Primer on Options and Volatility Strategies - CBOE

Option structures incorpo
delta & vol view

Choice of structure depends on view

For any given equity and volatility view a
referring to the below diagram
As 1x2 put spread has a theoretical prof
months) we consider it to be a bullish tra

Bearish Volatility View

Market View

CBOE

orate

w on equity and volatility markets

a suitable structure can be chosen by
file similar to short put (for maturities over c3
ade (often used as pseudo-protection)

Implied expensive

Bullish

Market
View

Implied
cheap

26

VIX and Volatility
Trading



What Does Implied Volatili

CBOE

ity Look Like?

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 28

What is VIX?

A measure of implied volatility:
Derived from S&P 500 index option
Calculated from nearby expirations
Uses the entire range of available s
– VIX is calculated from the va
the square of 30-day volatilit

CBOE

n prices
s for constant, 30-day volatility measure
strike prices
alue of a portfolio of options that replicates
ty

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 29

VegaThe Option Strip

A specially designed portfolio of options
Option weights inversely proportional to
Constant volatility exposure over sever
Delta-hedging P&L not path-dependent

Vega exposure of single option

50 65 80 95 110 125 140 155
UnderlyingPrice

CBOE

Vegas
o the strike price (K) squared
ral strike prices
t

Vega exposure of option “strip”

50 65 80 95 110 125 140 155
Underlying Price

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 30

VIX Futures/Options Tradi

Multiplier is 100 for options
Multiplier is 1000 for futures
Settlement is cash,
European-style options
Expiration is 30 days before the
following month’s SPX expiry.
Expires on opening print.

CBOE

ing & Settlement

Series Used in Settlement - August 20, 2014
173 Strikes used, 174 options prices

Date Expiration Strike P/C Trade Price Volume

20-Aug-14 19-Sep-14 1275 Put 0.05 673

20-Aug-14 19-Sep-14 1280 Put 0.05 505

20-Aug-14 19-Sep-14 1285 Put 0.05 470

20-Aug-14 19-Sep-14 1290 Put 0.05 467

20-Aug-14 19-Sep-14 1295 Put 0.05 463

20-Aug-14 19-Sep-14 1300 Put 0.05 489

20-Aug-14 19-Sep-14 1305 Put 0.05 486

20-Aug-14 19-Sep-14 1310 Put 0.05 483

20-Aug-14 19-Sep-14 1315 Put 0.05 478

20-Aug-14 19-Sep-14 1320 Put 0.05 475

………. ………. ………. ………. ………. ……….

………. ………. ………. ………. ………. ……….

………. ………. ………. ………. ………. ……….

20-Aug-14 19-Sep-14 1975 Put 21.9 387

20-Aug-14 19-Sep-14 1975 Call 22.6 64

………. ………. ………. ………. ………. ……….

………. ………. ………. ………. ………. ……….

………. ………. ………. ………. ………. ……….

20-Aug-14 19-Sep-14 2090 Call 0.35 721

20-Aug-14 19-Sep-14 2095 Call 0.2 366

20-Aug-14 19-Sep-14 2100 Call 0.2 364

20-Aug-14 19-Sep-14 2105 Call 0.15 333

20-Aug-14 19-Sep-14 2110 Call 0.15 333

20-Aug-14 19-Sep-14 2115 Call 0.25 719

20-Aug-14 19-Sep-14 2120 Call 0.15 330

20-Aug-14 19-Sep-14 2125 Call 0.1 807

20-Aug-14 19-Sep-14 2150 Call 0.1 1,045

20-Aug-14 19-Sep-14 2175 Call 0.05 1,132

95,301

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 31

VIX Futures and Options B

VIX is 30-day vol
Futures are 30-day forward vol

All options priced on that month’s futur

On Bloomberg: Futures Quotes - “V
Options Quotes - “V
Settlement Price - “

CBOE

Basics

res contract
VIX <index> CT”
VIX <index> OMON”
“VRO <index>”

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 32

VIX Futures Term Structur

CBOE

re

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 33

VIX and VVIXSM (VIX of VIX

CBOE

X)

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 34

SPX and VIX Indices

CBOE

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 35

Correlations

CBOE

Copyright © 2014 Chicago Board Options Exchange, Incorporated. All rights reserved. 36

Question

Is close to close volatility an unb

No (RED)
Yes (GREEN)

CBOE

biased measure of volatility?

37

Markets do not random
walk in crisis

In normal markets equities random

• Market makers and stat arb funds remove

autocorrelation. In developed liquid markets with
short selling restrictions market makers and stat a
funds should remove any autocorrelation, hence m
normally random walk.

• In crisis equities no longer random walk. Beca

the risk, many market makers and stat arb funds
withdraw from stressed markets.

Reasons why not always random w

• Panic trading. Stop losses & panic trading can ca

market overreaction intraday, but this is normalise
a few days.

• Political “pin risk”. Politicians only do what is

necessary when markets plummet, and backtrack
they rise.

• Low volumes. Market moved by few big trades o

volume.

• Correction / misunderstanding of statements.

Markets moved by central bank comments, which
misread.

CBOE

m walk 115 Random walk / normal markets

110 Integrated vol = close to close vol = weekly vol
1234
h no 105 Random walk / normal markets
arb
Whipsaw / stressed markets
markets 100

ause of 95
90

walk 85 5
0
ause Days
ed after

k when
on low

h can be

38

Close to close overestima
volatility

Using intraday prices can improve

• When comparing volatility between regions, week

different time zones. This is only appropriate for la
advanced volatility measure is better.

• Close to close volatility needs c20 or more days o

close to close volatility is very noisy. An advanced
(C) is better for small samples.

Estimate Prices Handle Drift
Taken

Close to close C No

Parkinson HL No

Garman-Klass OHLC No

Rogers-Satchell OHLC Yes
OHLC No
G-K Yang-Zhang
ext

Yang-Zhang OHLC Yes

CBOE

ates

historical volatility measurement

kly volatility is better than daily to reduce effect of
arge data samples, if this is not available / practical an

of data to be accurate, for smaller periods e.g. 5 days
d measuring Open (O), High (H), Low (L) and Close

t? Handle Overnight Jumps? Efficiency
(max)
No 1
No 5.2
No 7.4
No 8

Yes 8

Yes 14

39

2 ways to profit from stres
markets

1) Delta hedging frequency

Hedge long gamma positions on the close. Wh
close to close volatility overestimates true volatility
crisis, you can extract this premium by delta hedg
close.
Hedge short gamma positions intraday. By del
hedging intraday (as frequently as is practical) you
extract the implied volatility premium to the true
(approximated by Yang-Zhang) volatility.

2) Long daily var and short weekly

Markets overreact when they are stressed. In a
markets often overreact (potentially due to stop lo
then correct after a few days. Investors can profit
this by going long daily variance and short weekly
variance.
No options or variance swaps need to be trade
variance swap is simply a delta hedged log contra
portfolio of long daily variance and short weekly v
can be replicated by delta hedging only (as log co
cancel). Alternatively a structured product can be

CBOE

ssed

hile Close to close – Yang-Zhang vol (30 day)
y in a
ging on 20%

lta 15%
u can
10%

5%

0%

var -5%

a crisis Performance long daily var short weekly
osses), 260 var

from 240 Long daily variance short weekly
y variance outperforms in a crisis

220

200

ed. As a 180
act, a 160
variance 140
ontracts 120
bought. 100

40

Question

Square root of time rule has vola

Near dated implieds move more than far da
Can adjust whole surface by adjusting impli
“one year implied vol move / T^p”.
P is the power of the move (rule of thumb is

If 1 year implied volatility rise
month implied rise?

More than 2 pts, i.e. power more tha

2pts, i.e. power = 0.5 or square root

Less than 2pts, i.e. power less than

NB: 3 months = 0.25 years, and square root of

CBOE

atility surfaces move power 0.5

ated implieds.
ieds for maturity T by
s P=0.5, or square root of time rule).

es 1pt, how much should 3

an 0.5 (WHITE)
of time rule (RED)
0.5 (GREEN)

0.25 = 0.5 (& dividing by 0.5 = 2).

41

Surfaces move by
“square root of time”

Vol move weighted by square ro

• Near dated implieds move more than far da

adjusting implieds for maturity T by “one ye

move.

• Typically volatility move weighted by square

0.5).

• Surfaces also sometimes move in parallel (

• On average surfaces move power 0.44, hen

parallel. Volatility moving by s

23%
1 year implied moves ha

22% amount of 3 month impli

Implied vol 21% +2% +1%
20% -1%
19%

18%

17% 1 yea
3 months 6 months Fla
Rise in implied

CBOE

oot of time is roughly constant

ated implieds. Can adjust whole surface by
ear implied vol move / Tp”. P is the power of the

e root of time is approximately constant (power

(power 0).
nce usually square root of time but sometimes

square root of time

half
ied

%

% -0.5%

4 year implied moves half
amount of 1 year implied

ar 2 years 3 years 4 years
at term structure Fall in implied

42

Can compare different
term structure & skew

Term structures can be normalis

If assume term structure is a fixed vol for in
maturity and a square root of time bump, th
different term structures can be compared
Multiplying standard V2 – V1 term structure
√(T2T1)/ (√T2- √ T1) allows different term
structures to be compared
Normalised term structure puts term structu
same units as 1 year – 3 month term struct

Skew multiplied by square root
time is roughly constant

Skew is greater for near dated implieds tha
dated
Can compare different skews when multiply
square root of time

CBOE

sed Term structure (normalised)

nfinite Term structure x
hen √(T2T1)
e by (√T2-√T1)

ure in 5
ture
0
of
-5 Dec-06
an far Apr-07
y by A ug-07
Dec-07
Apr-08
A ug-08
Dec-08
Apr-09
A ug-09
Dec-09
Apr-10
A ug-10
Dec-10
Apr-11
A ug-11
Dec-11

-10

-15

-20

6 mths - 3 mths (normalised) 1 year - 6 mths (normalised)

Skew Skew (normalised)
(normalised √T) In 2010 Q2 skew spiked, particularly at the far end,
3.8 due to changes in US regulation

3.6

3.4

3.2
3

2.8
2.6

2.4
2.2

2
Dec-09 Mar-10 Jun-10 Sep-10 Dec-10 Mar-11 Jun-11 Sep-11 Dec-11

3 month skew (90-100%) 6 month skew (90-100%)

43

Question

How does the realised volatility o
compare to the realised volatility

Realised post earnings > reali
Realised post earnings = reali
Realised post earnings < reali

CBOE

of a stock after earnings
y pre-earnings?

ised pre earnings (WHITE)
ised pre earnings (RED)
ised pre earnings (GREEN)

44

Option prices include implied
on reporting

Near dated expiries usually best

Backing out implied jump needs the “diffusi
volatility (volatility without jumps) to be estim
If an expiry exists before earnings date then
can be used, if not then forward volatility ne
be calculated
As a jump has a bigger relative effect for ne
dated expiries, using near dated expiries is

Stocks c25% less volatile after
reporting

Before reporting the uncertainty of the resu
lift volatility
In the 1-2 week period before reporting ana
typically issue research publications, which
move stock prices
After reporting stocks are usually ¾ as vola
they were before reporting
Most analysis for implied jumps assume co
diffusive volatility

CBOE

jump

t Using implied vol as vol assumption

ive” σJump
mated

n this Expiry before jump Expiry after jump
eeds to Time now
(T)

ear σDiffusive (σBefore jump)
best σExpiry after jump

ults can Using forward vol as vol assumption

σJump

alysts Time now (First) Expiry after jump Second Expiry

h can (T1) (T2)

atile as σExpiry after jump (σ1) σDiffusive (σ12)
onstant σ2

45

Need to adjust for index term s

Most analysis assumes flat term
structure

Assumption of constant diffusive volatility
implies flat term structure
Front end of volatility surfaces often have th
steepest term structure

Adjusting term structure improv
results

Adjusting equity term structure by index term
structure gives more accurate results
Using current index term structure, rather th
historic average equity term structure, ensu
the current market risks are priced in
Using average of peers term structure is les
accurate, due to wider bid offer spreads

CBOE

structure

m Equity and index term structure

he Implied volatility Implied jump is too big as expiry 3 implied is Implied
40% lifted by term structure and reporting date difference
ves 35% due to
30% reporting
m
han 25%
ures
ss 20%

15%

10%

5%

0% 23 Expiry
1 Reporting date

Equity Index Index term structure (diff to expiry 1)

Equity term structure adjusted by index

Implied volatility Adjusting for index term structure flattens equity
40% term structure to give more accurate implied jump

35% Implied
difference

30% due to

25% reporting

20%

15%

10%

5%

0% 23 Expiry
1 Reporting date

Equity - Index term structure Index term structure (diff to expiry 1)

46

Question

How much should ATM implied vola
(we assume skew is fairly priced)?

Amount equal to skew, i.e. stic
Between 1x and 2x skew (RED
Twice skew (GREEN)

CBOE

atility move by if markets rise/fall?
cky strike (WHITE)
D)

47

Local volatility is instantaneou
of underlying

Local volatility skew is double B

Black-Scholes is the average volatility of all
average of ATM local volatility and the local

ATM local volatility and ATM Black-Scholes v
Black-Scholes skew is half the local volatility

ATM volatility moves by twice the Black

If ATM is 20% and the 90% local volatility is 2
(average of 20% and 22%).
Local volatility 90-100% skew is 2% while Bl
If spot moves down 10% then the ATM Black

Underlying
price

S

Spot

Expiry

CBOE

us volatility

Black-Scholes skew

l paths from spot to strike, which is approx the
l volatility of the strike. This leads to 2 results:

volatility are identical
y skew

k-Scholes skew

22%, then the 90% Black-Scholes volatility is 21%

lack-Scholes 90-100% skew is 1%.
k Scholes (= ATM local volatility) is now 22%.

Low local volatility

Black-Scholes
implied volatility is

Strike

average volatility of
all paths between

spot and strike

High local volatility

y

48

Skew trading profitability dete
by volatility regime

There are 4 idealised regimes to

volatility surfaces

Sticky delta / moneyness. Constant volatility for
ATM constant)
Sticky strike. Constant volatility for options with s
Sticky local volatility. When markets fall Black-S
Jumpy volatility. Very high negative correlation b

Volatility surface with equities falling 10%

30%

28% Fixed strike implieds rise as markets fall
26%

24%

Implied vol 22%

20% Fixed strike implieds
18% decline as markets fall
16%

14% Markets fall 10%
12%

10% 40 45 50 55 60 65
35 Sticky strike (and before) Strike (€)

Sticky delta Sticky local vol Jumpy vol

CBOE

ermined

o describe movement of

options of same strike as percentage of spot (e.g.

same fixed currency strike (e.g. €50 strike constant)
Scholes implied volatility rises, and vice versa
between spot and implied volatility (panicked markets)

Volatility surface with equities rising 10%

30% Markets rise 10%
28%

26%

Implied vol 24% Fixed strike implieds increase
22% as markets rise
20%

18%

16%

14% Fixed strike implieds decline as markets rise
12%

10% 40 45 50 55 60 65
35 Sticky strike (and before) Strike (€)

Sticky delta Sticky local vol Jumpy vol

49

Skew trades breakeven with
sticky local volatility

Fixed strike implied
volatility change

Volatility Equity Equity
regime decline rise

Sticky delta Falls Rises

Sticky strike - -

Sticky local Rises Falls
volatility

Jumpy Rises Falls

volatility significantly significantly

CBOE

P&L breakdown for long skew
(e.g. long put, short call)

Remark Skew theta Total

+=
+=
+=
+=

50