what drives interest rates volatility? · pdf filewhat drives interest rates volatility? ......

What Drives Interest Rates Volatility?

Piotr Karasinski

European Bank for Reconstruction and Development

CASS Seminar in Financial Engineering

26 May, 2011

2

Disclaimer

• The contents of this presentation reflect the opinions of the author

and do not necessarily reflect the views of the EBRD

3

Data Sources

• Barclays Capital – I would like to thank Barclays Capital for generously allowing me to use their

interest rate and implied swaption volatility data (EUR, GBP, USD).

• US Federal Reserve Statistical Release: H.15 Publication

• www.rateinflation.com

• Drivatives Trading Systems Ltd.

4

Outline

• Introduction

• Historical moving window basis point volatility

• Implied ATM swaption volatilities since the late 90’s

• Conclusions

5

Introduction• The purpose of this presentation is to review the old question

“What drives interest rate volatility?” especially in light of the recent “credit-crunch” and market behaviour in its wake.

• The choice of the dependence of rates volatility on the term- structure of interest rates plays a fundamental role in interest rate models building. In forward-libor model we write:

• Traditional models: lognormal, shifted-lognormal (Q-model, norm-log), normal, CEV: square-root, 3/2.

dWLfdtdL })({(...)

6

Introduction: continued

Empirical Questions:

• What is the rate-level dependence of:– the moving window historical volatilities?– the at-the-money implied swaption volatilities?

• Does rate volatility depend on curve slope?

• Does rate volatility depend on whether we are in rate rising/falling environment?

Historical Moving Window Volatilities

8

Calculating Moving Window Volatility

• We estimate volatility for a given day in the past by taking the weighted average of absolute daily changes of the preceding and the following 30 daily observations (in total 60 observations)

• Weights decay exponentially with the time distance from the given day

• Volatility formula:

• We use a = 0.98

),30min(

)1,30max(

||

),30min(

)1,30max(

||

2 Nni

ni

in

Nni

nii

in

n

a

ra

A Bit of History• DECEMBER 1969 – NOVEMBER 1970

• Oil Crisis November 1973 – March 1975

• 1970s stagflation: “Persistent high inflation combined with high unemployment and stagnant demand in a country's economy”

• September 1979 – December 1982 Volcker’s Monetary Experiment

• JULY 1990 – MARCH 1991

• Tightening of 1994

• MARCH 2001 – NOVEMBER 2001– The bursting of the dot-com bubble, corporate scandals: Enron and Worldcom, deflationary

pressures, 9/11

• DECEMBER 2007 – JUNE 2009

9

10

1970 1980 1990 2000 2010

05

1015

Date

Infla

tion

/ 1Y

CM

T R

ate

US Inflation and 1Y CMT

US InflationUS 1Y CMT

11

1970 1980 1990 2000 2010

05

1015

Date

CM

T Y

ield

010

020

030

040

050

0

Mov

ing

Win

dow

CM

T Y

ield

BP

Vol

USD 1Y CMT Yield and Moving Wnd BP Vol: Jan1962 to Feb2011

CMT YieldCMT Yield BP Vol

12

1970 1980 1990 2000 2010

24

68

1012

1416

Date

CM

T Y

ield

050

100

150

200

250

300

350

Mov

ing

Win

dow

CM

T Y

ield

BP

Vol



13

1979 1980 1981 1982 1983

810

1214

16

Date

CM

T Y

ield

100

200

300

400

500

Mov

ing

Win

dow

CM

T Y

ield

BP

Vol



14

0 5 10 15

010

020

030

040

050

0

CMT Yield

CM

T W

indo

w V

olat

ility

USD 1Y CMT Historical Window Vol vs Yield: Jan 1962 to Feb 2011

Before Sep1979Sep1979 to Dec1982Jan1983 to May2007Jun2007 to Mar2009After Mar2009

15

0 5 10 15

010

020

030

0

C M T Yie ld

CM

T M

ovin

g W

indo

w B

P V

olat

ility

US D 5 Y C M T M o v in g W in d o w B P V o l v s Y ie ld : J a n 1 9 6 2 to F e b 2 0 1 1

B efo re S ep1979S ep1979 to D ec1982Jan1983 to M ay2007Jun2007 to M ar2009A fte r M ar2009

16

0 5 10 15

-200

-100

010

020

0

1Y CMT Yield

5Y -

1Y Y

ield

Spr

ead

5Y - 1Y CMT Spread vs 1Y CMT Yield: Jan1962 to Feb2011

Before Sep1979Sep1979 to Dec1982Jan1983 to May2007Jun2007 to Mar2009After Mar2009

17

1970 1980 1990 2000 2010

-500

050

0

Date

Bas

is P

oint

s

Volatility, Real Rate and Curve Steepness: Jan1963 to Feb2011

1Y CMT Yield BP Vol1Y CMT Yield - Inflation3Y - 1Y CMT BP Spread

18

0 2 4 6 8 10

050

100

150

200

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

USD 2Y CMS Moving Window BP Vol vs CMS Rate: Feb1986 to Feb2011

Before Jun2007Jun2007 to Mar2009After Mar2009

0 2 4 6 8 100

5010

015

020

0

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

USD 10Y CMS Moving Window BP Vol vs CMS Rate: Feb1986 to Feb2011


19

0 1 2 3 4 5 6

020

4060

8010

012

0

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

EUR 2Y CMS Moving Window BP Vol vs CMS Rate: Feb1997 to Feb2011


0 1 2 3 4 5 60

2040

6080

100

120

140

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

EUR 10Y CMS Moving Window BP Vol vs CMS Rate: Feb1997 to Feb2011


20

0 5 10 15

050

100

150

200

250

300

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

GBP 2Y CMS Moving Window BP Vol vs CMS Rate: Feb1986 to Feb2011


0 2 4 6 8 10 12 140

5010

015

020

0

CMS Rate

CM

S M

ovin

g W

indo

w B

P V

olat

ility

GBP 10Y CMS Moving Window BP Vol vs CMS Rate: Feb1986 to Feb2011


Implied ATM Swaption Volatilities

Since the Late 90’s

22

1998 2000 2002 2004 2006 2008 2010

02

46

8

Year

Sw

ap R

ate

USDEURGBP

Comparing 6Mx2Y Swap Rates: USD, EUR, GBP

1998 2000 2002 2004 2006 2008 20100

5010

015

020

0

Year

BP

ATM

Vol

USDEURGBP

Comparing 6Mx2Y ATM Vols: USD, EUR, GBP

23

1998 2000 2002 2004 2006 2008 20100

5010

015

020

0

Year

BP

ATM

Vol

USDEURGBP

Comparing 3M x 10Y AT M Vols: USD, EUR, GBP

1998 2000 2002 2004 2006 2008 2010

02

46

8

Year

BP

ATM

Vol

USDEURGBP

Comparing 3M x 10Y FWD Swap Rates: USD, EUR, GBP

240 1 2 3 4 5

-50

050

100

150

200

1 Y S w a p R a te

Sw

ap S

prea

d in

BP

: 5Y

- 1Y

E U R 5 Y - 1 Y S p r e a d v s 1 Y S w a p R a te

M a r1 9 9 7 to M a y2 0 0 7J un2 0 0 7 to M a r2 0 0 9A fte r M a r2 0 0 9

0 2 4 6 8

-100

010

020

0

1 Y S w a p R a te

Sw

ap S

prea

d in

BP

: 5Y

- 1Y

G B P 5 Y - 1 Y S p r e a d v s 1 Y S w a p R a te


0 2 4 6

-50

050

100

150

200

250

300

1 Y S w a p R a te

Sw

ap S

prea

d in

BP

: 5Y

- 1Y

U S D 5 Y - 1 Y S p r e a d v s 1 Y S w a p R a te


USD 6Mx2Y Swaption 1997 - 2011

25

26

1997.5 1998.0 1998.5 1999.0 1999.5 2000.0

01

23

45

67

Date

6M.2

Y S

wap

Rat

e

-20

020

4060

80

2Y -

6M S

wap

Spr

ead

in B

P

USD 6M.2Y Rate vs Spread: Mar1997 to Dec1999

6M.2Y Swap Rate2Y - 6M Spread

-20 0 20 40 60 80 100

6080

100

120

140

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP V

ol

USD 6Mx2Y ATM Vol vs 2y - 6m Spread: Mar1997 to Dec1999

0 1 2 3 4 5 6 7

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP V

olUSD 6Mx2Y ATM Vol vs FwdSwapRate: Mar1997 to Dec1999

0 1 2 3 4 5 6 7

-20

020

4060

80

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP:

2y -

6m

USD 2y - 6m Spread vs 6Mx2Y Swap Rate: Mar1997 to Dec1999

27-5 0 0 5 0 1 0 0 1 5 0 2 0 0

8010

012

014

016

018

0

2 y - 6 m S w a p S p re a d

6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s 2 y - 6 m S p r e a d : J a n 2 0 0 0 to D e c 2 0 0 3

0 2 4 6 8

-50

050

100

150

6 M x2 Y F w d S w a p R a te

Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 6 M x 2 Y S w a p R a te : J a n 2 0 0 0 to D e c 2 0 0 3

0 2 4 6 8

050

100

150


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s F w d S w a p R a te : J a n 2 0 0 0 to D e c 2 0 0 3

2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4

02

46

8

D a te

6Mx2

Y S

wap

Rat

e

050

100

150

2Y -

6M S

wap

Spr

ead

in B

P

U S D 6 M x 2 Y R a te v s 2 Y - 6 M S p r e a d : J a n 2 0 0 0 to D e c 2 0 0 3

6 M x2 Y S w a p R a te2 Y S w a p - 6 M L ib o r S p re a d

28

0 1 2 3 4 5 6

050

100

150


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s F w d S w a p R a te : J a n 2 0 0 4 to D e c 2 0 0 6

-5 0 0 5 0 1 0 0 1 5 0

6080

100

120

140


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s 2 y - 6 m S p r e a d : J a n 2 0 0 4 to D e c 2 0 0 6

0 1 2 3 4 5 6

-50

050

100

150


Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 6 M x 2 Y S w a p R a te : J a n 2 0 0 4 to D e c 2 0 0 6

2 0 0 4 .0 2 0 0 4 .5 2 0 0 5 .0 2 0 0 5 .5 2 0 0 6 .0 2 0 0 6 .5 2 0 0 7 .0

01

23

45

6

D a te

6Mx2

Y S

wap

Rat

e

-50

050

100

150

2Y -

6M S

wap

Spr

ead

in B

P

U S D 6 M x 2 Y R a te v s 2 Y - 6 M S p r e a d : J a n 2 0 0 4 to D e c 2 0 0 6


29

0 1 2 3 4 5

050

100

150

200


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s F w d S w a p R a te : J a n 2 0 0 7 to A p r 2 0 0 9

-5 0 0 5 0 1 0 0

5010

015

020

0


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s 2 y - 6 m S p r e a d : J a n 2 0 0 7 to A p r 2 0 0 9

0 1 2 3 4 5

-50

050


Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 6 M x 2 Y S w a p R a te : J a n 2 0 0 7 to A p r 2 0 0 9

2 0 0 7 .0 2 0 0 7 .5 2 0 0 8 .0 2 0 0 8 .5 2 0 0 9 .0

01

23

45

D a te

6Mx2

Y S

wap

Rat

e

-50

050

100

150

2Y -

6M S

wap

Spr

ead

in B

P

U S D 6 M x 2 Y R a te v s 2 Y - 6 M S p r e a d : J a n 2 0 0 7 to A p r 2 0 0 9


30

2 0 0 9 .5 2 0 1 0 .0 2 0 1 0 .5 2 0 1 1 .0

0.0

0.5

1.0

1.5

2.0

2.5

D a te

6Mx2

Y S

wap

Rat

e

050

100

150

2Y -

6M S

wap

Spr

ead

in B

P

U S D 6 M x 2 Y R a te v s 2 Y - 6 M S p r e a d : A p r 2 0 0 9 to F e b 2 0 1 1


0 .0 0 .5 1 .0 1 .5 2 .0 2 .5

050

100

150


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s F w d S w a p R a te : A p r 2 0 0 9 to F e b 2 0 1 1

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0

4060

8010

012

014

016

0


6Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 6 M x 2 Y A T M V o l v s 2 y - 6 m S p r e a d : A p r 2 0 0 9 to F e b 2 0 1 1

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5

020

4060

8010

012

0


Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 6 M x 2 Y S w a p R a te : A p r 2 0 0 9 to F e b 2 0 1 1

31

0 2 4 6 8

050

100

150

200

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

USD 6Mx2Y Swaption ATM BP Vol vs Fwd Swap Rate

Mar1997 to May2007Jun2007 to Mar2009After Mar2009

32

-50 0 50 100 150

5010

015

020

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

USD 6Mx2Y Swaption ATM BP Vol vs 2y - 6m Swap Spread


EUR 6Mx2Y Swaption 1999 - 2011

33

34

0 1 2 3 4 5

020

4060

8010

012

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Jan1999 to Dec1999

1999.0 1999.2 1999.4 1999.6 1999.8 2000.0

01

23

45

Date

6M.2

Y S

wap

Rat

e

020

4060

8010

0

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: Jan1999 to Dec1999


0 20 40 60 80 100

4060

8010

012

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: Jan1999 to Dec1999

0 1 2 3 4 5

020

4060

8010

0

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: Jan1999 to Dec1999

350 20 40 60 80 100

5060

7080

9010

011

012

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: Jan2000 to Dec2000

2000.0 2000.2 2000.4 2000.6 2000.8 2001.0

01

23

45

Date

6M.2

Y S

wap

Rat

e

020

4060

8010

0

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: Jan2000 to Dec2000


0 1 2 3 4 5

020

4060

8010

0

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: Jan2000 to Dec2000

0 1 2 3 4 5

020

4060

8010

012

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Jan2000 to Dec2000

36

0 1 2 3 4 5

020

4060

8010

012

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Jan2001 to May2003

2001.0 2001.5 2002.0 2002.5 2003.0

01

23

45

Date

6M.2

Y S

wap

Rat

e

-20

020

4060

80

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: Jan2001 to May2003


0 1 2 3 4 5

-20

020

4060

80

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: Jan2001 to May2003

-20 0 20 40 60 80 100

6070

8090

100

110

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: Jan2001 to May2003

37

0 1 2 3 4 5

020

4060

8010

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Jul2003 to Jul2007

2004 2005 2006 2007

01

23

45

Date

6M.2

Y S

wap

Rat

e

020

4060

80

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: May2003 to Jul2007


0 20 40 60 80

4060

8010

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: May2003 to Jul2007

0 1 2 3 4 5

020

4060

80

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: May2003 to Jul2007

38

0 1 2 3 4 5

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Jul2007 to Apr2009

2007.5 2008.0 2008.5 2009.0

01

23

45

Date

6M.2

Y S

wap

Rat

e

-80

-60

-40

-20

020

40

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: Jul2007 to Apr2009


-80 -60 -40 -20 0 20 40

4060

8010

012

014

016

018

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: Jul2007 to Apr2009

0 1 2 3 4 5

-80

-60

-40

-20

020

40

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: Jul2007 to Apr2009

39

0.0 0.5 1.0 1.5 2.0 2.5

020

4060

8010

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs FwdSwapRate: Apr2009 to Feb2011

2009.5 2010.0 2010.5 2011.0

0.0

0.5

1.0

1.5

2.0

2.5

Date

6M.2

Y S

wap

Rat

e

2040

6080

100

2Y -

6M S

wap

Spr

ead

in B

P

EUR 6M.2Y Rate vs Spread: Apr2009 to Feb2011


0.0 0.5 1.0 1.5 2.0 2.5

2040

6080

100

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR 2y - 6m Spread vs 6Mx2Y Swap Rate: Apr2009 to Feb2011

20 40 60 80 100

5060

7080

9010

011

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y ATM Vol vs 2y - 6m Spread: Apr2009 to Feb2011

40

0 1 2 3 4 5

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y Swaption ATM BP Vol vs Fwd Swap Rate


41

-50 0 50 100

5010

015

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

EUR 6Mx2Y Swaption ATM BP Vol vs 2y - 6m Swap Spread


GBP 6Mx2Y Swaption 1997 - 2011

42

43

0 2 4 6

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs FwdSwapRate: Jan1997 to Mar2000

-50 0 50 100

6080

100

120

140

160

180

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Jan1997 to Mar2000

1997.0 1997.5 1998.0 1998.5 1999.0 1999.5 2000.0

02

46

Date

6M.2

Y S

wap

Rat

e

-50

050

100

2Y -

6M S

wap

Spr

ead

in B

P

GBP 6M.2Y Rate vs Spread: Jan1997 to Mar2000


0 2 4 6

-50

050

100

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

GBP 2y - 6m Spread vs 6Mx2Y Swap Rate: Jan1997 to Mar2000

44

0 1 2 3 4 5 6 7

020

4060

8010

012

014

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs FwdSwapRate: Apr2000 to Jul2003

2000.5 2001.0 2001.5 2002.0 2002.5 2003.0 2003.5

01

23

45

67

Date

6M.2

Y S

wap

Rat

e

-20

020

4060

8010

0

2Y -

6M S

wap

Spr

ead

in B

P

GBP 6M.2Y Rate vs Spread: Apr2000 to Jul2003


-20 0 20 40 60 80 100

7080

9010

011

012

013

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Apr2000 to Jul2003

0 1 2 3 4 5 6 7

-20

020

4060

8010

0

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

GBP 2y - 6m Spread vs 6Mx2Y Swap Rate: Apr2000 to Jul2003

45-20 0 20 40 60 80

4060

8010

012

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Jul2003 to Jul2007

0 1 2 3 4 5 6

020

4060

8010

012

0

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs FwdSwapRate: Jul2003 to Jul2007

2004 2005 2006 2007

01

23

45

6

Date

6M.2

Y S

wap

Rat

e

-20

020

4060

80

2Y -

6M S

wap

Spr

ead

in B

P

GBP 6M.2Y Rate vs Spread: Jul2003 to Jul2007


0 1 2 3 4 5 6

-20

020

4060

80

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

GBP 2y - 6m Spread vs 6Mx2Y Swap Rate: Jul2003 to Jul2007

46-100 -50 0 50

6080

100

120

140

160

180

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Jul2007 to Apr2009

0 1 2 3 4 5 6

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y ATM Vol vs FwdSwapRate: Jul2007 to Apr2009

0 1 2 3 4 5 6

-100

-50

0

6Mx2Y Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

GBP 2y - 6m Spread vs 6Mx2Y Swap Rate: Jul2007 to Apr2009

2007.5 2008.0 2008.5 2009.0

01

23

45

6

Date

6M.2

Y S

wap

Rat

e

-100

-50

0

2Y -

6M S

wap

Spr

ead

in B

P

GBP 6M.2Y Rate vs Spread: Jul2007 to Apr2009


47

0.0 0.5 1.0 1.5 2.0 2.5 3.0

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP V

olGBP 6Mx2Y ATM Vol vs FwdSwapRate: Apr2009 to Feb2011

2009.5 2010.0 2010.5 2011.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Date

6M.2

Y S

wap

Rat

e

2040

6080

100

120

140

2Y -

6M S

wap

Spr

ead

in B

P

GBP 6M.2Y Rate vs Spread: Apr2009 to Feb2011


20 40 60 80 100 120 140

6080

100

120

140

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP V

ol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Apr2009 to Feb2011

20 40 60 80 100 120 140

6080

100

120

140

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP V

ol

GBP 6Mx2Y ATM Vol vs 2y - 6m Spread: Apr2009 to Feb2011

48

0 2 4 6

050

100

150

6Mx2Y Fwd Swap Rate

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y Swaption ATM BP Vol vs Fwd Swap Rate


49

-100 -50 0 50 100

4060

8010

012

014

016

018

0

2y - 6m Swap Spread

6Mx2

Y S

wap

ion

ATM

BP

Vol

GBP 6Mx2Y Swaption ATM BP Vol vs 2y - 6m Swap Spread


USD Swaptions

50

51

0 2 4 6

050

100

150

200

250


3Mx1

Y S

wap

ion

ATM

BP

Vol

U S D 3 M x 1 Y S w a p t io n A T M B P V o l v s F w d S w a p R a te

M a r1 9 9 7 to M a y2 0 0 7J u n 2 0 0 7 to M a r2 0 0 9A fte r M a r2 0 0 9

0 2 4 6

-50

050

100

150


Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 3 M x 1 Y S w a p R a te


-50 0 50 100 150

5010

015

020

025

0

2y - 6m S wap S pread

3Mx1

Y S

wap

ion

ATM

BP

Vol

US D 3M x1Y S w ap tio n AT M B P V o l vs 2y - 6m Sw ap S pread

Mar1997 to May2007Jun2007 to Mar2009A fter Mar2009

52

0 2 4 6 8

050

100

150

200

250


3Mx2

Y S

wap

ion

ATM

BP

Vol

U S D 3 M x 2 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te


0 2 4 6 8

-50

050

100

150

3Mx2Y Fwd Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

USD r2y - r6m Spread vs 3M x2Y Sw ap Rate


-50 0 50 100 150

5010

015

020

025

0

2y - 6m S wap S pread

3Mx2

Y S

wap

ion

ATM

BP

Vol

USD 3M x2Y Sw aption AT M B P Vo l vs 2y - 6m S w ap S pread

Mar1997 to May2007Jun2007 to Mar2009A fter Mar2009

53-50 0 50 100 150

5010

015

020

0

2 y - 6m S wap S p read

1Yx2

Y S

wap

ion

ATM

BP

Vol

US D 1 Y x 2 Y S w a p tio n AT M B P V o l v s 2 y - 6 m S w a p S p re a d

M ar1997 to M ay2007Jun2007 to M ar2009A fte r M ar2009

0 2 4 6 8

-50

050

100

150

1Yx2Y Fwd Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

USD r2y - r6m Spread vs 1Yx2Y Swap Rate


0 2 4 6 8

050

100

150

200

1 Yx2 Y F w d S w a p R a te

1Yx2

Y S

wap

ion

ATM

BP

Vol

U S D 1 Y x 2 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te


54

0 2 4 6 8

050

100

150


5Yx2

Y S

wap

ion

ATM

BP

Vol

U S D 5 Y x 2 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te


0 2 4 6 8

-50

050

100

150


Sw

ap S

prea

d in

BP

: 2y

- 6m

U S D r 2 y - r 6 m S p r e a d v s 5 Y x 2 Y S w a p R a te


-5 0 0 5 0 1 0 0 1 5 0

8010

012

014

016

0


5Yx2

Y S

wap

ion

ATM

BP

Vol

U S D 5 Y x 2 Y S w a p tio n A T M B P V o l v s 2 y - 6 m S w a p S p r e a d


EUR Swaptions

55

56

0 1 2 3 4 5

050

100

150

3Mx1Y Fwd Swap Rate

3Mx1

Y S

wap

ion

ATM

BP

Vol

EUR 3Mx1Y Swaption ATM BP Vol vs Fwd Swap Rate


-50 0 50 100

5010

015

0

2y - 6m Swap Spread

3Mx1

Y S

wap

ion

ATM

BP

Vol

EUR 3Mx1Y Swaption ATM BP Vol vs 2y - 6m Swap Spread


0 1 2 3 4 5

-50

050

100

3Mx1Y Fwd Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR r2y - r6m Spread vs 3Mx1Y Swap Rate


57

0 1 2 3 4 5 6

050

100

150


6Mx5

Y S

wap

ion

ATM

BP

Vol

E U R 6 M x 5 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

M a r1 9 9 7 to M a y2 0 0 7

J un2 0 0 7 to M a r2 0 0 9

A fte r M a r2 0 0 9

0 1 2 3 4 5 6

-50

050

100


Sw

ap S

prea

d in

BP

: 2y

- 6m

E U R r 2 y - r 6 m S p r e a d v s 6 M x 5 Y S w a p R a te


-5 0 0 5 0 1 0 0

4060

8010

012

014

016

0


6Mx5

Y S

wap

ion

ATM

BP

Vol

E U R 6 M x 5 Y S w a p tio n A T M B P V o l v s 2 y - 6 m S w a p S p r e a d


580 1 2 3 4 5 6

-50

050

100

1Yx2Y Fwd Swap Rate

Sw

ap S

prea

d in

BP

: 2y

- 6m

EUR r2y - r6m Spread vs 1Yx2Y Swap Rate


0 1 2 3 4 5 6

020

4060

8010

012

014

0


1Yx2

Y S

wap

ion

ATM

BP

Vol

E U R 1 Y x 2 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

M a r1 9 9 7 to M a y2 0 0 7Jun2 0 0 7 to M a r2 0 0 9A fte r M a r2 0 0 9

-50 0 50 100

4060

8010

012

014

0

2y - 6m Swap Spread

1Yx2

Y S

wap

ion

ATM

BP

Vol

EUR 1Yx2Y Swaption AT M BP Vol vs 2y - 6m Swap Spread


59-5 0 0 5 0 1 0 0

4060

8010

012

0


2Yx5

Y S

wap

ion

ATM

BP

Vol

E U R 2 Y x 5 Y S w a p tio n A T M B P V o l v s 2 y - 6 m S w a p S p r e a d


0 1 2 3 4 5 6

-50

050

100


Sw

ap S

prea

d in

BP

: 2y

- 6m

E U R r 2 y - r 6 m S p r e a d v s 2 Y x 5 Y S w a p R a te


0 1 2 3 4 5 6

020

4060

8010

0


2Yx5

Y S

wap

ion

ATM

BP

Vol

E U R 2 Y x 5 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te


GBP Swaptions

60

61

0 2 4 6 8

050

100

150

3Mx1Y Fwd Swap Rate

3Mx1

Y S

wap

ion

ATM

BP

Vol

GBP 3M x1Y Swaption AT M BP Vol vs Fwd Swap Rate


-1 0 0 -5 0 0 5 0 1 0 0

5010

015

020

0


3Mx1

Y S

wap

ion

ATM

BP

Vol

G B P 3 M x 1 Y S w a p tio n A T M B P V o l v s 2 y - 6 m S w a p S p r e a d


0 2 4 6 8

-100

-50

050

100


Sw

ap S

prea

d in

BP

: 2y

- 6m

G B P r 2 y - r 6 m S p r e a d v s 3 M x 1 Y S w a p R a te


62-1 0 0 -5 0 0 5 0 10 0

6080

100

120

140

160

180

2 y - 6 m S wap S p re ad

1Yx1

Y S

wap

ion

ATM

BP

Vol

G B P 1 Y x 1 Y S w a p tio n AT M B P V o l v s 2 y - 6 m S w a p S p re a d

M ar1 99 7 to M a y2 0 0 7Jun2 0 0 7 to M a r2 0 09A fte r M a r2 0 09

0 2 4 6 8

-100

-50

050

100

1 Yx1 Y F wd S wa p Ra te

Sw

ap S

prea

d in

BP

: 2y

- 6m

G B P r2 y - r6 m S p re a d v s 1 Y x 1 Y S w a p Ra te

M a r19 9 7 to M a y2 0 0 7Jun2 0 0 7 to M a r2 00 9A fte r M a r2 0 09

0 2 4 6 8

050

100

150


1Yx1

Y S

wap

ion

ATM

BP

Vol

G B P 1 Y x 1 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te


63

0 2 4 6 8

050

100

150


1Yx5

Y S

wap

ion

ATM

BP

Vol

G B P 1 Y x 5 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

M a r1 9 9 7 to M a y2 0 0 7J un 2 0 0 7 to M a r2 0 0 9A fte r M a r2 0 0 9

0 2 4 6 8

-100

-50

050

100


Sw

ap S

prea

d in

BP

: 2y

- 6m

G B P r 2 y - r 6 m S p r e a d v s 1 Y x 5 Y S w a p R a te


-1 0 0 -5 0 0 5 0 1 0 0

4060

8010

012

014

016

0


1Yx5

Y S

wap

ion

ATM

BP

Vol

G B P 1 Y x 5 Y S w a p tio n A T M B P V o l v s 2 y - 6 m S w a p S p r e a d


JPY Data: May 1996 to March 2008

Source: Derivative Trading Systems

65

0 .0 0 .5 1 .0 1 .5

020

4060

8010

0

3 M x 1 Y S w a p R a te

Impl

ied

ATM

BP

Vol

: 3M

x 1

YJ P Y 3 M x 1 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5

020

4060

8010

012

0

3 M x 5 Y S w a p R a te

Impl

ied

ATM

BP

Vol

: 3M

x 5

Y

J P Y 3 M x 5 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

0 1 2 3

050

100

150

2 Y x 1 Y S w a p R a te

Impl

ied

ATM

BP

Vol

: 2Y

x 1

Y

J P Y 2 Y x 1 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

0 1 2 3 4

020

4060

8010

0

2 Y x 5 Y S w a p R a te

Impl

ied

ATM

BP

Vol

: 2Y

x 5

Y

J P Y 2 Y x 5 Y S w a p tio n A T M B P V o l v s F w d S w a p R a te

66

Conclusions

• Slope of the curve at short-end plays an important role in determining implied ATM BP volatility of rates. Volatility appears to be bounded by V-shaped curve with respect to short-end slope with the minimum reached when the curve is flat.

• From the model building perspective we have the following “educated” guess for AVERAGE rate-level dependence of volatility F(R):

– F(R) ~ R for R < R-breakeven (around 2%)

– F(R) ~ a + b*R, levels off for R > R-breakeven and gróws with R for 2% < R < 8%-10%

• Volatility of rates can reach extreme values for high rate levels when the yield curve is downward sloping and real rate reach negative values and its levels are undergoing wild swings (Monetary Experiment in the USA: Sept1979 – Dec 1982).

what drives interest rates volatility? · pdf filewhat drives interest rates volatility? ......

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