SIX Swiss Exchange Indices. Guide Governing Volatility Index VSMI

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2 able of Content 1 Index Structure Concept... 3 General prncples... 3 Bass... 3 Volatlty Sub-Indces... 4 Selecton of Input Data... 4 Publcaton... 5 Hstorcal Data... 5 Revew of ndex concept... 5 ermnaton of the ndex calculaton... 5 Index Calculaton Calculaton Method... 6 Extractng Data... 7 Flterng of Data... 7 Preparng Data... 7 Calculaton Example Determnng the Forward Prce F and the Excercse Prce K, Determnng the Opton Prce M(K,j) Determnng the Sub-Indces Constructng the Volatlty Index Informaton on ndex events rade suspensons and market dstorsons... 1 Index correctons rademark Protecton, Use And Lcensng Protecton Lcensng Free usage Usage subject to lcence Contact Statc Data Page

3 1 Index Structure 1.1 Concept Volatlty s a measure of the level of uncertanty prevalng n certan markets, or wth respect to ndvdual underlyng nstruments. In prncple, there are two dfferent approaches for the estmaton of volatlty: on the one hand, t s possble to determne hstorcal volatlty by measurng the standard devaton of prces for any partcular securty over a gven perod of tme. On the other hand, volatlty can be derved mplctly from opton prces ( mpled volatlty ); ths knd of volatlty represents the estmates and assumptons of market partcpants nvolved n a trade, on the bass of a gven opton prce. he VSMI does not measure mpled volatltes of at-the-money SMI optons but the mpled varance across all optons of a gven tme to expraton. hs model offers great advantages n terms of tradng, hedgng and ntroducng dervatve products on ths ndex. he man ndex (whch s not lnked to a specfc tme to expraton) has a fxed remanng tme to expraton of 30 days. he VSMI and ts varous sub-ndces are also updated every mnute. 1. General prncples In order to acheve the stated ndex objectve SIX Swss Exchange defnes the general prncples that govern the ndex methodology. SIX Swss Exchange publshes the ndex objectve and rules for all ndces. Representatve: he development of the market s represented by the ndex. radable: he ndex components are tradable n terms of company sze and market. Replcable: he development of the ndex can be replcated n practse wth a portfolo. Stable: Hgh ndex contnuty. Rules-based: Index changes and calculatons are rule-based. Projectable: Changes n rules are wth approprate lead tme (usually at least tradng days) no retrospectve rule changes. ransparent: Decsons are based on publc nformaton. 1.3 Bass he SMI (Swss Market Index) s the man blue chp ndex for the Swss equty market. It tracks the 0 most lqud and largest components of the SPI. It s equvalent to the SPI Large. he SMI s prmarly avalable as a not dvdend adjusted ndex (prce ndex), however a total return ndex s publshed under the name SMIC (SMI Cum Dvdend). he ndex s publshed every 5 seconds. he optons contract on ths ndex s one of the products of Eurex wth the hghest tradng volume, the nternatonal dervatves exchange, and ranks among the top ndex optons contracts worldwde. he VSMI s calculated on the bass of eght expry months wth a maxmum tme to expraton of two years. Volatlty represents the key rsk factor for the prce determnaton n optons tradng. he hgher the estmated or expected volatlty, the hgher the prce of an opton. Page

4 1.4 Volatlty Sub-Indces Apart from the man ndex VSMI (whch s rrespectve of a specfc tme to expraton), sub-ndces for each tme to expraton of the SMI optons rangng from one month up to two years are calculated and dstrbuted for both models. For optons wth longer tme to expratons, no such sub-ndces are currently avalable. he varous VSMI sub-ndces are calculated on the bass of all optons avalable. he calculatons are based on the best bd and best ask avalable for these optons n the Eurex system. Each man ndex s determned by way of lnear nterpolaton usng the two sub-ndces whch nclude to the remanng tme to expraton of 30 days for VSMI. he man ndex s therefore rrespectve of a specfc tme to expraton,.e. t does not expre. hs helps to elmnate effects that typcally result n strong volatlty fluctuatons close to expraton. 1.5 Selecton of Input Data Durng the calculaton hours of the VSMI and the respectve sub-ndces (8.50am to 5.30pm CE) a snapshot of the followng data s taken every mnute: SMI OSMI LIBOR the SMI Index Best bd and best ask of all SMI-Optons London Interbank Offered Rates - money market reference rates for 1,, 1 months (calculated once a day, 1.00 p.m. CE, by the brtsh bankers assocaton) Index Name LIBOR 1 day (CHF) LIBOR 1 week (CHF) LIBOR 1 month (CHF) LIBOR months (CHF) LIBOR 3 months (CHF) LIBOR 6 months (CHF) LIBOR 1 months (CHF) Perod 1 day 1 week 1 month months 3 months 6 months 1 months Page

5 1.6 Publcaton he VSMI and ts sub-ndces are calculated on every Eurex exchange tradng day, n the perod from 8:50 a.m. to 5:30 p.m. CE. he contnuous calculaton of a sub-ndex does, however, only commence as soon as all requred nput data s avalable. he dssemnaton of the man ndex commences as soon as two sub-ndces become avalable, the maturtes of whch nclude the 30-day tme to expraton, and thus allow for an nterpolaton. In lne wth the expraton structure of SMI optons, each of the VSMI sub-ndces s assgned to a specfc expraton, whch can be drectly dentfed from the respectve code. here s a system of 10 codes and ISINs, only eght of each of whch are n smultaneous use at any tme. 1.7 Hstorcal Data Index ISIN Daly Closng Prces snce VSMI CH VSMI-Subndex 1 (1 M.) Secton VSMI-Subndex ( M.) Secton VSMI-Subndex 3 (3 M.) Secton VSMI-Subndex 4 (6 M.) Secton VSMI-Subndex 5 (9 M.) Secton VSMI-Subndex 6 (1 M.) Secton VSMI-Subndex 7 (18 M.) Secton VSMI-Subndex 8 (4 M.) Secton m represents the respectve expry month (A = Jan,..., L = Dec) j represents the respectve year (0,...,9) he contnuous calculaton of the VSMI s conducted snce 18 Aprl 005. he hstorcal ndex seres of the man ndex and the frst fve subndces reach back to January 1999 based on daly settlement prces. SMI Optons wth longer terms (1, 18 or 4 months) and the correspondng VSMI subndces exst snce 18 March Revew of ndex concept he valdty of the ndex concepts and rules s revewed on a regular bass. In exceptonal cases a broad market consultaton can be conducted. he changes to the ndex rules are publcly announced wth approprate lead tme (usually 3 months). 1.9 ermnaton of the ndex calculaton A decson to dscontnue wll be publcly announced by SIX Swss Exchange wth approprate lead tme. In case of exstng fnancal products lnked to the ndex, of whch SIX Swss Exchange s aware, a market consultaton s conducted n advance and a transton perod s ntroduced before the defntve termnaton. Page

6 Index Calculaton.1 Calculaton Method he model for VSMI ams at makng pure volatlty tradable.e. the ndex should be trackable by a portfolo whch does not react to prce fluctuatons, but only to changes n volatlty. hs s not drectly acheved through volatlty, but rather through varance or squared volatlty. A portfolo of SMI optons wth dfferent exercse prces wth a gven weghtng, as descrbed below, meets ths requrement. So the mpled volatltes of all optons of a gven tme to expraton are consdered. he sub-ndces are calculated accordng to the formula shown below: (1) VSMI = 100 σ wherby () K,j 1 F σ = R M(K,j) 1 j K,j, =1,,..8 K,0 and F me to expraton of the th OSMI Forward prce derved from the prces of the th OSMI, for whch the absolute dfference between call and put prces (C and P) s smallest. herefore: (3) F = K mn C P + R *(C P) (Note: If a clear mnmum does not exst, the average value of the relevant forward prces wll be used nstead.) K,j K,j Exercse prce of the j th out-of-the-money opton of the th OSMI expry month n ascendng order Interval between the relevant exercse prces or half the nterval between the one hgher and one lower exercse prce. On the boundares, the smple nterval between the hghest and second hghest exercse prce (or lowest and second lowest exercse prce) s used: (4) ΔK K = + 1 K 1 K,0 R Hghest exercse prce below forward prce F Refnancng factor of the th OSMI (5) R = e r* r Rsk-free nterest rate to expraton of the th OSMI M(K,j) Prce of the opton K,j, whereby K,j K,0 M(K,0) Average of the put and call prces at exercse prce K,0 he sub-ndces are calculated up untl two days pror to expraton. Each new sub-ndex s dssemnated for the frst tme on the second tradng day of the relevant SMI optons. he ndvdual steps wth regard to data extracton are explaned n the followng chapters, sometmes wth examples, as s the calculaton process for the varous factors used. Page

7 . Extractng Data Durng the calculaton hours from 8:50 a.m. to 5:30 p.m. CE, the respectve best bd and best ask of all SMI optons contracts lsted on Eurex are extracted from the stream of data generated by the Eurex system. o ths end, a snapshot s taken at one mnute ntervals. he varous nterest rates mentoned under 1.5 are recorded smultaneously..3 Flterng of Data a. Opton prce data s subject to flterng. All opton prces that are one-sded.e. wth ether a bd or an ask prce only are dsregarded. Naturally, the same apples to optons wthout any prce data. b. Another flter verfes whether these remanng optons are quoted wthn the establshed maxmum spreads for Eurex market-makers. he maxmum spread s derved from bd prces as shown n the table below: Bd (Index Ponts) Maxmum Spread % Example: Bd = 45.3 und Ask = 54.3 Max. Spread: 45.3 * 0.10 = 4.53 => both prces (bd and ask) are rejected If Eurex actvates Fast Market status, permttng market-makers to ncrease ther quotaton spreads under very turbulent tradng condtons, maxmum spreads are set hgher accordngly. hs s also taken nto account for the calculaton of the VSMI, wth the applcable flter crtera beng adjusted accordngly..4 Preparng Data a. Determnng the prces used he md prce s calculated for fltered opton prces, usng the respectve best bd and best ask. he most recent of each of the followng peces of nformaton s used subsequently:settlement-pres (Vortag) Settlement prce (prevous day) Md prce Last traded prce Page

8 Example: Underlyng Settlement Bd (tme) Ask (tme) Md (tme) Last-traded (tme) Prce Underlyng (09:05) (09:04) (09:05) (09:05) (09:03) (09:05) (09:05) 0.1 (09:01) b. Cuttng the wngs Yet another flter ensures that the varous prces used (settlement, md and last traded prce) do not fall short of a mnmum value of 0.5 ndex ponts. If there are two or more optons wth dfferent exercse prces and md prces exactly equal the mnmum value of 0.5 just the one nearest to the at-the-money pont s taken nto consderaton. Wth ths, optons that are far out-of-the money and that do not have much nfluence on the result of the calculaton are fltered out and do not need to be consdered. c. Determnng the tme to expraton (6) = Settlement-Calculaton/ Jahr Settlement-Calculaton Year Seconds between ndex calculaton and settlement Seconds per annum Bespel: Index calculaton: Expraton(=1): um 1:00:00 mdnght CE um 08:30:00 noon CE 1 = / (365 *60*60*4) = d. Determnng rsk-free nterest rates Lnear nterpolaton s used to determne nterest rates, the terms of whch match the tme to expraton of the OSMI. = k + k+ 1 k < k + 1 k+ 1 k k+ 1 k (7) r r( ) r( k ) r( k + 1); e. he refnancng factor R s determned accordng to equaton (5) Page

9 .5 Calculaton Example.5.1 Determnng the Forward Prce F and the Excercse Prce K,0 he forward prce of the th expry month s derved from OSMI prces, for whch the dfference (n absolute terms) between call and put prces s smallest. Accordngly, the forward prce F 1 of the 1 st expry month and the exercse prce K,0, whch s the closest exercse prce below the forward prce F, are subject to the followng: F ( Call Put ) = K, 0 + R * Example: R 1 = K 1,0 = 6000 F 1 = Where there are several pars of calls and puts wth dentcal dfferences, a forward prce wll be calculated for each of the correspondng exercse prces. K,0 s accordngly defned as the closest exercse prce below the smple average of these forward prces..5. Determnng the Opton Prce M(K,j) he prce M(K,j), whch s used for the j th out-of-the-money opton of the th expry month, s determned as follows: M ( K, j Put Put + Call ) = Call : K : K, j : K, j, j < K = K > K,0,0,0.5.3 Determnng the Sub-Indces VSMI = 100 σ ΔK, j 1 F *R * M(K, j) - -1 K = j K, 0 σ Under-lyng K,j ΔK,j Call Put Call Put M(K.j) Δ K K R M(K ) Page

10 Under-lyng K,j ΔK,j Call Put Call Put M(K.j) Δ K K R M(K ) Page

11 Under-lyng K,j ΔK,j Call Put Call Put M(K.j) Δ K K R M(K ) Σ σ = = VSMI 1 = = Constructng the Volatlty Index Apart from the sub-ndces for the varous ndvdual tme to expraton, the VSMI s determned as the man ndex wth a constant remanng tme to expraton of 30 days (ths ndex s not lnked to a specfc tme to expraton). he VSMI s determned by lnear nterpolaton of the sub-ndces whch are nearest to a remanng tme to expraton of 30 days. If there are no such surroundng sub-ndces, the VSMI s calculated usng extrapolaton. In ths case, the two nearest avalable ndces are used, whch are as close to the tme to expraton of 30 calendar days as possble. VSMI = 100 = N σ N VSMI N N N + N N + N + 1 σ + 1 N N VSMI N N N N + 1 N * N N N 365 N * N 365 N N +1 N N 365 me to expraton of the th OSMI me to expraton of the +1 th OSMI me for next x days me for a standard year.7 Informaton on ndex events Any relevant forthcomng extraordnary corporate events that result n an adjustment to the ndces are publshed by e-mal va Investor Servce. he regstraton form s avalable on the SIX Swss Exchange Webste. SIX Swss Exchange accepts no lablty for Investor Servce Equty. Page

12 .8 rade suspensons and market dstorsons Should a data source (for example a prce source) not be avalable as result of challengng economc condtons or other market dstortons the last avalable data wll normally be used. In extreme cases a devaton from the rules defned n ths rulebook can occur, for example, shftng the schedule of a regular ndex revew. All changes wll be publcly announced at least two tradng days n advance..9 Index correctons Index correctons dstngush between calculaton errors and ncorrect nput data. Calculaton errors detected wthn a tradng day are corrected mmedately. Intraday tck data are not corrected retrospectvely. Calculaton errors that are older or based on erroneous nput data are corrected f techncally possble and economcally vable. If sgnfcant dfferences exst, ndex values can also be corrected retrospectvely. Interested partes may subscrbe to an e-mal notfcatons servce on the webste. SIX Swss Exchange dstrbutes notfcatons over ths channel on Changes n corporate actons and dvdends Updates to the perodc ndex revews Problems and error n the ndex calculaton he launch of new ndces General nformaton on SMI ndces Page

13 3 rademark Protecton, Use And Lcensng 3.1 Protecton he rademarks are nternatonally regstered trademarks of SIX Swss Exchange. 3. Lcensng 3..1 Free usage he rademarks may be freely used for the purpose of honest reportng of the relevant ndex. Insofar as t s techncally possble, the symbols and should be used, possbly wth a footnote statng that these names are regstered trademarks of SIX Swss Exchange, Zurch. 3.. Usage subject to lcence Any addtonal use of the rademarks or any commercal use of the ndex fgures (e.g., ssue of ndex-lnked fnancal nstruments or captal nsurance wth or wthout menton of the trademark n the name or descrpton) s only permssble wth a vald lcensng agreement. Offerng prospectuses must nclude the dsclamer whch s avalable on the SIX Swss Exchange Webste. 4 Contact Informaton concernng the ndces of SIX Swss Exchange (ndex adjustments, announcements etc.) s avalable at the followng Internet address: Any requests wth respect to the ndces may be drected to the followng address: SIX Swss Exchange Ltd Selnaustrasse 30 P.O. Box CH-801 Zurch Emal: ndexsupport@sx-group.com Phone: +41(0) Statc Data A current lst of all ndces calculated by SIX Swss Exchange s accessble at the SIX Swss Exchange Webste: Page

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