthe same as trade 1 in Table 9-1. He sells 10 of the 55 Calls at the askprice of 1.85 and purchases 400 shares at 54.01 to hedge the options.Table 9-2
Theory of the Bid-Ask Spread Part 2
10:00 a.m.
Stock quote:55 Call quote:55 Call delta:
Bid
Ask
53.991.800.40
54.011.85
Trade 1: Sell 10 55 Calls at the ask price and hedge delta-neutral with stock:Numberof SharesSell 10 55 CallsBuy 400 shares
11:00 a.m.
1.8554.01
1,000 400
Stock quote:55 Call quote:

PositionDelta
 0.40 1.00Position delta 
4004000

Delta
Bid
Ask
52.991.40
53.011.45
Trade 2: Buy 10 55 Calls on the bid and close the stock position:Buy 10 55 Calls
1.40
Sell 400 shares
52.99
(Closes positionfrom Trade 1)(Closes positionfrom Trade 1)
Calculation of proﬁt or loss:
Sell priceBuy priceP/L per share number of sharesProﬁt or loss
Stock Trade
Option Trade
Net Proﬁt/Loss
52.9954.011.02 400408
1.851.400.45 1,000450
42
Setting Bid-Ask Prices • 283
Trade 2 in Table 9-2 occurs at 11:00 a.m. after the stock pricedeclines $1.00 and the bid and ask prices for the 55 Call decline by40 cents. In trade 2, Alex purchases the short options at the bid priceof 1.40 and sells the stock at the bid price of 52.99.Proﬁt and loss are calculated at the bottom of Table 9-2. Alex sold10 of the 55 Calls at 1.85 per share and repurchased them for 1.40 fora proﬁt of 45 cents per share, or $45 per option or $450 total for 10options. He bought 400 shares of stock at 54.01 and sold them at 52.99for a loss of 1.02 per share, or $408 total. The net result is a proﬁt of$42, not including transaction costs. This is exactly the same result asin Table 9-1. A stock-price decline therefore yields the same result asa stock-price rally.
Real-World FactorsThe exercises in Tables 9-1 and 9-2 show, conceptually, that buyingoptions on the bid, selling them at the ask, and trading delta-neutral can yield proﬁts for market makers regardless of which way thestock price changes and even if they have to give up the bid-askspread in the underlying stock. In the real world, of course, thereare several complicating factors. First, traders must pay transactioncosts. Even if they are very low for professional market makers, transaction costs can have an impact on trading results and must beincluded when planning trades. Second, the size of the bid-askspread in the underlying stock is signiﬁcant. In these two examples,the stock’s bid-ask spread was 40 percent of the bid-ask spread in theoptions: 2 cents per share for the stock versus 5 cents for the options.There is clearly a point at which the bid-ask spread in the stockrequires an adjustment to the bid-ask spread in the options. Third,since stock prices ﬂuctuate, market makers must learn to adjust theirbid and ask prices for options in a manner consistent with stockprice changes. Using the delta is one tool of the market maker is thisregard, but as will be shown below, there are other tools that aremore important.
284 • Trading Options As a Professional
The Need to Adjust Bid and Ask PricesOption prices do not always change exactly as the delta and gammapredict they will because the level of implied volatility can change.The impact of implied volatility was illustrated in Table 7-6. For thisreason, market makers must respond in two ways. They must set risklimits, and they must scale into and out of positions.A limit on risk can be stated in dollars, in exposure to volatility, orin the number of option contracts. For the following example, the market maker, whose name is Anna, will set a risk limit of 100 contracts,long or short. Also, in this example, Anna will buy or sell a maximumof 20 contracts before adjusting the bid and ask prices.Scaling in means buying at successively lower prices or selling atsuccessively higher prices so that the average price of a large positionis more favorable than the initial price. The concept is that if a seriesof buy orders or sell orders comes into the market, one right afteranother, then a market maker can scale in, or average in, up to thepredetermined maximum contract position. In the following example,the market maker, Anna, sells 20 contracts at the initial price, then 20more at a higher price, then 20 more at a still higher price, and so onuntil the maximum of 100 contracts is reached or she is able to buyand close some of the short contracts.By adjusting bid and ask prices in this manner, Anna accomplishestwo things. First, she manages her position by getting a better price(higher in this case) with each sale. Second, the higher bid mightentice sellers into the marketplace. Remember, a market maker’s goalis to buy on the bid price and sell at the ask price, make a proﬁt, andeliminate risk by closing the position.In real trading, a trader applies personal judgment in this process.Why 20 contracts at each level and not 10 contracts or 25? How muchshould the price be adjusted after each purchase or sale? Should bidand ask prices be raised or lowered by one tick, two ticks, or more?And when should the size of the adjustment be changed—when aposition reaches 40 contracts, 60 contracts, or some other number?
Setting Bid-Ask Prices • 285
There are no scientiﬁcally “right” answers to these questions. Everymarket maker must make an individual determination based on experience and willingness to accept risk.
The Process of Adjusting Bid and Ask PricesMarket maker Anna makes four trades in the following example. Asthree successive 20-contract buy orders enter the market followed bya 60-contract sell order, Anna sells to the buy orders and then buysfrom the sell order. After each sale, she raises the bid and ask prices.For the sake of simplicity, the example assumes that the stock pricedoes not change. The issue of changing stock prices will be discussedin later exercises.Table 9-3 starts with the essential information. The stock has a bidprice of 80.40 and an ask price of 80.42. The 80 Call has a bid priceof 4.50, an ask price of 4.60, and a delta of 0.60. It is assumed thatthe necessary number of shares and options can be traded at the pricesindicated.In step 1 in Table 9-3, Anna sells 20 of the 80 Calls at the ask priceof 4.60 and purchases 1,200 shares of stock at 80.42 to hedge theoption position. Given the call delta of 0.60, Anna calculates thenumber of shares as follows: The underlying for 20 short calls is 2,000short shares, but given the delta, the market exposure is equivalent toshort 1,200 shares (2,000  0.60  1,200). To be delta-neutraland offset this short market exposure, Anna immediately buys 1,200shares at the ask price of 80.42.Since Anna’s position now has 20 short calls, she must adjust thebid and ask prices in compliance with her predetermined rule to manage risk. In step 2, therefore, she raises the bid and ask prices by 2 centseach, changing the market for the 80 Call to 4.52 bid and 4.62 ask. Instep 3, Anna sells 20 more of the 80 Calls at the new ask price of 4.62and purchases 1,200 more shares of stock at 80.42 to hedge the newlysold calls.
286 • Trading Options As a Professional
Table 9-3
Adjusting Bid and Ask Prices
Stock quote:80 Call quote:80 Call delta:
Bid
Ask
80.404.500.60
80.424.60
Step 1: Sell 20 80 Calls at the ask price and hedge delta-neutral with stock:Numberof SharesTrade 1: Sell 20 80 Calls4.60Buy 1,200 shares 80.42
2,0001,200
Delta

PositionDelta
 0.60 1.00Total delta

1,2001,2000

Step 2: Raise the call bid and ask prices by 2 cents: bid, 4.52; ask, 4.62.Step 3: Sell 20 80 Calls at the ask price and hedge delta-neutral with stock:Numberof SharesTrade 2: Sell 20 80 Calls4.62Buy 1,200 shares 80.42
2,0001,200
Delta

PositionDelta
 0.60 1.00Total delta

1,2001,2000

Step 4: Raise the call bid and ask prices by 2 cents: bid, 4.54; ask, 4.64.Step 5: Sell 20 80 Calls at the ask price and hedge delta-neutral with stock:Numberof SharesTrade 3: Sell 20 80 Calls4.64Buy 1,200 shares 80.42
2,0001,200
Delta

PositionDelta
 0.60 1.00Total delta

1,2001,2000

Step 6: Raise the call bid and ask prices by 2 cents: bid, 4.56; ask, 4.66.Step 7: Buy 60 80 Calls on the bid price and close the stock position:Trade 4: Buy 60 80 Calls4.56Sell 3,600 shares 80.40Step 8: Proﬁt or loss:
Sell priceBuy priceP/L per share number of sharesProﬁt or loss
(Closes position)(Closes position)
StockTrade
OptionTrade 1
OptionTrade 2
OptionTrade 3
CombinedProﬁt/Loss
80.4080.420.023,60072
4.604.560.042,00080
4.624.560.062,000120
4.644.560.082,000160
288
Setting Bid-Ask Prices • 287
After step 3 in Table 9-3, Anna’s position has increased to 40 shortcalls, the next 20-contract increment. The bid and ask prices therefore have to be raised again in step 4, when she raises the bid and askprices by another 2 cents each, this time to 4.54 bid and 4.64 ask. Instep 5, Anna sells 20 more of the 80 Calls at the new ask price of 4.64and again buys 1,200 more shares of stock at 80.42 to hedge the newlysold options.With Anna’s position now at the next 20-contract increment of 60,Anna again raises the bid and ask prices to 4.56 bid and 4.66 ask,another 2-cent increase shown in step 6. Finally, in step 7, a sell orderof 60 contracts enters the market. As a market maker, Anna buys all60 of the 80 Calls at the bid price of 4.56 and simultaneously sells all3,600 shares at the bid price of 80.40.
Calculating Proﬁt and LossStep 8 in Table 9-3 calculates Anna’s proﬁt and loss. In this example,Anna bought all 3,600 shares of stock at 80.42 and sold them all at80.40. This loss of 2 cents per share amounts to a total loss of $72, notincluding transaction costs.Turning to the option proﬁt/loss calculation, Anna purchased alloptions at the same price of 4.56 but sold them at three differentprices, 4.60, 4.62, and 4.64. As indicated under option trade 1, optiontrade 2, and option trade 3, the proﬁts on these trades were $80, $120,and $160, respectively. Combining the loss on the stock trades withthe proﬁts on the option trades yields Anna a net proﬁt of $288.The eight steps in Table 9-3 show that scaling into positions is atechnique that market makers can use to avoid taking on a large position all at one price. Also, by adjusting the bid and ask prices, the profitability of a position can be maintained. The exercise, however, raisestwo questions.First, how many times can the bid and ask be raised before a profitable trade becomes a losing one, and second, how are bid and askprices monitored and adjusted in the face of ﬂuctuating stock prices?These questions will be addressed with some examples.
288 • Trading Options As a Professional
The Limit on Adjusting Bid and Ask PricesTable 9-4 calculates the maximum number of times that a bid-askspread can be adjusted (raised or lowered) so that a break-even resultstill can be achieved on the last adjustment. It is assumed that thesame number of contracts are purchased or sold at each price.Table 9-4 contains six columns. Column 1 indicates the number oftimes that the bid-ask spread is raised. The bid and ask prices are incolumns 2 and 3, respectively, and column 4 describes each trade andits price. Each row of column 5 indicates the average sale price of allTable 9-4
The Limit on Adjusting Bid and Ask Prices
Col 1
Col 2
Col 3
TimesRaised
Bid
Ask
123456789
1.751.761.771.781.791.801.811.821.831.84
1.801.811.821.831.841.851.861.871.881.89
Col 4
Col 5
Col 6
Trade
Avg. SalePrice
No. ofShortContracts
Sell 1 at 1.801.8001Sell 1 at 1.811.8052Sell 1 at 1.821.8103Sell 1 at 1.831.8154Sell 1 at 1.841.8205Sell 1 at 1.851.8256Sell 1 at 1.861.8307Sell 1 at 1.871.8358Sell 1 at 1.881.8409Buy 9 at 1.840Result  0 (break even)
Conclusion: If the initial bid-ask spread is 5 cents, and if bid and ask prices areraised by 1 cent after each sale transaction, then prices can be raised nine timesbefore buying on the bid causes a net break-even for all the trades up to thatpoint. The ninth sale would create a situation where buying on the next bid wouldcause a loss.General formula: The break-even point is equal to two times the bid-ask spreadminus one divided by the increment of increase/decrease. This is the number oftimes the bid-ask spread can be adjusted (raised or lowered) until closing thetotal position at the current bid or ask would result in breaking even.
Setting Bid-Ask Prices • 289
the contracts sold up to that point. Column 6 keeps a running totalafter each trade of contracts sold up to that point.In the ﬁrst row of