Option Greeks in Plain English: Mastery in Under 60...

OptionGreeksinPlainEnglish:

MasteryinUnder60Minutes

ByStevenPlace

http://www.investingwithoptions.com/

Copyright©2012byStevenPlace

Allrightsreserved.Nopartofthisbookmaybe

reproducedinanyformwithoutpermissioninwritingfromtheauthor.Reviewersmayquotebriefportionsin

reviews.

DISCLAIMERNopart of this publication

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While all attempts havebeen made to verify theinformation provided in thispublication,neithertheauthornorthepublisherassumesanyresponsibility for errors,omissions, or contraryinterpretations of the subjectmatterherein.

This book is forinformational purposes only.The views expressed arethoseoftheauthoralone,and

shouldnotbetakenasexpertinstructionorcommands.Thereader is responsible for hisorherownactions.

Adherencetoallapplicablelaws and regulations,including international,federal, state and localgoverning professionallicensing, business practices,advertising, and all otheraspects of doing business intheUS, Canada or any other

jurisdiction is the soleresponsibility of thepurchaserorreader.

Neither the author nor thepublisher assume anyresponsibility or liabilitywhatsoever on the behalf ofthe purchaser or reader ofthesematerials.

Any perceived slight ofanyindividualororganizationispurelyunintentional.

COMMONSENSE

TRADINGDISCLAIMEROptions are, by nature,

leveraged instruments. Youcan lose a ton of money ifyou don't know how tomanage risk, and you'reresponsible for any trades orinvestments you make. I'm

not trying to sell you anysecurity or derivative. Doyour own homework if youaregoingtoputonanytradesorinvestments.

To see a full disclaimer,checkoutAppendixD

YOURFREEGIFT

Iwanttosaythankyouforpicking up this ebook. Ifyou're reading this, youwanttobecomeabettertrader,andIwanttohelp.

There are many ways thatpeople learn. Some will dowellwiththistext,andothersneed a different mentalpathway.Withthisinmind,I

am opening access to a fewtrainingvideosforthosewhopurchased this ebook. It willbe a "chalk and talk"visualization of the optiongreeks,sothatyouwillbetterunderstandtheconcepts.

This in-depth video isavailablethroughthislink:

http://investingwithoptions.com/option-greeks-video/

WHYOPTIONGREEKSMATTER

Imagine that it's your firstday as a trader or investor.You're excited to get startedandmakesomerealmoney!

So you open up yourbrokerage software and stareatalltheflashyredandgreenlights on your screen. Looks

likefun,right?

From there you randomlychoose a stock and buyshares. You do so with noregard to what the companyis, their fundamentals, or theunderlyingmarketstructure.

Terribleidea-butwhy?

Because you got into atrade without knowing therisksofthetrade.

From a fundamentalperspective,it'sagoodideatoknow about the companyyou're trading--how theymake money, whether theywillcontinuetomakemoney,and how fast they aregrowing.

From a technicalperspective, you probablywant to know the key pricelevels where buyers andsellershavebeentrading.

Whateveryourapproachormethodology, financialspeculation is all aboutunderstanding the riskswhenyou put on a position andknowing how to manage therisks.

Butwhatmakesoptionssodifferent?

I've helped hundreds ofpeople become better optiontraders, and one of the key

problems I see is that tradersdon't understand the risks intheoptionsmarket.

They stare at the red andgreen flashy lights andchoose a stock option to buyor sell without knowingexactly how the market willaffecttheirposition.

Andthentheywillsay"thestockmovedinthedirectionIexpected, but why did I lose

money?"

It's because you don'tunderstandtherisks.

Inanyassetyoutrade,youcare about how the value oftheassetwillmoveovertime.

With most vehicles likestocks, bonds, currencies,commodities and futures, theonly thing that can affect theprice of the asset is thechangeinthestructureof the

buyersorsellersofthatasset.

Upordown.That'sallthatmatters.Eitherthestockgoeshigher, or the stock goeslower.

But options are a uniqueasset, because it is a riskmarket,notacapitalmarket.There are other things thatcan affect the value of anoption besides the stockmovement.

The things that can affectoption pricing are known as"thegreeks," and that'swhatthiseBookisallabout.

By properly understandingthe greeks and how optionpricesmove,youwill have abettergraspoftherisksintheoptions market, and it willbecome a better optionstrader.

The title of this book says

you can master the optiongreeks in under 60 minutes,and I think that's veryfeasible. The meat of thisbook clocks in around 9,000words. Technical materialsare read very slowly--sometimes under 200 wordsper minute. But even withthat, you should be able tofully read and comprehendthis book in about under anhour.

Good luck and happytrading!

HOWTOLEARNTHEGREEKS

A major problem optiontraders face when learningoption pricing is that the"textbook method" isn't formostpeople.

Sure, theoptiongreeksareverywellexplainedincollegeclasses, but they are usually

accompanied by somethinglikethis:

For thosewithheavymathbackgrounds, that makessense.

But for most people, thismethodoflearningisentirelytoo abstract and not reallypractical in day-to-dayoperationsasatrader.

Leave the complexequations to the financeundergrads and thecomputers.

From my experience as atrader and a teacher, I'vefound that mastery of the

greeks comes through twochannels: analogies, andvisualreferences.

These are different neuralpathways that we can usecompared to the hard math,left-brained side that isineffective.

This ebook will be full ofreferencesto"normal"eventslike sportsandhow it carriesover into the optionsmarket.

There will also be plenty ofgraphs of actual option riskprofiles so you can see thegreeks as well as hear aboutthem.

HOWTOVISUALIZE

RISKWaybackintheday,floor

traders would rely on hand-pressed papyrus and theirtrustyabacustofigureoutthefair value of an option.Option orders were sent viasmokesignalsandhorseback,which led to a very smelly

Chicago.

This, of course, is anexaggeration. But relative tothepast, theaverage investorhas a lot more computingpowerintheiriPadthanwhatentire exchanges had a fewdecadesago.

Because of this, we canrely on technology tocalculate risk pricing for usand model our risk as a

function of price, time andvolatility.

This allows you to gobeyondthecomplexmathandseethehigher-levelconcepts,whicharemore importantonapracticallevel.

These risk managementplatforms are now availablewith a brokerage account orforafee--youcanseewhatIuse and recommend in

AppendixA.

SOMECOMMONTERMS

Beforewecandiveintothegreeks,youmusthaveabasicunderstandingofhowoptionsarepriced.

Moneyness is a term thattellsuswhatkindofdealweget with an option atexpiration.

There are three kinds ofmoneyness:

AtTheMoney(ATM) - This is where thestrikepriceofanoptionisthesame or nearly the same asthe underlying stock. A 50strike call would be ATM ifthestockweretradingat50

OutoftheMoney(OTM) - This is where it isnot advantageous for the

option buyer to exercise theoption at expiration. If youhavea$40callandthestockis trading at $35, it wouldmake more sense just to gobuy the stock at the marketprice $35 than to use youroptionandbuyitat$40.

In theMoney(ITM) - This means it isadvantageous for the optionbuyertoexercisetheoptionatexpiration.A $40 call option

would be ITM if theunderlying stock is tradinggreater than $40 because itwould make more sense touse your option to buy thestock at 40 compared tobuying iton theopenmarketatahigherprice.

Moneyness is key tounderstanding the two partstothevalueofanoption.

Options have twocomponents in their pricing:

Intrinsic value and extrinsicvalue.

The intrinsic value is howfarinthemoneytheoptionis.A $50 call with a stocktradingat$55wouldhaveanintrinsicvalueof$5.

Keep in mind that not alloptions have intrinsic value--only those that are ITMwillhaveintrinsicvalue.

The extrinsic value is

whateverisleftoveraftertheintrinsic value is accountedfor.Thisisalsoknownasthe"risk premium" of theoption.

Theextrinsicvalueiswhatmakes options trading funandprofitable, and it'swhereyouwill gain an edge in theoptionsmarket.

The greeks are not justabout how the option value

will change, it's also abouthowtheriskwillchange.

Thefirstordergreeksarethose that directly affect thepriceofanoption.

The second order greeksare those that affect otheroptiongreeks.

Wewillfirsttakealookatwhat I consider to be themain greeks: delta, gamma,theta, vega, and rho. These

are the easiest to understandand also the most importantwhen considering entering atrade.

Fromtherewewill lookatforces that can occur on themain greeks-- these are thesecondordergreeks.

THEBIGBELLCURVEThe options market is a

riskmarket.The risk that themarket prices in is in theextrinsic value, but how dowe define "risk" in the firstplace?

Stocks tend to move insuchafashionthattheirdailyreturns tend to cluster.Moreoften you see 1% days than

5%daysinthemarket.

A clustering of dailychangemeansthatthemarketis a "lognormal distribution."That just means the dailychange tends to fit under abigbellcurve.

Now we could get allmath-happy and show howstep functions and geometricBrownianmotioncanleadusto a binomial pricing model,

and how integrating thebinomial model somehowgetsustomorecomplexstuffliketheBlack-Scholespricingmodel.

ButallwecareaboutistheBigBellCurve.

TheBigBellCurveishowwe derive a lot of optiongreeks,soyouwillseeitpop

upeveryonceinawhile.

It is related to what themarket is expecting in termsof price action in the future.Sometimes themarketgets itright, sometimes the marketgetsitwrong.

And sometimes themarketcan change its mind, whichmeanstheBigBellcurvecanexpandandcontract.

Don't worry too much

aboutthemechanicsjustyet--as we go further on in thebook you will see how theBig Bell Curve comes intoplaywiththegreeks.

DELTADelta is the first greekwe

willcoverandisthesimplesttounderstand.Itistheriskinyour position as it relates totheunderlyingstock.

Consider just buying 100sharesofastockat$50.Ifthestockmovesup$1pointthenyouhavemade$100.Simpleright?

That means you have a

deltaof100.

With stock it's simple.

Each share is 1 delta, and itwill stay at 1 delta until youexittheposition.

But with options itbecomes more complicated.We'reno longerdealingwitha "static" exposure, but adynamic position thatchanges over time and price(we will get to those greeksshortly). Each option strikewill have a different delta,and each option month will

carrydifferentdeltas.

Consider a long call. Thisis a limited risk, limitedrewardplaythat isbullishontheunderlyingstock.

Specificallywewilllookatthe risk profile of an IWM(Russell2000ETF)longcall:

The black line is the

position value right now (y-axis)as it relates to thestock(x-axis). The red line is theposition value at optionsexpiration.

We are going to zoom inon this risk profile a bit andseewhathappens ifwegeta$1moveineitherdirection:

If the stock rallies $1, thepositionwillmakeabout$48.

If the stock drops $1, thepositionwillloseabout$44.

There are reasonswhy thedrop is not equivalent to therise- that will be detailed inthenextsection.

But overall, if the stockmoves up or down $1, thenthe value of this option willmove about $46 eitherway--

that means this option has adeltaof46.

Whenwevisualizeitaswedid above, the delta can beviewed as a rise/runrelationship-- this is alsoknownastheslope.

Andwhen the change getsvery, very small, theinstantaneous slope will bethetangentlinetothecurve.

That's also a fancywayof

saying the delta is the firstderivativetotheP/Lgraph.

A good way to approachthe delta of an option is tounderstand how it relates totheoddsoftheposition.

The delta of an option is(almost) equivalent to theodds that the option willexpireinthemoney.

An exact at-the-moneyoption has a strike price thatis thesameas theunderlyingstock. So a $50 call option

will be exactly at themoneyif the stock is trading at $50pershare.

What are theodds that theoption will expire in themoney?

Keep in mind; we aren'ttalking about our opinion onthestock,butastatisticalone.Given any current price, themarketstatisticssayit'sacoinflip higher or lower-- 50%

odds.

Sotheatthemoneyoptionhas odds of expiration at50%,whichmeansitsdeltais50.

What about an option thatisdeepinthemoney?Ifacalloptionhasastrikepriceof30and the underlying stock istrading at 50, it will be verydifficult for the option tomove out of the money-- it

would require over a $20move!

The odds of a deep in themoney (DITM) optionexpiring in the money arevery high-- near 100%. Thattells us the option delta willbenear100.

Because DITM optionshave such a high delta, theywill behave very similarly tostock, and can be considered

ifyouwant tohavea"stock-like" position with limitedrisk.

Nowfinally,whataboutanoptionthatisverydeepoutofthe money (DOTM). If astockistradingat$50andtheunderlying strike is at 70, itwould require the stock totrade up more than $20 forthe option to go ITM-- theodds of this happening areverylow.

Therefore,aDOTMoptionwill have a very low delta,because the odds ofexpirationareverylow.

Understanding the

relationshipbetweenthedeltaand the statistical oddsimpliedintheoptionsmarketis a very powerful concept,one that we will approachagain.

Anotherkeyconceptaboutdeltaisthattheabsolutedeltaof an option will never goabove100andbelow0.Whyisthat?

Standardized option

contractsdealwithaunitsizeof100shares,whichprovidestheupperlimit.Andcallswillnever have short exposure,because then it would becalledaput!

We can visualize the deltaofpositionsaswell:

By looking at the pictureabove,youcan see thatdeltachanges as it relates to stockprice.

That brings us to our nextgreek.

GAMMAGamma is the change in

theoptiondeltaasitrelatestothe change in the underlyingprice.

That may seem like a

complicated sentence, buthopefully if you understoodthe relationship with deltaand "moneyness" then youcanseehowthisworksout.

Ifanoption isveryfaroutof the money it will have alowdelta,becausetheoddsofbeing ITM at expiration arelow. But if the underlyingstock moves and the optiongoes from out of the moneytoatthemoney,thentheodds

of being ITM increase--thereforethedeltaincreases.

Consider long stock for amoment. 100 shares of longstockwillhaveadeltaof100no matter if the stock istrading at $1/share or$1000/share.

If the delta never changeswith stock, it means thatstock positions will alwayshavezerogamma.

Let's go back to our IWMlongcallpositionagain.

This time instead oflooking at a $1 move up ordown, we will be looking attwo separate $3 steps. Thiswaywe can see the effect ofgammamuchbetter.

Let'ssayIWMmovesfrom82 to 85-- that's a $3 move,then you're looking at achange of +$165 on the

option.

ButifIWMmovesfrom82to85, thevalueof theoptionwould increase+$221on topofthat$165.

This proves to us visuallythat the delta of this optionisnon-linear.

When the IWM call isATM, the delta is 50. If thestock rallies, then the optiongoes ITM and the deltaincreases.

This means that yourdirectional exposureincreases as the stock rallies.That can be fun if you're

usingleverage--butthereisatradeoff (more to come onthatlater).

A great analogy here iswithsimplephysics.

A car travels at a certainvelocity, or speed.While thecar is at a constant velocity(think cruise control) thenyou don't feel any externalforces.

But if you hit the gas or

slam on the breaks, thevelocity will change-- thechange in the velocity isknownastheacceleration.

If you're traveling in a caror a train or a plane with aconstant velocity, you don'tfeel anything.Relative to thethingyou'retravellingin,itislikeyouaresittingstill.

Butifthereisacceleration,that'swhatyoufeel--ifthings

accelerate (or decelerate) toofast you endupwith abit ofdiscomfort.

Gamma is the sameway--it's a greek that you can*feel*, especially if theunderlying stock is movingvery,veryfast.

This analogy carries overwell into the relationshipbetween value, delta andgamma:

Ifanoptiondeltaisthe1stderivative to yourP/Lgraph,

then theoptiongammais the1stderivativetothedeltaandthe2ndderivativetoyourP/Lgraph.

Ipromisednoheavymath,right?Humorme.

The 2nd derivative of agraphisdirectlyrelatedtothe"curviness"ofthegraph.

Take a look at the calloptionagain:

Instead of relying on anyheavy math, you can simplyeyeball a graph to see whatyourgammalookslike.

You can also be shortgamma, where yourdirectionalexposureincreasesonamove--but it is adversetoyou.

A good example of this iswhat's known as a straddlesale--thisisacombinationof

acallsaleandaputsale.

If you sell an ATMstraddle, thenthedeltaof thecall and the delta of the putoffset each other exactly andyou are left with what isknown as a "delta neutral"trade. But this is a shortgamma trade, which meansyourdeltacanchange.

If the underlying stocksells off, then you start toaccumulatelongdeltas.Ifthestock selling continues

further, the long deltas causelosses in the position. If thestockseesnomeanreversionand the underlying continuesto run down evenmore, youcan end up with significantlosses.

If you accumulate toomuchshortgamma, thenyouwill experience what I call"gamma heartburn,"meaningtheunderlyingstockismoving too fast foryou to

properlyadjustyourtradeandyoustarttolosemoneymuchfasterthanyouplanned.

This leaves youwith a pitin your stomach, and createstheheartburn.

So why would you evenconsider getting shortgamma-- it doesn'tmake anysense to do that unless youhadsomesortofrewardtogowithyourrisk!

Which leads us into ournextgreek...

THETAImagine yourself in Las

Vegas, sipping on anoverpriceddrinkandsittingatthecasino'ssportbook.

With sports betting, youplay the "spread," whichmeans the winning team hasto beat the opponent by acertain amount of points ifyouwanttogetapayout.

But what if you had the

ability to bet on the spreadduringthegame?

At the beginning of thegame, the score is 0-0, andthere is a full game to playwith plenty of uncertainty.The variance in the outcomeisverylarge.

But maybe at halftime thescore is 48-52, which is aspread of 4 points.We don'tknowwhat'sgoing tohappen

inthe2ndhalf,butmaybeweknownow that the first teamhas lost their star forward,and the second team has ashootingguard that ison firetonight-- with thatinformation and with onlyhalf a game left, we have abetterideaabouttheoutcomeof the game-- and there isonly a half left instead of afullgame.

The variance in the spread

willbelowernowthanwhenthegamestarted.

Now consider the gamewith 30 seconds left, and thescore is99-105.Thewinningteamhastheballandjusthastorunouttheclock.Withthatlittle time left, there is notmuch either team can do toaffect the point spread. Thevarianceoftheoutcomenearszero,untilthebuzzerends.

See how as we got closerto the end of the game, thevariance continued todecrease? The same thinghappens in the optionsmarket.

Options at their core are a

riskmanagementproduct.

Theoptionstrikepriceandits relation to where theunderlying stock will movedriveakeypartoftheoptionpricing.

Optionswillexpireatsomepoint, andwhen they do, theOTM options will expireworthless and the ITMoptionswillhavesomesortoftransaction that occurs at

expiration.

Do we know in the futurewhat the underlying stockwill do? No, but we have amuchbetterideaofwherethestock will be tomorrowcompared towhere itwill bein3months.

The option's extrinsicvalueistheriskpremiuminanoption--itisrelatedtotheodds that the option will

expireITM.

Options will always haveextrinsic value until theyexpire, because there isalwaysgoingtoberiskinthemarketuntilthetimerunsoutinthecontract.

Butaswegetcloser to thebuzzer,theexpectedvariancedecreases, which leads to adecreaseintheextrinsicvalueandtheoptionvalueoverall.

Thelossofvalueovertimein theoption isknownas thetheta of an option. It is theamount of decay per day intheoptions'extrinsicvalue.

Long options will alwaysbe short theta, and shortoptions will always be longtheta.

THEBIGTRADEOFFRemember how it didn't

make sense to take on shortgamma risk without somesortofreward?

Therewardis theta.Ifyouare short gamma that meansyouarelongtheta--youmakemoneyovertime.

This is the major tradeoffonwhetheryouwanttobeanoption buyer or an optionseller.

Ifyouareanoptionbuyer,thatmeansyouareputtingonlong gamma trades lookingfor an acceleration in the

underlying stock, regardlessofwhatdirectionyouchoose.In exchange for thisopportunity,youendupwithshort theta, which means ifthe stock doesn't see thatmoveovertime,thenyouwillstart to lose money on yourposition.

An option seller issomeonewhoisshortgammaandwilling toassumeriskoflarge movement, because

they think that the risk oflargemovesisnotasgreataswhat the options are pricingin. Inexchange for that shortgamma, they end up gettinglongtheta,whichallowsthemtomakemoneyovertime.

So what is better? Longoptionsorshortoptions?

There's no right answer tothis and it requires a ton ofcontext. For some trades, it

makes sense tobe theoptionbuyer,forotherstheseller.

But there's one thing Iknow for sure: there is nowaytobelongthetaandlonggamma in the same position.If you find it, then you havehit the jackpot and shouldstartahedgefund.

For us mere mortals, wewillalwayshavetoworkwiththistradeoff.

VEGAI have friends who are

straight up "soccer moms"--they are in their mid 30's,have2.2kidsandamortgage.They drive some form ofbeige or silver minivan athilariouslyslowspeeds.Theyhaven'tbeeninacaraccidentin over a decade and onlyhave that one parking ticketthat theygot in frontof theirfavoritebikramyogaspot.

I also have a few friendswhoarethe"hotshots"--andown some formof sports carthey drive way too fast.They're single and still intheirmid20's.They text anddrive. A few fender benders,maybe a totaled car a fewyearsago.Andtheyshowofftheir speeding tickets like abadgeofhonor.

Let's say they both golooking for car insurance.

Who will pay the higherpremiums?

Theriskieroneofcourse.

Thesamethinghappensinthe options market-- not allstocks have the same riskpricing. An early stagebiotech company with anupcoming FDA event willhave different risks than amultibillion dollar utilitycompany.

The options market is ariskmarket.When there is ahigher perceptionof risk, themarketplaceshigheroddsonoptions going ITM. Thisperception of risk is pricedinto the options through theextrinsic value, from whichwe derive a reading of"impliedvolatility"(IV).

Ifyouneedaquickprimeron how implied volatilityworks, check out my blog

post here:http://investingwithoptions.com/blog/2012/01/04/implied-volatility-guide-video/

So we know that the IVcanchange,andweknowtheIVisderivedfromtheoptionvalue.

Therefore, the optionvalue can change as theperception of risk changes.This is the greek known asvega- it is the sensitivity of

theoptionpricing tochangesinimpliedvolatility.

If a stock has been in aslow trading range that'ssuper boring, the optionsmarket will have a lowimpliedvolatilitybecause the

expectation is that the stockwill trade in a very smallrange.Low impliedvolatilitymeans low demand for theoptions, which means lowpricinginthoseoptions.

Butwhatifthatstockallofa sudden collapses becausetheir main product is beingrecalled?

This is the market's "holyshit" moment, and the

perception of risksignificantly increasesbecausewedon'tknowif therecall is unfounded or if thecompany is going bankruptbecause of it. Because of ahigher risk, the stock hasmoved from "soccer mom"mode to"hot rod"mode,andtheIVspikeshigher.Demandrisesforoptionsandthevalueof the options increasesacrosstheboard.

AgoodwaytolookatlongvegaisanATMstraddle.

This is a combination of a

longcallandalongput.Andbecausethecallandputhavethe samedeltamagnitudes, itisadeltaneutraltrade.

Now if there is no pricemovement,buttheperceptionof risk changes, what will itdo to the long straddle? Theextrinsicvalueinthecallwillriseandtheextrinsicvalueinthe put will rise-- vegamovement doesn't care aboutthedirectionof risk, just that

theriskrises.

RHORho is the red-headed

stepchild of all the otheroptiongreeks.

Andtobehonest,itdoesn'treallymatter,fornow.

Rho is simply the changeintheoptionpriceasitrelatestotherisk-freeinterestrate.

HowThisWorks

This has to do with howoptions are priced-- the costofcarrycomesintoplay.

Withoptionswecantakeastock-based position andconvert it into an option-basedposition.

For example, a protectiveputisacombinationofalongstockpositioncoupledwithalongput.

A long call has the exactsameriskparameters.

But the long call requiresonly10%ofthecapitaltoputon the trade. Since this freesup capital, you could put theextracashintonewtrades,orjust plow it into an account

thatpaystheriskfreeinterestrate.

If interest rates weren'ttaken into account withoptions pricing, then therewouldbeawaytocompletelyarbitragetheriskfreeinterestrate.Themarket,beingprettyefficient, won't let thathappen.

Either way, rho doesn'treally matter until the US

Federal Reserve raisesinterest rates, which at thetimeofthiswritingisabout3monthsfromnever.

THESECONDORDERGREEKS

Imagine if you were long100sharesofAAPLonedayand then 500 shares the nextday.You'dgetprettynervous,right? And confused! Howthe heck did your directionalexposurechangethatmuch?

Many new option traders

go through that same tradingproblem in options, becausethey don't understand whatcould change the risks in anoptionposition.

Now we get into some ofthe deeper "voodoo" behindoptions,becauseitrequiresanextradimensioninthinking.

ASecondOrderGreek issomethingthataffectsanothergreekrather than thepriceof

theoption.

We've already discussedone second order greek:gamma--itishowunderlyingprice movement affects thedelta(anothergreek).

Second order greeks arejust as important tounderstand because they cansignificantly affect how yourpositionwilltradeindifferentenvironments.

There are essentially 3things that can change agreek-- underlying pricemovement, impliedvolatility,andtime.

Thechartbelowshowsthemain greeks-- and lists thematrix of what can affectthem.

Also note that 2nd Ordertheta greeks don't have anysetnames.AsofthiswritingI

couldn't find the "official"names,andwecanjustmakethemupaswegoalong.

Nowwe will step througheachmajorgreekandwewillsee how each of thesechangesaffectsthegreek.

DELTA-CHANGE

OVERPRICEThis is known as the

gamma, which we havediscussedalreadyindetail.

DELTA-CHANGE

OVERTIMEThis is known as "delta

decay,"orcharm.Anditisn'tthe same for every singleoption.

Remember, thedelta of anoption is roughly related tothe odds that the option willexpireinthemoney.

Nowconsideranoutofthemoneyoption.Doesithaveahigher chance of expiring

ITM with 3 months of timeleft or 1 day? The former ofcourse; more time meansmore potential pricemovement, which increasestheodds.

The converse occurs withan in the money option-- asexpiration approaches, theoddsthattheoptionwillbeinthemoney continues towards100%,or100delta.

Thiscanalsobeviewedbylooking at risk profile of acall option, comparing thedelta today and the delta atexpiration.

Atoptionsexpiration thereare two outcomes for delta:eitheradeltaof0,orthedeltaof100.

OTM options willapproach a delta of 0, andITM options will approach adeltaof100.

Wecanalsolookatachartofthedeltaofalongcallovertime:

Youcanseethatthecloserwe are to expiration, thehigher thedeltavariancewillbe-- that will be importantwhen we tackle the gammasectionagain.

WhyThisisImportant

Your delta is the exposureyou have to the underlyingstock. If you are net long 10shares of stock and the nextdayyouarenetlong100,you

would certainly beconcerned. Managing yourdeltas over time is a keyriskmanagement techniqueused by professional optiontraders.

Italsorelatestohowitcanbe difficult to make moneywithlongOTMoptions.

If you buy a 30 deltaoption,youmake30bucksifthe underlying stock moves

$1.But as timegoeson,youlose money due to the timedecay (theta) in the longoption, and it becomesmoredifficult to make it backbecause the delta of theoption may have moveddownto25.

Atadeltaof25,inordertomake the same $30 gain, theunderlying stock would needto move $1.20 - a 20%increase. The odds continue

to go against long optiontraders as expirationapproaches.

DELTA-CHANGEOVERVOL

This greek is known asVanna.IguesssomeonelikesWheelofFortune

.

Let's go back to our bigbellcurve--itisrelatedtotheexpected movement of theunderlyingstockovertime.

In lower volatilityenvironments, the expectedpriceactionismuchsmaller--thatmeanstheperceptionofa

big move is lower, and theOTM options have lowerdelta.

But ifahighervolatility ispricedin,thoseOTMoptionswill see their deltas (andpremiums)rise!Whyis that?Becausethemarketispricingin a higher odds that theunderlyingstockwillmovetothat strike compared to alowervolatilityinstrument.

The same thing happenswith the ITM options. If theimplied volatility in a stockrallies, it's no longer aguarantee that ITM optionswill stay ITM-- so the odds,and therefore the delta,decreasesasvolatilityrises.

Do note that the ATMoptions will always have adelta around .50, so theirdelta is not nearly as"volatility sensitive"

comparedtoOTMoptions.

We can view this bylookingat thedeltaofa longcall option as a function ofchangesinvolatility.

WhyThisIsImportant

This has significantramifications for net optionsellers.

Ifyouare short aput,youaretakingonriskinexchangefor the premium of the put.You make money if theunderlying stock stays aboveyourshortstrike.

It is a long delta, short

gamma, and short vegaposition.

If this is an OTM optionyou are selling and impliedvolatility rises, not only willyour position suffer becauseof the vega exposure, butyour position will now bemuchmore sensitive to pricechanges in the underlying. Ifyouaretryingtomakemoneyfrom a "non-move" in thestock, this can become an

issue as your planned deltarisk becomes greater thanwhatyouhadanticipated.

GAMMA-CHANGES

OVERPRICEThisgreekistheSpeed.Of

an option position, whichmakes little sense becausespeed (velocity) is the 1stderivative of a particle'sposition, and option speed isactuallythe3rdderivative.

Below is a chart of thegammainacalloption:

(Thislooksawfullysimilartoour "bigbell curve" right?They're related-- seeAppendix B for a moredetailedexplanation.)

Rememberhowwefiguredoutthatthedeltawasjusttheslopeofthep/lline?

And that gamma is theslopeofthedeltaline?

Well speed is simply the

slopeofthegammaline.Itisthe change in the gamma aspricemoves.

So just by looking at theslope we can figure out thevalueofthespeed:

There are three things wecan conceptually grasp byeyeballingtheslope:

1. As the option goesOTM,thegammaisreduced.

2.AstheoptiongoesITM,thegammaisreduced.

3. The gamma ismaximized around the ATMstrikes, but doesn't change awholelotunlessitstartstogo

ITMorOTM.

The actual quantity ofspeed is not important here--it's understanding how thegamma will act as pricemoves.

WhyThisMatters

We'vetalkedalreadyabout"gamma heartburn." Thisconcept is centered on shortoption strategies like spreadsalesandironcondors.Ifyou

sell OTM options and theoptionsmovetoATM,whichmeans your gamma hassignificantlyincreased.

If your gamma hasincreased,itmeansyourdeltasensitivity in your positionhas rocketed higher-- in thewrongwayyouwantittogo.Net shortdeltasgetmorenetshortandviceversaforlongs.

This leads to an unholy

storm of risk, which issomething that gives meheartburn whenever I selloptionsthatgoagainstmebigtime.

This iswhy it's imperativeto be very, very proactivewhen selling options--knowing how to roll optionsand hedge your delta andgamma,allwhilekeepingthecostofthetradeverylow.

This concept also appliesto option buyers as well. Ifyou like to tradesingle stockoptions, you have to choosetherightstrikeprice.

Choosingtherightstrikeisall about getting the best"bang for your buck." Longoptions are not aboutmaximizing your overalldelta-- if you wanted to dothat you would trade thestock!

Long options are aboutmaximizingyourgammaasitrelates to the cost of theoption.

If you always buy ATMoptions but the underlyingstockmovesveryfastinyourfavor, it would have been abettertradetogoalittleOTMasitcostslessandthegammawould have "accelerated"favorablyinyourposition.

ButifyougotoofarOTM,then you have greater thetarisks, and the risk that thegammawillnevercome.

It'satrickygame,andthereisn't always a single rightanswer-- but understandinghow the gamma curveworksisahiddentalentthatyoucanuseinyourtrading.

GAMMA-CHANGESOVERTIMEThis greek is related to

charm, and it is known ascolor.

This is a little tricky toexplain because it requires afewmorestepsgraphicallytoarriveatourconclusion.

Let's first look at a p/lgraph of a long call optiontodayvs.expiration:

Ona long callwith plentyof time left, the delta is anever changing, dynamicthing. If the delta is alwayschanging, then the gamma(change in the delta) willalwaysbeanon-zeronumber.

However at expiration,there are two possibilities:OTM options will have adelta of 0, and ITM optionswillhaveadeltaof100.

They don't change. Thatmeans gamma is 0 atexpiration.

Except... and this iswhereitgetsinteresting.

Let'sbackupforasecond,and just look at the delta atexpiration:

So delta is at 0 or 100,except this area where thedelta has a theoreticallyinstantaneouschange.

Now I'm going to have togeekoutforasecond.

In electrical systems, youhave 1's and 0's...theoretically.

But when you turn on alight switch or any other

circuit,somefunnythingscanhappen-- electricity is not aninstantoneffect.

There'safancytermcalledthe "hysteresis" which saysthat the system can bedependent on past eventswhenitchangesitsstate.

Well thishysteresisarea isthe transitionbetweenhavingno exposure in a stock andhaving 100 shares of

exposure. It's a massivevarianceinyourdelta.

Let'stakealookatgammaovertime:

Astimegoeson,ATMoptiongamma will riseexponentially,whileITMandOTMgammaapproachzero.

Here is what the gammalookslikeatexpiration:

The ATM gamma goesthroughtheroof!

Remember, the gamma isrelatedtothe"bigbellcurve"and the statisticalexpectations of theunderlyingstock.Asthetimenears 0, the expectation willreach a single number-- theentire probability will becenteredaroundasinglearea.

This graph is also known

as a Dirac function, or animpulse function. So whenoptions get very close toexpiration,wehitwhat I callthegammaimpulsefunction.

It's alsowhat I so lovinglycallthegammaknifeedge.

WhyThisIsImportant

Ifyoushortoptionsaroundthe gamma knife edge, youcould endupwithmore thangammaheartburn--youcould

land too hard on the knifeedge and end up getting cutupwaytoomuch.

Optionshavean incrediblyhighoutcomevarianceasweget closer to expiration. Youcaneasilysee300%+swingsin an option's value in a fewhours.

Ifyouwanttotradeweeklyoptions or trade near optionsexpiration, then you MUST

knowabout thegammaknifeedge. It'swhatmakes tradinglong options around opex sopowerful, because you canendupwithatonofexposureforaverylittlecost.

It's also why it is a goodidea for more conservativeinvestors to stay away fromthe gamma knife edge as itcreates a much higherportfoliovariance.

GAMMA-CHANGESOVERVOL

Gamma's sensitivity tovolatility is known asZomma,which sounds like itis straight out of a BuckRogerscomicbook.

Below is a chart of thegamma as a function ofvolatility:

Do note that we arelooking at the SPY andpricing in massive moves inIV -- this is simply toillustrateextremes.

Remember-- the gamma isdirectly related to the bellcurve.

The higher the perceptionof risk the wider the bellcurvewillbe.

That means on a rise inimpliedvolatility,thegammatendsto"spreadout"overthestrikes. AnATM option willtendtostayaround50deltas,butOTMoptionswillhaveamuchlargerdeltavariance.

WhyThisIsImportant

In higher volatility names,youcangetasimilaramountof gamma for a lower cost.On a low beta stock like

MCDorWMT,buyingOTMoptions don't really have agood "kick" because thegammaissolow.

Butwithhigherbetanameslike AAPL, GOOG, BIDUandothers,youcangetawaywithpickingupfurtherOTMoptions because the gammaon the ATM option and theoptions a few strikes OTMaregoingtobeprettysimilar.

THETA-CHANGE

OVERPRICEHere'sacoollittletrick.

Gamma is effectively theinverse of theta, and theytend to correlate in terms ofmagnitude.

So if you have a highgamma, youwill also have a

hightheta.

All the concepts we justcovered with gamma? Justtaketheoppositeandyouendup with how theta worksaroundtheseoptions.

But because theta can beapproached from a differentangle, it gives us theopportunity to approach theconceptsintwoways.

The chart below was a

measurement of the extrinsicvalue in AAPL options on asinglemonth.

Think about this in termsofcommonsense:

If there is no extrinsicvalue,whatwillthethetabe?

Zeroofcourse.Thetaisthedecay of the extrinsic valueand if there is none, there isnotheta.

We can draw thisconclusion: the higher theextrinsicvalue,thehigherthe

theta.

And since ATM optionshave the highest extrinsicvalue, they will have thehighest theta. As we gofurtherOTMor further ITM,extrinsic declines andthereforethetadeclines.

Keep in mind that we aretalking in absolute terms.OftenOTMoptionswillhavea much higher theta as a

percentageof the total value,whichmustgo intoyour riskanalysis when considering atrade.

THETA-CHANGE

OVERTIMEIf you read anything on

theta,you'regoingtoseethispicture:

Thisshowsusthatthetimedecayofextrinsicvalueisanexponentialfunction.

It makes sense intuitively:the uncertainty of where astock will be tomorrow ismuch,much smaller than theuncertainty one month fromnow.

The exponential nature oftheta is also baked in due tohowoptionsarepriced--they

assume lognormaldistributions-- again, relatedtoourbellcurve.

This means the differencein expected price actionbetween 1 month and 2months will be much higherthanthedifferencebetween6and7months.

WhyThisMatters

So if the theta is greatestright at expiration, that is

where you want to selloptions,right?

Notsofast.

In financial speculation,there is always a tradeoffbetweenriskandreward.

Ifyouwanthigherrewards,you will have to take higherrisks.

If you want higher odds,you'll have to take lower

rewards.

The same thing applies inthe relationship betweengammaandtheta.

Want higher thetarewards? You'll have toaccepthighergammarisks.

Want super fast gamma?You'll pay for it with thetarisk.

Again, there is no "right"

answerhere-- therearemanydifferent styles and riskprofiles for traders to follow.But one thing is for sure--you can't blindly follow "fattheta" or "fat premium" as awaytoputonnewtrades.

THETA-CHANGEOVER

VOLATILITYHereisachartofthetaasa

functionofvolatility:

With this chart we aremore focused on themagnitude. So when I say"higher," I mean in absoluteterms.

Now if you have beenfollowing along, we've beenviewing gamma and theta astwo sides of the same coin--they trade inverse each otherbut run together inmagnitude.

But if you compare thetheta vs. volatility and thegamma vs. volatility, themagnitude rises for the firstandshrinksforthesecond.

Whatgives?

There's probably a fancyway to prove it by reverseengineeringtheoptionpricingmodels,butjustthinkaboutitintuitively:

Asshownearlier,ifthereis

higher extrinsic value, thenthereishighertheta.

If implied volatility rises,thatmeanstheextrinsicvaluerises.

If the extrinsic value risesthen there will be highertheta.

Simple.

WhyThisMatters

As to applications, it ties

back into the risk/rewardequation.

If you want to play thehigh volatility, fast names,you're going to be paying upintermsofabsolutetheta.

There'salwaysatradeoff.

VEGA-CHANGE

OVERPRICEInmyopinionriskanalysis

as a function of volatility ismore important for globalderivativesdeskscomparedtosmaller retail players. Moreadvanced strategies likevolatility dispersion tradingand market making require

more attention to changes invega.

Vegaasitrelatestopriceisknown as Vanna. We'vealready talked about vanna,right?

That's because they areinterchangeablemathematically.Don'taskmetoproveit,theyjustare.

Remember: don't get vegaand implied volatilityconfused, it'sveryeasy todothat!Vegaisthesensitivityintheoptionvaluetochangesinimpliedvolatility.

Vanna is the change invega over price. Here's what

itlookslike:

Back to the "big bellcurve"again.

Remember how theta ishighestwhere extrinsic valueisthehighest?

It's the same thing withvega.ATMoptionswillhavethe highest extrinsic value,and since vega only affectsthe extrinsic value, thehighest vanna will be withATMstrikes.

WhyThisIsImportant

This means if you're keenon taking a straight up shortvega position, the ATMoptions will be the highestpossiblevannaavailable.

But again, these optionswillhavethehighestgamma,so the short gamma riskwould be the tradeoff to anyshortvegaexposure.

As another quick sidenote:

not all volatilities are thesame.TheATMoptionswillhaveadifferentIVcomparedto OTM options-- this isknownas theoptionskew. Ifyou want to trade volatility,you can't just blindly look atvega but you must alsoconsider volatility skew andtermstructure.

VEGA-CHANGE

OVERTIMEThis greek is known as

DvegaDtime, because optiontraders got tired of beingcleverwiththeirnaming.

Ifthevegachartlookslikea bell curve, can you guesswhat it will look like whenweviewitovertime?

As time goes on, thesensitivity to changes inimpliedvolatilitydecreasesinall options. Putting aside themath,thismakessenseastheextrinsic value becomesdriven more by time (theta)than vol (vega) as we getclosertooptionsexpiration.

WhyThisIsImportant

If you trade a ton ofcalendars, you must

understand that volatilitysensitivitywillbedifferentinfront month vs. back monthoptions(youwillalsohavetoconsider term structure).There are also some funthings that you can do withshort term options, volatilitysensitivity,andearnings/FDAevents.

VOLATILITY-CHANGEOVER

VOLATILITYNowwe are getting into a

strangeloop.

Vega is the sensitivity tovolatility, but how will thatsensitivity act as IV moves?ThisisknownasVomma.

Let's takea lookatachartof vega as implied volexpands:

For ATM options, it doesnothing. The vega sensitivityremains the same no matterwhat the IV reading. Thisprobably is related to whyATM options have adelta/odds around 50regardlessoftimeorvol.

ButifyougofurtherOTMor ITM, the vega rises asimpliedvolatilityrises.

We can go back to our

analogy:moreextrinsic,morevega. So if IV rises, theextrinsic in all options willrise, therefore the sensitivitytovolwillriseaswell.

WhyThisisImportant

For short option players,thiscanbeakintothegammaheartburnImentionedearlier.Ifyouareshortvolatility,andIV rises, not only will youlose money on the vol rise,

but you will also increaseyour exposure to said volthrough the increase in vega.If vol explodes (combinedwith your short gamma),thingscangetuglyinahurry.

This is where it may behelpful to learn theimportance of managing riskas a function of vol-- usingunitputstoprotectdownside,or if the portfolio is right,trading VIX options and

futures to hedge off someoverallvega.

PUTTINGITALL

TOGETHERIfyouhavenevertradedan

optionbefore, thismay seemalittleoverwhelming.

Well,stopworrying.

On a practical level, ahigher-level understanding isneeded-- very rarely do you

have to dive this deep intoeverysinglegreektomanagea trade. Most option tradestructures are very simple tounderstand,and"tailrisks"onsecond order greeks rarelyoccur.

With an understanding ofthe greeks, you can gobeyond knowing what yourrisk is in an open position--you can now structure a riskon a trade before you put it

on,fullyawareofalltherisksyou are taking. From thereyouwilldevelopyourselfintoa happy, healthy, profitableoptionstrader.

THANKYOU

Before you wrap upreadingthiseBook,I'dliketosay "thank you" forpurchasingthis,andIhopeitwas a great investment inyourfinancialeducation.

I know there are a ton ofresources out there and it'shard to find good qualityeducation.

Soabigthanksforpickingup thisebookandreadingallthewaytotheend.

If you like what you'veread,thenI'dloveareview.

PleasetakeamomenttoletmeknowwhatyouthoughtofthisbookonAmazon:

http://www.investingwithoptions.com/greek-ebook/

Thisfeedbackwillhelpmewrite the kinds of Kindlebooks that will make you abettertrader.

APPENDIXA--SOFTWAREIn this book, we use

analytics software for visualdemonstrations.

Having access to thissoftware to interact withdifferent risk structures willgiveyouyetanotherlearningconduit for understandinghowthegreekswork.

The software screenshotsin this book were from thebrokerage platform ofthinkorswim, which is nowowned by TD Ameritrade.This is still one of the bestsolutions out there, and it isfree as long as you have anaccount.

There are a few othersolutions out there foranalytics.

LiveVol Pro - This is aslick web application thatcameoutafewyearsagoandI've been hooked since. Thisdoescostmoney,butyoucanget access to the software ifyou open an account withtheirbrokeragearm.

OptionsOracle - This isfreesoftwarethatyoucanuseto build out potential trades,and it interfaces withInteractive Brokers. You can

getitatsamoasky.com

Derivix - This software isgeared more towardsinstitutionalinvestors,butisavery powerful platform.Learnaboutithere.

APPENDIXB-SOMEHEAVY

MATHFor those mathematically

inclined,preparetohaveyourmind blown. For the entiretext I attempted to simplifythe greeks into easy tounderstand concepts andanalogies.

But if you have a

background in statistics orcalculus, or you want to getmore into the nitty gritty ofoption pricing, this is a goodstartingpoint.

The option pricingmodelswe use make a few keyassumptions.

First: stocks tend to havelognormal distributions-- thismeans that the price changedaytodaywillfitunderabell

curve.

For example, here is ahistogram of the daily pricechange in AAPL from 2005to2008:

This is our big bell curve,meaning that there is anexpected distribution ofreturns over time, and it'swhat the option marketimpliesinthefuture.

But what do we mean by"implied"? It's a measure ofthe extrinsic value, and weend up with a percentagereading-- this percentage isthe model for our implied,

futurereturns.

A20%IVisanannualizedreading, which means themarket is expecting theunderlying stock to be up20% or down 20% in 365calendardays.

This 20% is not amagicalnumber-- it's a statisticalapproximation of a singlestandard deviation, againgoingbacktoourbellcurve.

So the impliedvolatility isreally a 2 standard deviationapproximation-- 20% up (1stddev)and20%down(1stddev). Thatmeans themarketis assigning about a 2/3chance(+/-1stddev)thattheannualized return will bewithinthatbellcurvearea.

Now let's get back to thewhole odds of being in themoney.

Ifastockistradingat100,whatwould be the odds of a50 call expiring ITM? Verylow.

But the 150 call wouldhave very high odds ofexpiringITM.

Sothelowendapproaches0, and the high endapproaches100.

Ifwegraphthedeltaofalloptions in a single month,

you would get a chart likethis:

This is an S-curve, alsoknown as the cumulativedistribution function. Itencases all the odds for astockofanoutcomefrom0toreally,reallyhigh.

The cumulativedistribution function tells usthat we are "summing" theoutcomes. What happens ifwe just look at the expectedoutcomes themselves? Prettysimple, we just look at the

incremental change in theCDF and we get somethinglikethis:

itbringsusbacktoourbigbell curve- this is known asthe probability densityfunction of a normaldistribution.

And this is reallyinteresting, because thegamma of an option is thefirstderivativeofthedelta.

The gamma ismathematically related to theprobability density function,

andthedeltaistheintegralofthe PDF, which turns it intothe cumulative distributionfunction.

Time to expiration andimplied volatility in themarket drive how wide thebell curve actually is, and italsodictateswhatthegammaand deltawill be as they arederived from the distributionof expected returns on thatsamebellcurve.

Of course we know thatmarketsdon'thaveauniformdistribution of volatility--market crashes tend to haveclustersofhighvol,andslowgrinding bull markets haveclusters of low vol. This isknownas"heteroskedasticity"-- what a word! All thismeans is that volatility tendstocluster.

Knowing that volatility isnothomogenous iskeywhen

managing risk of really bignumbers. That's whyinstitutions tend to use somederivation of a GARCHmodelwhenfiguringouthowmuch theyreallyhaveat riskin a market. GARCH standsfor "generalizedautoregressive conditionalheteroskedasticity."

This is far down as I'mwilling to takeyoudown thequant rabbit hole, but for

more discussions on theheavy math part of things, Iwill referyou to theWilmottForums.

APPENDIXC-MY

SHAMELESSPLUG

Mygoal is tomakepeoplebetter option traders.HopefullyIdidthatwiththisbook.

If you're looking forfurther, broader help in

options trading, there are afew solutions for you toconsider.

InvestingWithOptions -This is the main website oftheIWONetwork.Thereisablogaswellasoptiontradingbasics resources for you toread.

IWO Premium - This isInvestingWithOption'strading service. We offer a

chat room, live webinars,nightly videos, trade alerts,andamodeltradingportfolio.Thisisagreatopportunityforthosewhowanttogostraightintotradingoptions,butneeda community of like-mindedtraders to work with duringtheday,

OptionFu-Ifyouhavenopre-existing options tradingmethodology, this will getyou started. This video

training course takes youfrom the very basics tolearning how to manage riskin the market as well asdeveloping your own tradingsystems. I then let you intomy trading playbook,showingyouthemaintradesIuseonadaytodaybasis.

APPENDIXD-FULL

DISCLAIMERThe content of this book

for educational purposesonly. Nothing in this textshall be construed as asolicitation and/orrecommendation to buy orsell a security. Tradingstocks, options, and other

securities involve risk. Therisk of loss in tradingsecurities can be substantial.The risk involved withtrading stocks, options andother securities are notsuitable for all investors.Prior to buying or selling anoption, an investor mustevaluatehis/herownpersonalfinancial situation andconsider all relevant riskfactors. See: Characteristicsand Risks of Standardized

Options(http://www.optionsclearing.com/publications/risks/riskstoc.pdf

TableofContents

CopyrightYourFreeGiftWhyOptionGreeksMatterHowtoLearntheGreeksHowtoVisualizeRiskSomeCommonTermsTheBigbellcurveDeltaGamma

ThetaTheBigTradeoffVegaRhoTheSecondOrderGreeksDelta-ChangeOverPriceDelta-ChangeOverTimeDelta-ChangeOverVolGamma-ChangesOverPriceGamma-ChangesOverTimeGamma-ChangesOverVolTheta-ChangeOverPriceTheta-ChangeOverTimeTheta - Change over

VolatilityVega-ChangeOverPriceVega-ChangeOverTimeVolatility - Change OverVolatility

PuttingitAllTogetherThankYouAppendixA--SoftwareAppendix B - Some HeavyMath

AppendixC -MyShamelessPlug

AppendixD-FullDisclaimer