Nikkei Stock Average Volatility Index Real-time Version Index Guidebook

Transcription

1 Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and publishing i on he real-ime basis since January 30, 01, which had been calculaed on he end-of-day basis since November 010, Nikkei drew up he Index Guidebook of he Nikkei Sock Average Volailiy Index Real-ime Version. I would be changed or modified corresponding o he revision of he index calculaion rule ec in he fuure. Copyrigh of his documen is owned by Nikkei, and any copies, reprins and reproducion of his documen are prohibied wihou he prior approval of Nikkei. This documen is prepared solely for he undersanding of he index ha Nikkei calculaes and publishes, and i is no o be consrued as a soliciaion or an offer o buy or sell any securiies or relaed financial insrumens. This English documen is a ranslaion of he original documen daed March in Japanese and may no be an enirely accurae ranslaion of he original Japanese documen. In any case where differences arise beween he English version and he original Japanese version, he original Japanese documen will prevail. (March 4, 014 version) GB-145-E

2 1: Concep s raded on opion markes are usually deermined, among ohers, by he volailiy of is underlying asse. From his price formaion, in he calculaion of he Nikkei Sock Average Volailiy index, he volailiy expeced by invesors is inferred from he opion prices (premiums) in he markes. A mehod widely used o esimae he fair variance rae in rading a variance swap ec on he OTC marke is used in he index calculaion. : Index Calculaion (1)Basic Poins The index value is expressed as he figures rounded o wo decimal places. Uni of he index value is poins. Use he prices of he Nikkei 5 fuures and Nikkei 5 opions on he Osaka Exchange (OSE), which he OSE publishes as he fuure and opion prices respecively. The index is calculaed every 15 seconds during he day session of he Nikkei 5 opions on he OSE ( excluding he pre-closing ). The index sars o be calculaed from 15 seconds afer he end of he opening aucion usually 15 seconds pas 9 A.M., and i is also calculaed a he end of he closing aucion. Cover he near-erm (he firs-erm) opion and he nex-erm (he second-erm) opion. The opions o calculae he index are rolled o he nex delivery monh on hree business days before he las rading dae of he near-erm opion. Also cover he near-erm (he firs-erm) fuure, and he fuure is rolled o he nex-erm fuure on hree business days before he las rading dae of he near-erm fuure. ()Selecion of he prices The prices of he fuures and opions used for he calculaion are seleced in he following order of he prioriy. 1Laes raded price in for he pas 15 seconds ( however, a he end of he closing aucion, a raded price obained when he orders are mached by so called Iayose mehod ) Middle price of bes bid and bes ask a he ime of he calculaion ( every 15 seconds ) while he orders are mached by he so called Zaraba mehod ( however, a he end of he closing aucion, he middle price of bes bid and bes ask afer he orders are mached by he Iayose mehod (*1) 3Las raded price of oday s session a he ime before he pas 15 seconds ( including he nigh session on he previous business day ) Copyrigh 01 Nikkei Inc. All righs reserved.

3 *1: Bes bid and bes ask prices o compue a middle price are invalid in cases ha 1)bes bid price is lower han or equal o 10yen and he difference beween he bes bid and bes ask is greaer han or equal o 4yen, )bes bid price is greaer han 10yen and bes ask is greaer han bes bid by 30% or more, 3) bes ask is lower han or equal o bes bid. (3)Formula The Nikkei Sock Average Volailiy Index is calculaed in accordance wih he following procedure. 1Calculae he volailiy 1, based on he near-erm (firs-erm) opion a a ime of, and he volailiy, based on he nex-erm (second-erm) opion a a ime of. T i : he expiraion dae of i h-erm opion ( 9:00:00am on SQ dae ) (*) Y : he number of seconds in a year on 365 day-basis (31,536,000 seconds ) 365 Y : he number of seconds in a year on 360 day-basis (31,104,000 seconds ) 360 L i, : Euroyen LIBOR (360 days basis) on he previous business day (1-monh rae for he near-erm and -monh rae for he nex-erm)(*3) K i j,, : j h lowes Srike price (i.e. ascending order) of i h-erm opion a a ime of : Closing price of pu opion wih he expiraion dae of T i a a ime of : Closing price of call opion wih he expiraion dae of T i a a ime of (however, F : he price of he near-erm fuure a a ime of p : minimum j saisfying F K i, j, q : j minimizing he absolue difference beween F and K i j,, a a ime of (*5) n, : he number of srike prices of i h-erm opions using for he calculaion a a ime of (*6,*7) i (however, ) (*4)) *: he erm o he expiraion dae is measured on he second ime scale. *3: In case ha he previous day for he calculaion was no a business day in he London marke or ha he Euroyen LIBOR was no published for any reason, use he LIBOR rae previously available on he neares day. Even if he previous day for he calculaion was no a business day in Japanese markes and was a business day in he London marke, he LIBOR rae on he day is used. *4: For he opion price whose srike price is neares from he fuure price a a ime of, use he adjused value calculaed from he pu opion price and call opion price a he srike price. In addiion, and are pu opion price and call opion price a srike price of a a ime of., and he expiraion dae of T i K i q, Copyrigh 01 Nikkei Inc. All righs reserved. 3

4 *5: If F < K i, q,,hen q = p and if F K i q,hen q,, = p -1 *6: Use ou-of-he-money (OTM) raded opions (which have some volume ) where he fuure price a he ime of he calculaion is defined as a-he-money(atm). However, he opions whose prices are invalid a he ime of he calculaion are reaed as if hese srike prices are no se (including cases by he Trading Suspension and he Immediaely Execuable Range Rule ). *7:In case ha he opion prices a 6 or more consecuive srike prices are invalid, he prices of pu opions a lower srike prices han hese consecyuve srike prices and he prices of call opions a higher srike prices han hese consecuive srike prices are no used for he calculaion even if hese opions are raded wih some volume.. Obain he index value by linear inerpolaion of expiraion 30 days (*8,*9,*10) 1, and, o make he ime o Index Value M : he number of seconds in 30 days (,59,000 seconds) *8: If he erm o expiraion dae is longer han 30 days, he index is calculaed by liner exrapolaion. *9: As a resul of he liner exrapolaion, in case ha he index value becomes imaginary number ( meaning ha he resul for he square roo becomes negaive ), he index value is calculaed a a ime of by using and 1, 1 used for he calculaion a a ime of -1 (jus before he calculaion of his ime), insead of, 1 and 1,, ( however, a he firs calculaion of he day, use closing price on he previous day) *10: In he calculaion of i h-erm opion a a ime of, 1)in case ha he number of he srike prices whose opion prices are valid is 0 or 1, or )in case ha he price of near-erm fuure is invalid, i, a a ime of is no calculaed, and he index value a a ime of is calculaed by using i, 1 which is used jus before he calculaion of his ime, insead of using i, (however excluding in case of 3:Miscellaneous (3)In case he Circui Breaker Rule is applied linked o Nikkei 5 Fuures ). 3: Miscellaneous (1)Previous and Reroacively Calculaion in he pas From he commencemen dae of he calculaion (November 19h 010) o January 7h 01, he index was calculaed on he end-of-day basis. And he index was calculaed reroacively daing back from June 1h 1989 o November 18h 010 by he same end-of-day basis mehod. () Modificaion of he index value If any even which affecs he index value occurs (e.g. correcion of he opion or fuures prices published by he OSE), as a general rule, reroacive calculaion for he modificaion will no be conduced. Copyrigh 01 Nikkei Inc. All righs reserved. 4

5 (3) In case he Circui Breaker Rule is applied linked o Nikkei 5 Fuures In case ha all rades of he Nikkei 5 fuures and Nikkei 5 opions are haled by he Circui Breaker Rule linked o Nikkei 5 fuures, Nikkei shall hal he updaing of he Nikkei Sock Average Volailiy Index. The complee rading suspensions of he OSE caused by is sysem failure ec., is reaed as he same above. 4: Calculaion Example (in case of he closing (3:15:00pm) on November 1s 011) (1) Condiions for he calculaion are described below: Closing price of he near-erm Nikkei 5 fuure (expiraion monh: December 011) = 8850 Euroyen LIBOR 1-monh rae = %, -monh rae = % The erm o he expiraion dae of near-erm opion (expiraion monh: November 011) = 841,500 seconds The erm o he expiraion dae of nex-erm opion (expiraion monh: December 011) = 3,60,700 seconds The neares srike price from ATM (fuure price) = 8750 () Decide Opions used for he calculaion for he near-erm; expiraion monh: Nov 011 (see grayed cells) Srike Call Opions Las Traded Middle beween Bid and Ask Srike Pu Opions Las Traded Middle beween Bid and Ask ( 9:00) (15:09) (13:6) ( 9:3) (13:00) (15:15) ( 9:11) (15:15) (15:15) (15:15) ( 9:49) (15:15) (14:53) (15:15) (13:54) (15:15) (14:57) (15:15) (15:09) (15:15) (15:15) (15:15) 17.5 Noe)Use he OTM opions (15:15) (15:05) (15:15) (13:0) (15:15) ( 9:8) Copyrigh 01 Nikkei Inc. All righs reserved. 5

6 Noe)'-' indicaes here was no raded opion price or no valid middle price beween Bid and Ask a he Srike price (3) Calculae he adjused value from opion prices a he srike price neares from he fuure price for he near-erm; expiraion monh: Nov 011 Adjused Value % / (4) Calculaion of he variance of he underlying asse price derived from he prices of he seleced near-erm opions (expiraion monh: Nov 011) Srike Number( j ) K s (*11) (*1) *11: α indicaes he value used wih he (i.e. summaion) in :Index Calculaion (3)Formula-1 *1: Use he adjused value for he neares sripe price from he fuure price % / (5) Decide Opions used for he calculaion for he nex-erm; expiraion monh: Dec 011 (see grayed cells) Srike Call Opions Las Traded Middle beween Bid and Ask Srike Pu Opions Las Traded Middle beween Bid and Ask ( 9:00) (15:06) 1.5 (*13) ( 9:00) 1.5 (*13) Copyrigh 01 Nikkei Inc. All righs reserved. 6

7 (14:57).5 (*13) (15:15) (15:15) (10:54) (14:47) 7.5 (*13) (15:15) (15:15) (15:15) (15:15) (10:01) (15:15) (15:05) (15:15) ( 9:3) (15:15) (14:47) (15:15) (15:15) (15:15) (15:15) (15:15) 37.5 Noe)Use he OTM opions (15:15) (14:38) (15:15) (15:15) ( 9:) (15:15) (15:15) (14:3) (*13) (14:06) ( 8:00) Noe)'-' indicaes here was no raded opion price or no valid middle price beween Bid and Ask a he Srike price *13: Use he middle price beween bes bid and bes ask a he end of he closing aucion. (6) Calculae he adjused value from opion prices a he srike price neares from he fuure price for he nex-erm; expiraion monh: Dec 011 Adjused Value % / (7) Calculaion of he variance of he underlying asse price derived from he prices of he seleced nex-erm opions (expiraion monh: Dec 011) Srike Number( j ) K s (*14) Copyrigh 01 Nikkei Inc. All righs reserved. 7

8 (*15) *14: αindicaes he value used wih he (i.e. summaion) in :Index Calculaion (3)Formula-1 *15: Use he adjused value calculaed from opions prices a he sripe price neares from he fuure price % / (8) Obain he index value by linear inerpolaion of and 1 o make he ime o expiraion 30 days (,59,000 seconds) Index Value Copyrigh 01 Nikkei Inc. All righs reserved. 8

9 5: Ohers (1)Licensing Nikkei Sock Average Volailiy Index is an inellecual propery ha belongs o Nikkei. All of he righs o he indices such as righ o calculae, publicize, disseminae, and use hese indices are reserved by Nikkei. Licensing agreemen wih Nikkei is necessary if companies inend o creae Index - linked funds and passive funds ec. I is also required o use his index for disseminaing, providing, showing and ec. o he hird pary in he way as Nikkei decides. ()Risk Nikkei calculaes and publishes he Nikkei Sock Average Volailiy Index in accordance wih he mehods described in his documen. In he even of circumsance no described in his documen, or if Nikkei deermines i is impossible o use he mehods described in his documen, Nikkei may use an alernaive mehod of he index calculaion as i deems valid. In case of a breakdown of compuer sysem, naural disasers or any oher unavoidable siuaions, Nikkei may pospone or cancel he calculaion of he indices. Nikkei, under any circumsance, does no guaranee he accuracy of hese indices. Should any error in he calculaion of he index ake place, Nikkei shall no be liable for any damages susained by any person or organizaion This documen could be changed corresponding o he revision of he index calculaion rule ec in he fuure. Informaion expressed in his documen is subjec o change wihou noice and in hose cases Nikkei is under no obligaion o updae any recipiens of his documen. Nikkei shall no accep any liabiliy for any loss or damage arising from he usage of all or any par of his documen. (3)Corporaion for he developmen of he index In developing he Nikkei Sock Average Volailiy Index, Nikkei has gained he cooperaion of Quaniaive Research Cener of Nomura Securiies CO., LTD. The disclaimers in he above () are also applied o Quaniaive Research Cener of Nomura Securiies. (4)Conac Index Business Office, Nikkei Inc. Tel: , mail: index@nex.nikkei.co.jp Copyrigh 01 Nikkei Inc. All righs reserved. 9

10 Appendix : Change hisory of Index Guidebook January 30, 01 version February 9, 01 version March 5, 01 version Sepember 30, 013 version March 4, 014 version Iniial version (deleed) in 4: Calculaion Example (in case of he closing (3:15:00pm) on November 1s 011) - modified he values a he srike prices of 8500 and 8750 in he able of (4) Calculaion of he variance of he underlying asse price derived from he prices of he seleced near-erm opions (expiraion monh: Nov 011) - modified he number of decimal places of he Adjused Value and a par of formula in he (6) Calculae he adjused value from opion prices a he srike price neares from he fuure price for he nex-erm; expiraion monh: Dec modified he number of decimal places of he s a he srike price of 8750 in he able of (7) Calculaion of he variance of he underlying asse price derived from he prices of he seleced nex-erm opions (expiraion monh: Dec 011) In :Index Calculaion (3)Formula noe(*7) - modified he number of consecuive srike prices from 3 o 6. In :Index Calculaion (1)Basic Poins - modified he exchange name o Osaka Exchange due o he rade name change. Copyrigh 01 Nikkei Inc. All righs reserved. 10