VDAX -NEW. Deutsche Börse AG Frankfurt am Main, April 2005

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Norma Sims
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1 VDAX -NEW Deutsche Börse AG Frankfurt am Main, April 2005

2 With VDAX -NEW, Deutsche Börse quantifies future market expectations of the German stock market Overview VDAX -NEW Quantifies the expected risk in the German stock market Launch: 20 April a) Index is strongly rule-based, transparent and easy to replicate b) Volatility is strongly un-correlated to equities and therefore offers perfect diversification for portfolios a) VDAX -NEW represents a separate asset class and is a perfect underlying for structured products 1

transparent and easy to replicate b) Volatility is strongly un-correlated to equities and therefore offers perfect

3 1 VDAX -NEW as a tradable volatility instrument How about volatility? Volatility tends to grow during times of uncertainty (fear gauge) Volatility tends to revert to its historical mean VDAX -NEW is the market barometer of the DAX 30 companies Volatility is un-correlated with its underlying Implied volatility tends to be larger than realized/historical volatility Volatility can be traded as implied, local and realized volatility The index expresses the market expectation of the amplitude of fluctuation in the DAX VDAX -NEW as a transparent, liquid and tradable volatility instrument 2

barometer of the DAX 30 companies Volatility is un-correlated with its underlying Implied volatility tends to be larger than realized/historical

4 1 The index specification of VDAX -NEW is simple, transparent and based on high liquidity Index Features VDAX -NEW Approach Underlying options Implied variances of all relevant options per duration performes analogue to implied volatility Implied variances are easier to hegde than implied volatility Relevant option subset is based on 8 option series with max. expiration of 2 years Calculation Rolling index has a fixed expiration of 30 days with linear interpolation Derived directly from option prices 3

variances are easier to hegde than implied volatility Relevant option subset is based on 8 option series with max.

5 1 The index design is rule-based, transparent and simple to rebuild Index Methodology Evaluation of Sub-index per option expiry based on the square-root of implied variance 100 times the square root of σ 2 Var The first 8 expirations are covered by sub-indices Stable and nice formula for evaluation using options prices directly not implied volatilities: summation of OTM prices More representative (strip of options) Index is closely related to implied ATM volatility Information on full skew is contained in strip of options All sub-indices are calculated real time Update frequency of 1 minute Construction of rolling index at 30 days to expiration through linear interpolation of the two nearest sub-indices 4

summation of OTM prices More representative (strip of options) Index is closely related to implied ATM volatility Information on full skew is contained in strip of options All

6 1 There are important differences in the methodology of VDAX and VDAX -NEW Differences between VDAX -NEW and VDAX VDAX Measures implied volatility using the ATM DAX options Calculation needs the Black-Scholes Option Pricing Model and is computationally intensive Main index has a rolling fixed maturity of 45 days VDAX - NEW Utilizes implied volatility derived from ATM and OTM-options per maturiry series Mathematical basis is not volatility but rather variance or volatility squared Calculation does not need option pricing model but only involves summations over option prices and is computationally less intensive Index measures the square root of the implied variance Main index has a rolling fixed maturity of 30 days 5

derived from ATM and OTM-options per maturiry series Mathematical basis is not volatility but rather variance or volatility squared Calculation does not need option pricing model

7 1 Relevant improvements of VDAX -NEW Relevant improvements in the methodology of VDAX -NEW Observed ATM and OTM-options covers and captures more of the volatility skew than the old methodology. Index is therefore less sensitive to individual options. Avoidance of an option pricing model makes the new index computationally less intensive VDAX -NEW is easier to hedge the coverage of a broader volatility skew makes it easier and cheaper to fine tune and dynamically hedge your option portfolio Whereas VDAX contains information about ATM option prices, the square root of implied variance contains information about the entire volatility surface. The methodology of VDAX -NEW measures expected volatility as financial theorists, risk managers and volatility traders so it is in dependence on financial and risk industry practices. 6

Avoidance of an option pricing model makes the new index computationally less intensive VDAX -NEW is easier to hedge the coverage of a broader volatility skew makes it easier and cheaper to fine tune

8 2 VDAX -NEW is highly correlated to VDAX and an ideal successor index Performance VDAX -NEW vs. VDAX 1) Price Correlation coefficient between VDAX -NEW AND VDAX is 0, Jan-99 May-99 Sep-99 Jan-00 May-00 Sep-00 Jan-01 May-01 Sep-01 Jan-02 Date May-02 Sep-02 Jan-03 May-03 Sep-03 Jan-04 May-04 Sep-04 VDAX -NEW is the perfect successor-index for VDAX VDAX -NEW VDAX 1) Indexed at 100 points on 4 January

May-99 Sep-99 Jan-00 May-00 Sep-00 Jan-01 May-01 Sep-01 Jan-02 Date May-02 Sep-02 Jan-03 May-03 Sep-03

9 2 VDAX -NEW is highly uncorrelated to DAX and MDAX and therefore interesting for diversification Performance VDAX -NEW vs. DAX and MDAX 1) 300 Price VDAX -NEW MDAX VDAX -NEW is highly uncorrelated to DAX and MDAX VDAX -NEW set-up volatility as a new asset class 50 Jan Apr-01 Jul-01 Oct-01 Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Date Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Establish risk-insurance product for DAX and MDAX related portfolios Price VDAX -NEW VDAX -NEW VDAX -NEW 1 DAX MDAX 50 DAX DAX - 0, Jan-01 Apr-01 Jul-01 Oct-01 Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 MDAX - 0,8896 0, Date 1) Indexed at 100 points on 2 January

Jul-01 Oct-01 Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Date Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Establish risk-insurance product for DAX and MDAX related portfolios Price 200 150

10 2 A portfolio diversification with VDAX -NEW generates better performance with lower risk exposure Performance DAX/VDAX -NEW Portfolio vs. DAX 1) 600 Price Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Date Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 DAX (80%) and VDAX - NEW (20%) portfolio generates on average nearly 3 percentage points better performance Diversification with VDAX -NEW generates additional performance with lower risk exposure DAX TR Portfolio: 80% DAX 20 % VDAX -NEW 1) Indexed at 100 points on 2 January

Jan-05 DAX (80%) and VDAX - NEW (20%) portfolio generates on average nearly 3 percentage points better performance Diversification with VDAX

11 3 VDAX -NEW as information tool and underlying for trading strategies Application of VDAX -NEW I. VDAX -NEW as Information tool For buy side, research and issuers of structured products II. VDAX -NEW as underlying for trading strategies Directional Trading: Betting on future levels of volatility/risk Spread Trading: Trade the spread between realized and implied volatilities Hedging: Cover short volatility positions 10

VDAX -NEW as underlying for trading strategies Directional Trading: Betting on future levels of

12 3 VDAX -NEW as a perfect underlying for structured products with a tactic investment perspective Possible use cases Investment function For heavy trader who want to speculate on pure volatility Diversification instrument For investors who want to diversify German equity portfolios Information and benchmarking Benchmark for German equity volatility VDAX -NEW allows the development of complex structured products looking for an exposure to volatility! 11

For investors who want to diversify German equity portfolios Information and benchmarking Benchmark for German

13 Fast Facts VDAX -NEW Index Performance 1) compared to DAX Index Features Price VDAX -NEW: start as of 20 April 2005 Expresses market expectation of the amplitude of fluctuation in DAX 1 rolling main index and 8 sub-indices Index is able to react only to changes in volatility 50 0 Index Methodology Jan-01 Apr-01 Jul-01 Oct-01 Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Date VDAX -NEW DAX 11) Indexed at 100 points on 2 January 2003 Index VDAX -NEW ISIN DE000A0DMX99 REUTERS.V1Xi Bloomberg V1X Jan-04 Apr-04 Jul-04 Calculation of implied variances of relevant DAX options Index is based on 8 sub-indices which include DAX options from 2-24 months expiration Rolling index is calculated on linear interpolation of two sub-indices with residual term of 30 days 12

Oct-03 Date VDAX -NEW DAX 11) Indexed at 100 points on 2 January 2003 Index VDAX -NEW ISIN DE000A0DMX99 REUTERS.

14 Contact Heiko Geiger (Marketing & Sales) Issuer Data & Analytics Konrad Sippel (Index Development) Issuer Data & Analytics

com Konrad Sippel (Index Development) Issuer Data &

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