Volatility Skew

  

Categories: Derivatives

If you have an option, there are three categories it can belong to at any given time: in-the-money, out-of-the-money, or at-the-money.

Let's take a quick step back. Options provide the right, but not the obligation, to buy or sell some underlying asset (like a stock, commodity, or currency) at a pre-set price at a prearranged time in the future. The pre-set price is known as the "strike price." The relationship between the strike price and the current price of the underlying asset determines whether the option is "in," "at," or "out" of the money.

You have a call option for MSFT with a strike price of $140, with a September expiration (which is two months from now). That option gives you the ability to buy shares of MSFT at a price of $140 in September. So if MSFT is trading at $135 at the September expiration, you are out-of-the-money. You'd rather buy the shares on the open market, so your option is useless. You would let it expire without exercising it.

However, if MSFT is trading at $145, you are in-the-money. You can exercise your option, buy shares at $140...and then instantly sell them for $145 on the open market. You book a profit of $5 a share (minus whatever the option cost you).

The last situation comes when the option strike price and the trading price are the same; MSFT is trading right at $140. Here, your option is at-the-money.

Now let's get to the concept of volatility skew. Volatility skew measures the difference in implied volatility between the three possible phases of your option. It compares implied volatility for out-of-the-money options with that for in-the-money options with that for at-the-money options.

In structure, it's similar to a yield curve, only in this case it deals with implied volatility rather than rates on various bonds. A yield curve shows the difference between the return of similar bonds with different maturities. How much can you get for a 1-year bond vs. a 5-year bond vs. a 30-year bond? That question underlies the concept of a yield curve. Along the same lines, the volatility skew plots out the various implied volatilities that come with the different possible results for your options.

You're planning to buy a call for MSFT. You can choose between a number of strike prices (kind of like picking from a menu). All the options have the same expiration, but they have different strike prices. You've got strike prices that are-at-the-money. You've got ones that are already in-the-money. You've got ones that are already out-of-the-money. Each of these possibilities comes with a different price (the in-the-money options are more expensive than the out-of-the-money ones).

When trying to determine which makes the most sense for your particular strategy, you can look at the volatility skew between them. It helps put the different possible strike prices into context.

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Finance: How does duration affect bonds ...2 Views

00:00

And finance Allah Shmoop How does duration affect bonds Okay

00:09

people It's a tale of two bond babies They're both

00:12

incubating in this well giant bond Womb Meet Harry Harry

00:16

the homunculus He's a bond He's almost ready to come

00:20

out and say hey to the world He'll turn right

00:22

into cash when he you know exits He carries in

00:25

his heart a short term bond with life We know

00:29

a ton about him We could see his excellent facial

00:31

features here in his strong arms here and his you

00:35

know excellent job They're incubating Harry Well Harry is a

00:38

short term bond We have only a very short period

00:41

of time until he matures and then is on his

00:44

own at least not directly You know swimming in our

00:46

bond Cool little ambiguity with tons of doctors looking in

00:50

on him Little risk that his AIPO are rather retirement

00:53

from incubating doesn't go well Short term bond Short duration

00:58

until maturity Not very volatile because well we can see

01:01

so much already and have clarity that he's healthy Like

01:04

the payments supporting him are right there We can identify

01:07

him No risk no worries Bond pays off And everyone

01:11

moves on Now Meet Justin fertilized a tiny dot ages

01:15

until he's born or matures We have no idea what

01:18

he'll look like how he'll perform in the incubation process

01:21

whether the womb will continue to be a healthy pool

01:24

to swim in or well frankly whether or not he'll

01:26

even make it Justin is a long term bond or

01:30

a bond with long duration like when a given company

01:34

sells one hundred million dollars worth of their bonds promising

01:36

to pay five percent a year in interest and then

01:38

pay back the principal in thirty years That's a long

01:41

bond Thirty years from now is eternity For a lot

01:44

of companies we'll think about what the world looked like

01:46

thirty years ago Yahoo was just coming into prominence Is

01:49

one of the largest companies in the world Well guess

01:52

what it died Nokia not Apple was the largest market

01:56

cap company in the world or most highly valued company

01:59

in the world It died Facebook and Google really weren't

02:03

even formed so long Duration bonds have extreme sensitivity to

02:07

very small inputs Early in there Jess Station Disney has

02:11

a hundred year bond Siri's that are about two decades

02:15

into their maturity Is there no risk that Disney will

02:18

be gone in eighty years Like Well could ABC Television

02:22

no longer exist because producers just stream their own TV

02:25

shows on the Web and they don't need a network

02:27

Is it possible ESPN is gone Because the NFL and

02:30

others just want to go direct to customers They don't

02:33

need ESPN anymore Could roaming gangs have taken over Disneyland

02:37

and Disney World and the other Disney thing He's making

02:39

it you know not the happiest place on Earth You

02:42

know like the Pirates of the Caribbean weren't menacing enough

02:45

So it's not like one in a million shot that

02:47

Disney joins Yahoo in Nokia in the next eighty years

02:51

When bonds have long durations tons of exogenous risk I

02:54

risk you can't imagine fathom believe or accept comes into

02:58

play And one other big element hits long duration bonds

03:01

Very hard That is prevailing interest rates like let's imagine

03:05

that when Justin was you know planted the world's economies

03:08

were fragile needing a boost from low interest rates Teo

03:12

Turbo charge things and help get the world's economies going

03:15

again So at that time for say a rated you

03:18

know best quality bond paper Well rates were four percent

03:22

But then a dozen years later inflation in a globally

03:26

heated mesh of economies started to be a real thing

03:29

and central banks around the world began raising rates So

03:32

twelve years later that prevailing rate was seven percent instead

03:36

of four And Justin was yielding just four Like his

03:39

yield doesn't change year after year or rather his coupon

03:43

or that four percent he's paying doesn't change Year after

03:46

year the price of the bond might go down and

03:48

it does so now for eighteen freaking more years until

03:52

that thirty year maturity bond of just and matures and

03:54

then pays cash well Justin will be paying three percent

03:57

per year less than his brethren who are being seven

04:01

percent essentially costing his parental investors in him One point

04:05

Oh three to the eighteenth power there That's how we

04:08

do the bond math on how much that cost them

04:10

Or set another way Investors in a seven percent yield

04:14

ER versus the four percent or in Justin would get

04:16

almost seventy percent more money by the time Justin pops

04:20

out of the oven then sticking with Justin So think

04:23

about this in extreme short case situations like let's say

04:26

you have Harry and Justin both yielding four percent Harry

04:29

is doing a year Justin is due in thirty years

04:32

If tomorrow rates suddenly jumped to seven percent overnight well

04:35

then Harry loses one year's worth of opportunity Cost meaning

04:39

Harry only yields four percent instead of the prevailing seven

04:42

percent right Yeah he could have been a seven percent

04:45

or he could have been somebody instead of a bum

04:48

So Harry loses three percent for one year Not great

04:51

but not a disaster either So if that rate hike

04:54

suddenly happened well what would Harry likely trade at one

04:58

year before his cash conversion in principle payoff Well if

05:01

Harry was a thousand dollar bond and he'd pay forty

05:04

bucks over that year the four percent there But the

05:07

new rates were paying seventy bucks over that year Wealth

05:10

Then you'd ask How does Harry's forty dollars in interest

05:12

payments and just so that they now pay seventy dollars

05:16

or set another way and ignoring some time value of

05:18

money things here for simplicity If Harry dropped in price

05:21

to nine hundred seventy dollars well then in the course

05:24

of a year He'd appreciate thirty bucks for the principal

05:27

while still paying the forty and interest And he deliver

05:30

seventy bucks in total return like thirty and appreciation in

05:34

forty and interest to his parental investors and match the

05:38

seven percent prevailing rates Okay so that's Harry in one

05:41

year What happens to just think about it He's got

05:44

only four percent a year yield That's got to adjust

05:46

to the new world reality of seven percent a year

05:49

RO rates that kind of class of a bond Well

05:51

his thousand dollars par value That market price drops a

05:55

lot In fact it dropped by one point Oh three

05:59

to the eighteenth power Or rather that becomes the denominator

06:03

in the new calculation So the thousand dollar bond value

06:06

drops to a thousand invited by one point seven ish

06:09

or about five hundred eighty five dollars and then slowly

06:13

slowly slowly over eighteen years It then crawls back tto

06:17

par assuming the parent company that issued Justin Will survives

06:21

the entire time And then finally mercifully eighteen years later

06:26

the emerges at par as a Philadelphia On paying off

06:29

in cash he goes out into the rial adult bond

06:32

world and it does you no adult bond things But

06:35

hopefully he makes good decisions and doesn't get too heavily 00:06:37.933 --> [endTime] into you know bondage Oh my

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