Day 3 Keynote.dupire

7/27/2019 Day 3 Keynote.dupire

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Quantitative Strategiesfor Trading Volatility

Bruno Dupire

Head of Quantitative Research

Bloomberg L.P.

CBOE

Dublin, September 7, 2012


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Known Unknowns

I know one thing, that I know nothing.

Plato
http://en.wikipedia.org/wiki/Donald_Rumsfeldhttp://en.wikipedia.org/wiki/Donald_Rumsfeld


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Known Unknowns

There are known knowns; there are things we know weknow.

We also know there are known unknowns; that is to say weknow there are some things we do not know.

But there are also unknown unknowns there are things

we do not know we don't know.

United States Secretary of Defense Donald Rumsfeld
http://en.wikipedia.org/wiki/United_States_Secretary_of_Defensehttp://en.wikipedia.org/wiki/Donald_Rumsfeldhttp://en.wikipedia.org/wiki/Donald_Rumsfeldhttp://en.wikipedia.org/wiki/United_States_Secretary_of_Defense


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Known Unknowns

I know very accurately how much I do not know.

VIX market
http://en.wikipedia.org/wiki/Donald_Rumsfeldhttp://en.wikipedia.org/wiki/Donald_Rumsfeld


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OUTLINE

I. Frequency games

II.Term structure games

III. Historical/implied games


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I. Frequency Games


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Historical volatility tends to depend on the sampling frequency

SPX 2006 to 2011 Data

0 5 10 1520

20.5

21

21.5

22

22.5

23

23.5

24

24.5

25

Periodicity

HistoricalVolatility

Data from 2006 to 2011


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0 5 10 157.5

8

8.5

9

9.5

10

Periodicity

Historicalv

olatility

Data from 2006

SPX 2006 Data


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0 5 10 1512

12.5

13

13.5

14

14.5

15

15.5

16

16.5

Periodicity

Historicalv

olatility

Data from 2007

SPX 2007 Data


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0 5 10 1530

32

34

36

38

40

42

Periodicity

Historicalv

olatility

Data from 2008

SPX 2008 Data


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0 5 10 1525

25.5

26

26.5

27

27.5

Periodicity

Historicalvo

latility

Data from 2009

SPX 2009 Data


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0 5 10 1516.8

17

17.2

17.4

17.6

17.8

18

18.2

Periodicity

Historicalvolatility

Data from 2010

SPX 2010 Data


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SPX 2011 Data

0 5 10 1518.5

19

19.5

20

20.5

21

21.5

22

22.5

23

23.5

Periodicity

HistoricalVolatility

Data from 2006 to 2011


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Bruno Dupire 14

Historical Vol / Historical Vol Arbitrage

weekly

TRV

daily

TRV

If weekly historical vol < daily historical vol :

buy strip of T options, -hedge daily

sell strip of T options, -hedge weekly

Adding up :

do not buy nor sell any option;

play intra-week mean reversion until T;

final P&L : weeklyT

daily

T RVRV


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Bruno Dupire 15

Daily Vol / weekly Vol Arbitrage

-On each leg: always keep $ invested in the index and update every t

-Resulting spot strategy: follow each week a mean reverting strategy

-Keep each day the following exposure:

where is the j-th day of the i-th week

-It amounts to follow an intra-week mean reversion strategy

jit ,

)11

.(

1,, iji ttSS


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Intra week mean reversion strategy

1 2 3 4 5 6 7 8 9 10 11880

885

890

895

900

905

910

915

920

925

930

SP500

Data from 05/04/2009 to 05/18/2009

Short

Long Long

Short


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II. Term Structure Games


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VIX and VSTOXX


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VIX and VSTOXX


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SPX and VIX (MR portfolio)

900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 145010

15

20

25

30

35

40

45

50

SPX Index

VIX

Ind

ex

SPX Index and VIX Index Data from 4/1/2010 to 4/1/2012


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900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 145010

15

20

25

30

35

40

45

50

SPX Index

VIXI

ndex



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900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450

10

15

20

25

30

35

40

45

50

SPX Index

VIX

Index



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0 200 400 600-1

0

1

2

3

4

5

Time series of portfolio P&L

Time0 50 100 150

-1

0

1

2

3

4

5

Occupation time


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04/01/10 09/06/10 02/11/11 07/20/11 12/25/11 06/01/12-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Time


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SPX and VIX

900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 145010

15

20

25

30

35

40

45

50

SPX Index

VIX

Ind

ex



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SPX and VIX

900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 14500

5

10

15

20

25

30

35

40

45

50

SPX Index

VIX

Inde

x



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SPX and VIX

950 1000 1050 1100 1150 1200 1250 1300 1350 1400

0

5

10

15

20

25

30

35

40

45

50

SPX

VIX

SPX and VIX Data from 4/1/2010 to 4/1/2012


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SPX and VIX

0 200 400 600

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Time0 50 100 150

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Occupation time


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SPX and VIX

04/01/10 09/06/10 02/11/11 07/20/11 12/25/11 06/01/12-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Time


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VIX and V2X (MR portfolio)

10 20 30 40 50 60 7015

20

25

30

35

40

45

50

55

60

VIX Index

V2XIn

dex

VIX Index and V2X Index Data from 1/1/2009 to 9/10/2011


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10 20 30 40 50 60 70

15

20

25

30

35

40

45

50

55

60

65

VIX Index

V2XI

ndex



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10 20 30 40 50 60 70

15

20

25

30

35

40

45

50

55

60

65

VIX Index

V2X

Index



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0 200 400 600 800

-1

0

1

2

3

4

5

6

7


Time0 50 100 150 200

-1

0

1

2

3

4

5

6

7

Occupation time


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01/01/09 09/26/09 06/22/10 03/17/11 12/11/11 09/05/12-2

-1

0

1

2

3

4

5

6

7


Time

VIX F t


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Jan Feb Mar Apr 18

20

22

24

26

28

30

32

34

Maturity

VIX

futu

res

2-D representation

VIX Futures

VIX Futures and VStoxx Futures


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Jan Feb Mar Apr

18

20

22

24

26

28

30

32

34

Maturity

V

IX&VStoxx

Futures

2-D representation



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Jan Feb Mar Apr 20

25

30

35

40

45

Maturity

VIX&VStoxx

Futures

2-D representation


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III. Historical/Implied Games

/


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Bruno Dupire 39

Historical/implied moments

Volatility Skew: slope of implied volatility as afunction of Strike

Link with Skewness (asymmetry) of the RiskNeutral density function ?

Moments Statistics Finance1 Expectation FWD price

2 Variance Level of implied vol3 Skewness Slope of implied vol

4 Kurtosis Convexity of implied vol

S&P 500 O ti P i


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Bruno Dupire 40

S&P 500: Option Prices

Non parametric fit


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Bruno Dupire 41

Non parametric fit

of implied vols

1000 1100 1200 1300 1400 1500 1600 170010

15

20

25

30

35

40

K

Implied

(%)

SPX Implied Vols on 31-Jan-2o12 (1M)

I li d V l tiliti


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Bruno Dupire 42

Implied Volatilities

L l V l tiliti


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Bruno Dupire 43

Local Volatilities

Ri k N t l D iti


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Bruno Dupire 44

Risk Neutral Densities

500 750 1000 1250 1500 1750 20000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01Risk Neutral Density SPX on 31-Jan-2o12 (1M, 3M, 1Y)

SPOT

PDF


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Theoretical Skew

From Price History

Theoretical Ske from Prices


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Bruno Dupire 46

Problem : How to compute option prices on an underlying withoutoptions?

For instance : compute 3 month 5% OTM Call from price history only.

1) Discounted average of the historical payoffs.

Bad : depends on bull/bear, no call/put parity.

2) Generate paths by sampling 1 day return recentered histogram.

Problem : CLT => converges quickly to same volatility for all

strike/maturity; breaks autocorrelation and vol/spot dependency.

Theoretical Skew from Prices

?

=>

Theoretical Skew from Prices (2)


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Bruno Dupire 47

Theoretical Skew from Prices (2)

3) Discounted average of the Intrinsic Value from recentered 3 monthhistogram.

4) -Hedging : compute the implied volatility which makes the -hedging a fair game.

Strike dependency


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Bruno Dupire 48

Strike dependency

Fair or Break-Even volatility is an average of squaredreturns, weighted by the Gammas, which depend on the

strike

Strike dependency for multiple paths


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Bruno Dupire 49

Strike dependency for multiple paths

Theoretical Skewf hi t i l i


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Bruno Dupire

from historical prices

50

S&P500 2006


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S&P500 2006

Bruno Dupire 51

80

90

100

110

120 1m2m

3m6m

1y18m

2y

0

0.2

0.4

0.6

0.8

1

maturity

SP500 1/3/2006 to 1/3/2009

moneyness

BEVL surface

1/3/2006 Implied vol surface

S&P500 2008


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S&P500 2008

Bruno Dupire 52

80

90

100

110

1201m

2m3m

6m1y

18m2y

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

maturity

SP500 10/1/2008 to 11/22/2010

moneyness

BEVL surface

10/1/2008 Implied vol surface

Conditional Realized Variance


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Bruno Dupire 53

variancerealizedhistoricalion toapproximatapply thisWe

][),(

summaryIn

),()],[(

][][][

thatfollowsIt

)],[(]][[][

then,Assume

2

20

00

'

KSRVETTK

TTKdttKSSEv

dtKSvEKSdtvEKSRVE

tKSSEvKSSESvEKSvE

dWvdS

TTimpl

impl

T

Ttloc

T

T

tT

T

tTT

TtlocTtttTt

ttt

=

==

=====

======

0 12

Realized Variance vs Final Return

S&P500 example


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85 90 95 100 105 1100

0.02

0.04

0.06

0.08

0.1

0.12

Final Return

Realize

dVariance

S&P500 exampleRealized Vol vs Final Return


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85 90 95 100 105 1100.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Final Return

RealizedVol

Density extracted from previous skew


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85 90 95 100 105 1100

0.02

0.04

0.06

0.08

0.1

0.12

Summary


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Summary

We can play with volatility even without options

Term structure of volatility can be exploited

Careful with implied/historical games

More complex games with more dimensions

Bruno Dupire 57

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