S&P/ASX 200 VIX Methodology

Transcription

1 S&P/ASX 00 VIX Methodolog S&P Dow Jes Indices: Index Methodolog Februar 018

2 Table of Ctents Introducti Index Objective Highlights Supporting Documents Index Cstructi 3 Approaches 3 Deriving VIX from ear-term and ext-term Optis 3 Calculating Time to Maturit 4 Interpolating Risk Free Rates 4 Forward Index Level 5 Opti Selecti Methodolog 5 General Formula to Calculate Implied Volatilities 6 Rolling Between Opti Ctract Mths 6 Start Date 6 Index Governance 7 Index Committee 7 Index Polic 8 Announcements 8 Holida Schedule 8 Unscheduled Exchange Closures 8 Ctact Informati 8 Index Disseminati 9 Tickers 9 FTP 9 Web site 9 Appendix 10 Methodolog Changes 10 Disclaimer 11 S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 1

3 Introducti Index Objective The S&P /ASX 00 VIX seeks to measure the 30-da implied volatilit (ASX VIX) of the S&P/ASX 00 Index. Highlights The S&P/ASX 00 VIX (ASX VIX) is a real-time index that reflects investor sentiment about the expected volatilit in the Australian benchmark equit index, the S&P/ASX 00. The ASX VIX reflects expected equit market volatilit over the next 30 das b using mid prices for S&P/ASX 00 put and call optis to calculate a weighted average of the implied volatilit of the optis. The ASX VIX at relativel high levels implies a market expectati of large changes in the S&P/ASX 00 over the next 30 das, indicating that investor sentiment is uncertain. Cversel, a relativel low ASX VIX value implies a market expectati of little change, suggesting greater levels of investor cfidence in the stabilit of the market. In 1993, the Chicago Board Optis Exchange (CBOE ) introduced the CBOE Volatilit Index, VIX, which was originall designed to measure the market s expectati of 30-da volatilit implied b the atthe-me S&P 100 Index (OEX ) opti prices. Ten ears later, in 003, VIX was updated to reflect a new wa to measure expected volatilit. The new VIX is based the S&P 500 (SPX SM ), the core index for U.S. equities, and estimates the expected volatilit b averaging the weighted prices of SPX puts and calls over a wide range of strike prices. B suppling a script for replicating volatilit exposure with a portfolio of SPX optis, this new methodolog transformed VIX from an abstract ccept into a practical standard for trading and hedging volatilit. Supporting Documents This methodolog is meant to be read in cjuncti with supporting documents providing greater detail with respect to the policies, procedures and calculatis described herein. References throughout the methodolog direct the reader to the relevant supporting document for further informati a specific topic. The list of the main supplemental documents for this methodolog and the hperlinks to those documents is as follows: Supporting Document S&P Dow Jes Indices Equit Indices Policies & Practices Methodolog S&P Dow Jes Indices Commodities Indices Policies & Practices Methodolog URL Equit Indices Policies & Practices Commodities Indices Policies & Practices This methodolog was created b S&P Dow Jes Indices to achieve the aforementied objective of measuring the underling interest of each index governed b this methodolog document. An changes to or deviatis from this methodolog are made in the sole judgment and discreti of S&P Dow Jes Indices so that the index ctinues to achieve its objective. S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog

4 Index Cstructi Approaches The S&P/ASX 00 VIX is derived from the near term and next term optis the S&P/ASX 00. To minimize the pricing anomalies from the heav trading the expiring optis during the last few trading das, optis roll to the next term and third term when the near-term optis have less than a week to expire. The overnight RBA rate, 1-mth, -mth and 3-mth BBSW rates are used to interpolate the risk free rates of each maturit. The index is calculated and published between 10:10AM and 4:15PM, local time. Deriving VIX from ear-term and ext-term Optis The ASX VIX generall uses put and call optis in the two nearest-term expirati mths in order to bracket a 30-da calendar period. However, when the near-term optis have less than a week to expire, the ASX VIX rolls to the secd and third ctract mths in order to minimize pricing anomalies that might occur close to expirati. For each maturit, put and call optis are used to calculate the implied volatilit. The detailed calculati is described in the next secti. We interpolate the near term volatilit σ 1 and the next term volatilit σ to arrive at a single value σ with a cstant maturit of 30 das to expirati. VIX is derived b taking σ (the square root of σ ) and multipling b 100. VIX σ * 100 σ m T 1σ 1 T T1 + Tσ T m m T T1 T1 (1) where: σ 30-da implied volatilit σ 1 ear-term volatilit derived from the near term optis (see formula 5) σ ext-term volatilit derived from the next term optis (see formula 5) umber of das in e ear m umber of das in e mth T 1 Time to expirati (in ears) of the near term optis T Time to expirati (in ears) of the next term optis T1 umber of das between the current time and the expirati time of the near term optis T umber of das between the current time and the expirati time of the next term optis S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 3

5 Calculating Time to Maturit The time to maturit (T) is measured in ears. It csists of three parts: 1 Fractial number of das remaining from the current calculati time until midnight of the current da umber of das between the current da and the settlement da 3 Fractial number of das from midnight of the da prior to expir to the settlement time (1:00 no) the expir date 1 3 T minutes remaining until midnight of the current da 4 * 60 minutes from midnight to settlement time expir 4 * T T 1 3 () where: umber of das in e ear T umber of das until opti expirati Calendar das are used in all da count calculatis. Interpolating Risk Free Rates We use the RBA overnight rate (R ), BBSW 1-mth rate (R ), and BBSW -mth rate (R m ) to interpolate the risk free rates used in near term (R 1 ) and next term (R ). R R 1 T1 T T T R R m m T1 + T T + T R m R m T1 T m (3) where: R 1 ear-term risk free rate R ext-term risk free rate R RBA overnight rate R BBSW 1-mth rate R m BBSW -mth rate umber of das remaining until the midnight of the next business da 30 das, as we are using a e-mth BBSW rate in the interpolati m 60 das, as we are using a two-mth BBSW rate in the interpolati T1 umber of das between the calculati time the current da and 1:00 no the expirati date of the near-term optis S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 4

6 T umber of das between the calculati time) the current da and 1:00 no the expirati date of the next-term optis umber of das in e ear T T T m m (4) ote that the interpolati works when the near-term and next-term expiratis are bracketed b the overnight - 1 mth and 1 mth - mth maturities of interest rates, respectivel. When the opti expiratis fall outside of the correspding interest rate expiratis, which will most likel happen during the roll period, we need to pick the correct BBSW rates. For example, if the near term expirati is between 1 and mths, we use the 1-mth and -mth BBSW rates to interpolate the near-term risk free rate R 1 ; if the next term expirati is between and 3 mths, we use the - and 3-mth BBSW rates to interpolate the next-term risk free rate R. Forward Index Level For both near-term and next-term, the formula used to calculate the forward index level is: where: RT * K K F K + e ( C P ) (5) F Forward index level K The strike price at which the absolute difference between the mid-price of the call and the put optis is the smallest T Time to expirati (see formula ) R Risk-free interest rate to expirati (se formula 3) C K Mid price of calls at strike K P K Mid price of puts at strike K Opti Selecti Methodolog To select the optis in the volatilit calculati for both near-term and next-term, Sort all the optis in ascending order b strike prices Determine at-the-me strike K 0. It is the strike nearest to the forward index level F. Both put and call optis at strike K 0 are selected Out-of-me call optis with strike prices higher than K 0 are selected. Start with call opti with strike price immediatel higher than K 0 and move to successivel higher strike prices. After encountering two csecutive calls with bid price of zero, no calls with higher strikes are csidered. Out-of-me put optis with strike prices lower than K 0 are selected. Start with put opti with strike price immediatel lower than K 0 and move to successivel lower strike prices. After S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 5

7 Where: encountering two csecutive puts with bid price of zero, no puts with lower strikes are csidered. Optis which are not good quotes will be excluded. A good quote is a quote with a bid price and an ask price available: 0 < bid price ask price (for all optis); and bid/ask price of selected call optis bid/ask price of the call opti at K 0 ; and bid/ask price of selected put optis bid/ask price of the put opti at K 0 General Formula to Calculate Implied Volatilities For the near-term and the next-term, respectivel, implied volatilities are calculated using the selected put and call optis. The general formula is: where: i RT e Q( K ) i T K T K i i 0 K 1 F σ 1 (6) σ Implied volatilit T Time to expirati (see formula ) F Forward index level (see formula 5) K i Strike price of the i th out-of-the-me opti Δ K i Interval between strike prices (see formula 7) K 0 At-the-me strike R Risk-free interest rate to expirati (see formula 3) Q(K i ) Mid-price of each selected opti with strike K i; Use the average mid-price of the put and call optis if K i K 0 Generall, Δ K i is half the distance between the strike either side of K i and is calculated as Ki + 1 Ki 1 K i (7) At the upper and lower edges of an given strip of optis, Δ K i is simpl the difference between K i and the adjacent strike price. Rolling Between Opti Ctract Mths In calculating the S&P/ASX 00 VIX, when the near-term optis have less than a week to expire, ASX VIX rolls to the secd and third ctract mths. When the optis expire a Thursda, the ASX VIX usuall rolls the prior Frida if the Australian Securities Exchange is open. If Frida is a holida, the index rolls the next business da when the Australian Securities Exchange is open. Start Date The index start date is Januar, 008. S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 6

8 Index Governance Index Committee Each of S&P Dow Jes Indices global indices is the respsibilit of an Index Committee that mitors overall polic guidelines and methodologies, as well as additis to and deletis from these indices. S&P Dow Jes Indices chairs the S&P/ASX Index Committee, which is comprised of five voting members representing both S&P Dow Jes Indices and the Australian Securities Exchange. Decisis made b the Index Committee include all matters relating to index cstructi and maintenance. The Index Committee meets regularl to review market developments and cvenes as needed to address major corporate actis. It is the sole respsibilit of the Index Committee to decide all matters relating to methodolog, maintenance, cstituent selecti and index procedures. The Index Committee makes decisis based all publicl available informati and discussis are kept cfidential to avoid an unnecessar impact market trading. S&P Dow Jes Indices Index Committees reserve the right to make exceptis when appling the methodolog if the need arises. In an scenario where the treatment differs from the general rules stated in this document or supplemental documents, clients will receive sufficient notice, whenever possible. In additi to the dail governance of indices and maintenance of index methodologies, at least ce within an 1-mth period, the Index Committee reviews the methodolog to ensure the indices ctinue to achieve the stated objectives, and that the data and methodolog remain effective. In certain instances, S&P Dow Jes Indices ma publish a csultati inviting comments from external parties. For informati Qualit Assurance and Internal Reviews of Methodolog, please refer to S&P Dow Jes Indices Commodities Indices Policies & Practices document. S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 7

9 Index Polic Announcements Announcements of the dail index values are made before the open of the next trading da. Holida Schedule The index is calculated dail, throughout the calendar ear. The l das the index is not calculated is das when the ASX is officiall closed. A complete holida schedule for the ear is available the S&P Dow Jes Indices Web site at Unscheduled Exchange Closures For informati Unexpected Exchange Closures, please refer to S&P Dow Jes Indices Equit Indices Policies & Practices document. For informati Calculatis and Pricing Disruptis, Expert Judgment, Data Hierarch, Unexpected Exchange Closures and Error Correctis, please refer to S&P Dow Jes Indices Commodities Indices Policies & Practices document. Ctact Informati For questis regarding an index, please ctact: index_services@spglobal.com. S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 8

10 Index Disseminati Historical index returns are available through S&P Dow Jes Indices index data group for subscripti via FTP. Tickers The table below lists headline indices covered b this document. All currenc, currenc hedged, risk ctrol, and return tpe versis of the below indices that ma exist are also covered b this document. Please ctact index_services@spglobal.com for a complete list of indices covered b this document. Index RIC Bloomberg S&P/ASX 00 VIX.AXVI AS51VIX FTP Dail index level data is available via FTP subscripti. For product informati, please ctact S&P Dow Jes Indices, Web site For further informati, please refer to S&P Dow Jes Indices Web site at S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 9

11 Appendix Methodolog Changes Methodolog changes since Januar 1, 015 are as follows: Effective Date Methodolog Change (After Close) Previous Updated 01-Dec-17 K 0 is set equal to F, the forward index level. Definiti of the at-the-me strike, K 0. Optis selected in the volatilit calculati. 01-Dec-17 If strike K < K 0, use put prices; if strike K > K 0, use call prices. After encountering two csecutive puts with a bid price of zero, do not select an other puts; after encountering two csecutive calls with a bid price of zero, do not select an other calls. K 0 is defined as the strike that is nearest to F, the forward index level. If strike K < K 0, use put prices; if strike K > K 0, use call prices; if strike K K 0, use the average price of the put and the call. Out-of-me call optis with strike prices higher than K 0 are selected. Start with call opti with strike price immediatel higher than K 0 and move to successivel higher strike prices. After encountering two csecutive calls with bid price of zero, no calls with higher strikes are csidered. Out-of-me put optis with strike prices lower than K 0 are selected. Start with put opti with strike price immediatel lower than K 0 and move to successivel lower strike prices. After encountering two csecutive puts with bid price of zero, no puts with lower strikes are csidered. Optis which are not good quotes will be excluded. S&P Dow Jes Indices: S&P/ASX 00 VIX Methodolog 10

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