馃攳
Introduction to Options Greeks (Delta, Gamma, Theta, Vega) with Brent Kochuba | SpotGamma - YouTube
Channel: SpotGamma
[0]
hello my name is brent kuchuba and i am
[2]
the founder of spot gamma
[3]
spot game offers traders and investors
[5]
daily analysis on the stock and options
[7]
markets
[8]
we are one of the leading providers of
[9]
market analytics and have been featured
[11]
in top publications like the wall street
[13]
journal and bloomberg
[14]
if you need a primer on equities or
[16]
options please visit videos one and two
[18]
in our educational series
[19]
where my co-founder matt covers the
[21]
basics before we dive into the greeks
[24]
here at spot gamma our goal is to
[25]
provide you with unique
[27]
information around stock movement based
[29]
on our valuation of the derivatives
[31]
markets
[32]
spot gamma is an information only site
[34]
and nothing contained in any of these
[36]
videos
[37]
constitutes investment advice if you're
[39]
going to make any investments please
[41]
consult a professionally licensed
[42]
investment advisor before making your
[44]
independent decisions
[46]
today we'll be covering key topics which
[48]
include the inputs that drive options
[50]
pricing
[51]
the definition and role of the greeks
[53]
the interrelationship between these
[55]
factors
[56]
the importance of understanding time and
[58]
volatility
[59]
and an example of how to apply this
[61]
knowledge to construct an options trade
[63]
so let's get started with the inputs
[65]
that go into options pricing
[67]
here on slide three we're going to cover
[69]
the basic of options pricing
[71]
using plain english let's start by
[72]
understanding the following terms
[74]
stock price the stock price is the
[76]
current price of the equity for a
[77]
company at a specific time
[79]
strike price this is the set price at
[81]
which an option contract can be bought
[83]
or sold when it is exercised
[85]
choosing the right strike price is
[86]
important when establishing an option
[88]
position
[88]
this is a topic we will cover more in
[90]
depth later in this discussion
[92]
dividends some companies pay dividends
[94]
usually quarterly
[95]
this value is imputed into the overall
[97]
options model
[98]
risk-free interest rate the risk-free
[100]
rate is the minimum amount you would
[102]
expect to return from assets in the
[103]
market
[104]
this value is linked to the greek row
[106]
covered in the next slide
[107]
time to expiration this is the time
[110]
measured in days between today and the
[111]
date the option must be executed or it
[114]
goes away
[114]
this value has an effect on the greek
[116]
theta covered in the next slide
[119]
volatility this relates to the amount of
[121]
expected fluctuation in the stock over a
[123]
period of time
[124]
if volatility is higher the option price
[126]
will be higher the effective volatility
[128]
in options is measured by the greek vega
[129]
covered in the next slide
[131]
to get an options price all these values
[133]
are taken into an options model like
[135]
black shoals
[136]
which then creates as its output a
[138]
specific price for a specific call and
[140]
put
[140]
it also calculates the greek values
[142]
which we'll be discussing today now that
[144]
we've discussed the
[145]
inputs to an options model let's talk
[147]
about the greeks and options model
[148]
derives
[150]
let's start with row which is a
[151]
measurement of the risk-free rates
[153]
impact on the options price this is a
[155]
relatively straightforward calculation
[157]
and we will not spend much time on it
[158]
throughout the rest of this video
[160]
next there are theta and vega theta is
[164]
the measurement
[165]
of an impact on an opposite price due to
[167]
time
[168]
and vega is the impact on an options
[170]
price relative to volatility
[172]
we'll dive more deeply into these
[174]
concepts when we get closer to our
[175]
example
[176]
lastly and where spot gamma focuses much
[179]
of its efforts is in delta and gamma
[182]
delta is a ratio which links the options
[184]
price to the stock price
[187]
gamma is a derivative of delta which is
[190]
the dynamic measurement depicting
[191]
the rate at which delta changes relative
[194]
to movements in the underlying stock
[196]
price
[198]
let's look at an example using the black
[200]
shows model and how these greeks play an
[201]
important role
[202]
here on slide 5 you can see that we've
[204]
entered some inputs into a black
[206]
shoals calculator in the top section we
[209]
can enter some key
[210]
inputs and then the calculator produces
[211]
both the options value
[213]
along with the greek variables we're
[215]
going to use this sample output to
[216]
discuss both delta and gamma
[219]
it's worth noting that most trading
[220]
systems run these calculations in real
[222]
time
[223]
through each trading day options pricing
[225]
is a dynamic
[226]
endeavor as stock prices time and trader
[228]
sentiment are constantly changing
[230]
this black shoals example is valuable
[232]
because it shows us a snapshot in time
[233]
which we can further examine
[235]
with that let's examine our first greek
[238]
which is called
[238]
delta now we're going to talk about
[240]
delta as defined by dollars
[243]
the official definition of delta is the
[245]
rate of change of an option
[246]
for a one dollar move in the underlying
[248]
stock
[249]
as we show here a call option with a
[252]
delta of 0.50
[254]
will gain 50 cents for every one dollar
[256]
rise in stock
[258]
now as my colleague matt explained in an
[260]
earlier video put options are a bet that
[262]
stocks will decline
[263]
therefore as you can see in the green
[265]
box puts carry a
[267]
negative delta and they will lose value
[269]
if a stock rises
[271]
now on the other hand if the stock price
[272]
declines the call option would lose
[274]
value and the put option would increase
[276]
in value
[276]
in accordance with this delta value the
[279]
screenshot here shows an
[280]
actual options market portrayed in the
[282]
trading software offered by the broker
[284]
td ameritrade
[285]
you can see the headers represent the
[286]
greeks we've initially described delta
[288]
gamma theta and vega these values are
[290]
calculated by td in real time
[292]
to place delta into practice you can
[294]
look at the table to see the
[296]
values for some listed options on the
[297]
stock acb for call options highlighted
[300]
by the green box on the left side
[302]
you can see that the options delta
[303]
increases as the strike price decreases
[306]
on the left hand side of the montage you
[307]
can see that the greeks and the prices
[309]
are available for each call option
[311]
for call options where the current stock
[313]
price is above the options strike price
[315]
investors use the term in the money to
[318]
describe those options
[319]
conversely for the times that the
[321]
current stock price is below
[322]
the call option strike price investors
[325]
use the term
[326]
out of the money to describe those
[327]
options for put options as you can see
[329]
on the right in red it is the opposite
[332]
where current stock prices are below the
[335]
strike price
[336]
those options are in the money what is
[338]
important to know is that options that
[340]
are in the money have a higher delta
[341]
value
[342]
with stock at ecb at nine dollars and
[344]
sixty cents
[345]
you can see that the delta for a nine
[347]
dollar call is 70
[348]
and that is roughly double the value for
[350]
a 10 call which is 35.
[353]
next we'll cover the relationship 2 and
[355]
the definition of the option greek
[357]
gamma now that we have discussed delta
[359]
and understand it is the ratio of the
[360]
movement of an
[361]
option relative to the underlying stock
[363]
we will move to gamma
[365]
game is defined as the rate of change of
[367]
delta this may sound confusing but think
[369]
of it as a metaphor
[371]
consider for a second that delta is the
[373]
constant speed of your car
[374]
at any point in time you may be driving
[376]
55 miles an hour down a highway
[378]
and again this is a fixed speed now
[380]
imagine that you need to pass another
[382]
car and you speed up to 60
[384]
that rate at which you increase your
[386]
speed which is called your acceleration
[388]
is equivalent to gamma as delta is a
[391]
fixed ratio of shares for a given stock
[393]
price
[394]
gamma explains how quickly your ratio of
[396]
shares would change for a given change
[398]
in the stock's price now when you buy
[401]
options
[401]
be it puts or calls you establish what's
[403]
called a positive gamma position
[406]
this means that you profit when the
[407]
underlying stock has a large move
[410]
if you were sell short an option you
[412]
would then have a negative gamma
[414]
position
[414]
this implies that you want the stock to
[416]
have very little movement
[418]
this concept will be repeated throughout
[420]
the discussion and detailed in later
[422]
examples
[424]
now let's take a look again at the same
[426]
options montage to further illustrate
[428]
the relative effects of gamma on pricing
[431]
just as we did with delta after that
[433]
we'll explore the other
[434]
relevant greeks to revisit the options
[436]
montage from the delta example let's
[438]
begin by reviewing
[440]
that delta is largest for options which
[442]
are in the money
[443]
however gamma works in a different way
[445]
gamma again being the rate of change of
[447]
delta is highest around the current
[449]
price of the stock
[450]
this is marked by the label atm which
[453]
stands for at
[454]
the money so the farther you go in
[456]
either direction away from the current
[458]
stock price
[459]
regardless of if you move in the money
[461]
or out of the money
[462]
the value of gamma declines since gamma
[465]
changes the most around the current
[466]
stock price the delta values will also
[469]
be more strongly affected
[471]
and change around the current stock
[472]
price this rate of change for both the
[475]
delta
[475]
and gamma are key to spot gamer's
[477]
modeling process and discussed in our
[479]
next
[480]
video let's now look at another chart to
[483]
further illustrate the relationship
[485]
between delta and gamma
[486]
now let's discuss the relationship
[488]
between delta and gamma
[490]
as a trader or investor you can see that
[492]
trading platforms provide you with a
[493]
montage describing and detailing the
[495]
greeks relative to stock prices on a
[497]
real-time basis
[499]
however the values shown to any trader
[501]
are a snapshot in time and therefore
[503]
essentially
[504]
static in our view the power of options
[506]
is unlocked
[507]
by understanding the dynamic
[509]
relationship between gamma and delta
[512]
earlier when defining gamma we explained
[514]
that gamma is the rate of change of
[515]
delta
[516]
there's a common saying in the options
[518]
industry that gammas manufacture
[520]
deltas and we'll explain that here view
[523]
the data table on the bottom right which
[525]
depicts the change in delta and gamma
[526]
for a given move in the underlying stock
[529]
with the stock at seven dollars per
[531]
share let's say you buy a ten dollar
[533]
strike
[534]
call option paying one dollar per
[535]
contract again this represents 100
[538]
shares of stock
[540]
this option has a delta of 35 and a
[542]
gamma of four
[543]
now how do we determine the theoretical
[545]
value of this option as the stock price
[547]
moves to eight dollars
[549]
to answer this question we start with
[551]
what we know we know that the delta
[553]
is the change in option value for a one
[555]
dollar move in stock
[556]
so our new value is calculated by taking
[559]
the current value
[560]
of one dollar adding 35 cents
[564]
or the option of delta this means if the
[566]
stock is at eight dollars
[567]
the option value should increase to one
[569]
dollar and 35 cents
[572]
however we cannot ignore gamma next
[575]
since we own the ten dollar call when
[577]
the stock moves
[578]
we need to update our delta value by
[580]
factoring in gamma
[582]
as the stock rises from seven to eight
[585]
to estimate the delta of this option
[587]
when the stock hits eight dollars we
[588]
simply add the gamma value
[590]
of four to the delta value of 35
[593]
to get a value of 39. this tells us
[596]
that a stock price increase makes our 10
[599]
call option rise by 39 cents
[602]
as the stock goes from eight to nine
[605]
the big takeaway is that if you bought
[606]
this seven dollar stock and it went to
[608]
eight
[609]
you make a 14 return if you bought the
[612]
10
[612]
call when the stock is at seven and then
[615]
the stock goes to eight
[616]
you make a 35 percent return this
[619]
leverage return is driven by gamma
[621]
and it's one of the main reasons a
[622]
trader would choose to buy options
[624]
rather than stock with this we're next
[627]
going to address the concept of
[629]
theta which represents time and its
[631]
impact on options prices
[633]
while there is a critical relationship
[634]
between delta and gamma
[636]
there is an additional dynamic we must
[638]
add in
[639]
that is the role of time which is
[641]
generally defined by the number of days
[643]
until your option contract
[644]
expires when you're purchasing an option
[647]
you are essentially long
[649]
gamma which means your option has a
[651]
positive gamma position
[652]
as we just illustrated in the previous
[654]
slide gamma is what drives the price
[656]
increase of your option
[658]
when the underlying stock moves however
[660]
nothing in life is free
[662]
in this case your cost for owning an
[664]
option and being long gamma is called
[666]
theta or time decay with each day that
[669]
passes towards expiration
[670]
everything else being equal your options
[673]
contract will lose value due to theta or
[675]
time decay
[676]
when purchasing an option you are
[678]
essentially going to assess your
[679]
potential profit which is gamma
[681]
in this offset to own the option which
[684]
is called theta
[685]
in the next slide we're going to show
[687]
this concept through actual examples
[689]
take a look at the options montage for
[691]
tesla which is below
[692]
with the stock trading near 647 dollars
[695]
per share
[696]
on the left side you can see the data
[697]
for the 650 strike call which expires
[700]
tomorrow
[701]
now compare this to the right side which
[703]
shows a march 2021
[705]
650 strike call that expires in three
[708]
months
[709]
for tomorrow's expiration the options
[711]
price is fourteen dollars and fifty
[713]
cents which would cost you one thousand
[715]
four hundred and fifty dollars in total
[717]
recall that there's a one hundred
[718]
multiplier
[719]
the option is a delta of forty seven a
[721]
gamma of nine point six
[723]
and has a theta of four point eight if
[726]
the stock does not move at all
[728]
this theta level implies you will lose
[730]
480
[731]
drew strictly to time decay again
[734]
there's a 100 multiplier
[736]
so you take 4.8 and multiply by 100
[739]
that is obviously a very expensive short
[742]
term play
[742]
due to the fact that the option expires
[744]
tomorrow at the market clove
[746]
however that option has a very high
[749]
gamma 9.6
[751]
this means it could have a very large
[752]
payout with a rapid stock
[754]
move let's compare this to an option
[756]
with more time to expiration
[759]
that same strike 650 for the march 2021
[762]
call is nine dollars and eighty cents
[764]
for a total cost of nine thousand eight
[766]
hundred dollars
[767]
there's a delta of 57 which is a bit
[769]
higher than the other option
[771]
however the gamma is only 1.6
[774]
compare that to the 9.6 value for the
[777]
other
[777]
option which expires earlier the theta
[780]
is only 50 which infers that it has a 50
[782]
dollars per day of time decay
[784]
this is obviously substantially less
[786]
than the 480
[787]
worth of time decay for the option that
[789]
expires tomorrow
[790]
so as you can see from this example the
[792]
near-term option has a very high gamma
[795]
but very high
[796]
theta well the cost to purchase this
[798]
option is much less
[799]
fourteen dollars and fifty cents versus
[800]
ninety eight dollars you're paying a
[802]
much higher
[803]
theta to make a more levered bet in
[806]
other words the longer dated option
[808]
costs you less time decay but also earns
[810]
you less for a given move
[811]
due to its lower gamma for purposes of
[814]
this session
[814]
when considering which option to trade
[816]
there is no right or wrong answer
[819]
there are myriad of options trading
[820]
strategies would seek to exploit
[822]
all these various aspects your best
[824]
choice is
[825]
likely to be made by assessing how much
[827]
you think the stock may move over a
[829]
given time period
[831]
with that we're going to shift gears and
[833]
talk about vega as related to volatility
[836]
at the outside of this presentation we
[837]
described vega as one of the outputs
[839]
from our black shells pricing model
[841]
and how it relates to volatility
[843]
specifically vega is defined as an
[846]
options
[846]
price change for a 1 change in the
[848]
implied volatility of the underlying
[850]
asset
[851]
the farther away an option is from
[853]
expiration the higher
[854]
options vega is that is options with a
[858]
larger time to expiration are more
[859]
sensitive to a change in implied
[861]
volatility
[862]
vega also has an impact on the other
[864]
greeks as you can see in the chart here
[866]
higher volatility increases the gamma
[868]
level on options that have a strike
[870]
price
[871]
which are further out of the money this
[873]
means
[874]
that out of the money options become
[875]
more reactive to changes in a stock's
[877]
price
[878]
for many traders this is an important
[880]
metric but first we need
[882]
to answer a more critical question just
[884]
what is volatility for the life of a
[886]
given option
[887]
often referred to as implied volatility
[889]
the concept of volatility and its impact
[891]
over the lifetime of an option is the
[893]
final key area
[895]
of our review of the greeks volatility
[898]
is a common trading phrase often
[899]
associated with stock crashes but
[901]
volatility simply means
[903]
movement when you buy an option you are
[905]
essentially expressing a view
[907]
that the stock will have a lot of
[909]
movement before the contract expires
[911]
now how do you gauge how much movement a
[914]
stock may have
[915]
let's look at an example to review the
[917]
impact of volatility on
[918]
tesla's stock the upper pane of the
[921]
chart here shows tesla stock
[923]
which is currently trading at hundred
[925]
and seventy dollars per share
[927]
now let's focus our attention to the
[929]
lower pane where you will see a single
[931]
yellow line which represents realized or
[934]
historical
[935]
volatility realized volatility is simply
[938]
a way to measure how much a stock has
[940]
moved over a given time period as part
[943]
of an overall investment approach
[945]
many investors will analyze the history
[947]
of an individual stocks movement
[949]
as a potential indicator for how much it
[952]
may move
[952]
in the future knowing how active a stock
[956]
has been
[956]
in the past is important to estimating
[959]
how much a stock
[960]
can move in the future so the big
[963]
takeaway
[964]
is that when you are trading an option
[965]
whether a call or a put
[967]
volatility is a key component that must
[969]
be measured and factored into your
[971]
decision
[972]
volatility strongly affects the pricing
[974]
of options and your potential to
[976]
generate
[977]
positive return from options trades now
[979]
that we have a sense of how much
[981]
movement a stock has had in the past
[983]
let's turn our attention to the next
[985]
important concept around volatility
[987]
which is what the market sees or expects
[990]
is future volatility
[991]
to ground the point from the last slide
[993]
that volatility has a large impact on
[995]
greeks and options prices
[997]
having spent time covering historical
[999]
volatility in the previous slides
[1000]
we will now apply these concepts towards
[1002]
assessing future volatility
[1004]
the expected movement of the stock for
[1006]
the remainder of the options life
[1008]
is at the core of an options price
[1010]
recall that volatility is a key input in
[1012]
our options pricing model
[1015]
the future volatility can be referred to
[1017]
as implied volatility because it is the
[1019]
expected volatility a trader will use
[1021]
to calculate an option's price consider
[1025]
our tesla example and imagine you are
[1026]
looking at options that expire in three
[1028]
weeks
[1029]
rather than being in the middle of
[1031]
august during a time when little news is
[1033]
expected
[1034]
we know that earnings is coming out in
[1036]
five days this event is important and
[1038]
gets calculated into the implied
[1040]
volatility and consequently it has a
[1042]
meaningful
[1042]
impact on options prices while the
[1045]
majority of our discussion has been
[1047]
about technical analysis
[1048]
all investors should be aware of
[1050]
expected news events such as quarterly
[1051]
earnings
[1053]
as they can have an additional effect on
[1055]
volatility which significantly
[1056]
impacts the price of options now let's
[1059]
take a final look at volatility as an
[1061]
expression of the overall options
[1063]
pricing
[1064]
in another options montage as a final
[1066]
takeaway we want to show you these two
[1068]
options montages which clearly reflect
[1070]
the impact of implied volatility on the
[1072]
price of an option
[1073]
in the top panel tesla stock has been on
[1075]
an absolute tear
[1077]
based on described enthusiasm for the
[1078]
electric car manufacturer
[1080]
as a result their stock has a very high
[1082]
implied volatility
[1084]
because investors expect that stock
[1085]
movement to continue
[1087]
this results in options which have a
[1089]
high cost
[1090]
relative for calls and puts on the other
[1093]
hand is colgate which makes things like
[1095]
toothpaste and mouthwash
[1097]
they are not expected to revolutionize
[1098]
the economy and investors do not
[1100]
anticipate a lot
[1101]
of stock movement in their future thus
[1104]
their options are much less expensive on
[1107]
an apples for apples comparison bases
[1109]
with tesla
[1110]
this should reinforce the concept that
[1111]
higher implied volatility
[1113]
means higher options prices and must be
[1115]
considered when buying or selling
[1117]
options the concepts discussed in this
[1119]
video are key to understanding the
[1120]
options market and how
[1122]
they in turn impact the stock market
[1124]
traders and investors use
[1125]
options for a variety of reasons many of
[1127]
them relating solely to these greeks
[1130]
i'd like to thank you for joining us on
[1131]
this explanation of how options are
[1133]
priced and the impact of the greeks
[1135]
in our next and final video we will
[1137]
reveal how spot gamma analyzes
[1139]
all of these dynamics before we go we
[1142]
want to remind you to go to spotgama.com
[1144]
right now and start a free five-day
[1146]
trial
[1147]
each day we share our unique approach to
[1148]
analyzing markets with thousands of
[1150]
subscribers
[1151]
just like you we look forward to seeing
[1153]
you on our next video
Most Recent Videos:
You can go back to the homepage right here: Homepage