Sibrand Drijver · 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 y Development implied volatilities S&P 500 Euro Stoxx 50 FTSE 100 CAC 40 DAX AEX. 6

8th Volatility and Tail Risk Educational Event, 16th of April 2015

London

Sibrand Drijver

Risk Management: implied or historical volatility?

2 For professional use only

Risk Management: implied or historical volatility?

Equity Interest rates

3 For professional use only

Risk Management: implied or historical volatility?

• Financial markets: volatile and calm periods

• Implied or historical volatility better estimator of realised volatility?

• Does the answer depend on the length of the option period?

• Is there a systematic bias?

• Is there a relation between volatility and return on equities?

• Risk management

4 For professional use only

Equity volatility

• 6 different markets

• 7 different option periods

– 1, 2, 3, 6, 9, 12 and 18 months

• Starting in 2000, because of availability reliable volatility data

5 For professional use only

• Markets move together

Equity volatility

0

10

20

30

40

50

60

70

80

90

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Im

pli

ed

vo

lati

lity

Development implied volatilities

S&P 500 Euro Stoxx 50 FTSE 100 CAC 40 DAX AEX

6 For professional use only

Equity volatility

• Linear regression analysis

– Realised volatility ~ intercept term and implied volatility

• F-test to measure whether implied volatility equals realised volatility

– Constraint realised volatility equals implied volatility

– How much information is lost due to constraint?

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6

Reali

sed

vo

lati

lity

Implied volatility

Euro Stoxx, 3 months

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

vo

lati

lity

Implied volatility

Euro Stoxx, 12 months

7 For professional use only

• Realised volatility equals implied volatility?

• For most equity markets, the implied volatility overestimates the realised volatility

• Risk premium

Equity volatility

8 For professional use only

Equity volatility

• Is the implied volatility a better predictor than historical volatility?

• Linear regression

– Realised volatility ~ intercept term, implied and historical volatility

• F-test to measure whether implied volatility equals realised volatility

– Test whether information in one measure is a subset of the other

– Constraint realised volatility equals implied volatility

– How much information is lost due to constraint?

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

vo

lati

lity

Implied volatility

Euro Stoxx, 12 months

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

vo

lati

lity

Historiscal volatility

Euro Stoxx 50, 12 months

9 For professional use only

• Does implied volatility contain more information than the historical volatility?

• For most equity markets, the implied volatility contains more information than the historical volatility

Equity volatility

10 For professional use only

Equity volatility

• Volatility and return

• Low volatility strategy (factor investing)

– Buckets

– Relative volatility levels

– Rebalancing

• Absolute level of volatility (current research)

• Behavioural finance

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

retu

rn

Implied volatility

Euro Stoxx, 12 months

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

retu

rn

Implied volatility

FTSE 100, 12 months

11 For professional use only

• Rolling horizon

• Requirement from statistics: independent observations….

• Conclusions do not change

Equity volatility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6

Reali

sed

vo

lati

lity

Implied volatility

Eur, 12 months

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 20 40 60 80

Reali

sed

retu

rn

Implied volatility

Eur, 12 months

12 For professional use only

Interest rate volatility

• Swaption volatility grids can change a lot!

1M

12M0

5

10

15

1 3 5 7 9 15 25

op

tio

n l

en

gth

Im

pli

ed

vo

lati

lity

maturity IRS

Eur swaption vol grid 22-2-2007

10-15

5-10

0-51M

12M0

50

100

1 3 5 7 9 15 25

op

tio

n l

en

gth

Im

pli

ed

vo

lati

lity

maturity IRS

Eur swaption vol grid 4-3-2014

50-100

0-50

13 For professional use only

• Spikes in volatility

Interest rate volatility

0

50

100

150

200

250

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Im

pli

ed

vo

lati

lity

Implied volatility EUR interest rate (1 year option)

1year IRS

3 year IRS

5 year IRS

10 year IRS

14 For professional use only

• Does the realised volatility equal the implied volatility?

Interest rate volatility

15 For professional use only

• Does the implied volatility contain more information

than the historical volatility?

Interest rate volatility

16 For professional use only

Interest rate volatility

• Implied volatility generally overestimates realised volatility

• Implied volatility generally contains more information than historical volatility

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4

Reali

sed

vo

lati

lity

Implied volatility

Eur, 12 mnd, 10 year swap

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

vo

lati

lity

Implied volatility

Eur, 12 mnd, 30 year swap

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6

Reali

sed

vo

lati

lity

Historical volatility

Eur, 12 mnd, 1 year swap

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8

Reali

sed

vo

lati

lity

Historical volatility

Eur, 12 mnd, 30 year swap

17 For professional use only

• Rolling horizon

• Conclusions do not change

Interest rate volatility

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5

Reali

sed

vo

lati

lity

Implied volatility

Eur, 12 months, 10 year swap

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Reali

sed

vo

lati

lity

Implied volatility

Eur, 12 months, 30 year swap

18 For professional use only

• Volatility important for risk return profile pension funds

• Impact on dispersion funding ratios, portfolio composition and hedge decisions

Risk Management

19 For professional use only

• Implied volatility generally better estimator of realised volatility than historical volatility for both equity and interest rate markets

• However, implied volatility tends to overestimate realised volatility

• Relationship depends on option period and length of underlying swap

• Important for risk management purposes

• Relationship between absolute level of equity volatility and return?

Conclusions

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