For Managing the. HSI Volatility Index. Jul 2012 Version 2.1

Transcription

1 For Managing the HSI Volatilit Index Jul 01 Version.1

2 Amendment Histor Date Description 1.0 Januar 011 First Issue 1.1 Februar 011 Adding the treatment of handling abnormal index value 1. March 011 Removing exact dissemination time in this methodolog book and adding the link for dissemination time instead..0 October 011 Technical Enhancements - Using Forward Index Level ( F ) to select options - Change the formula correspondingl - Rolling options on 3rd trading da prior to expiration - Using overnight and 1-week HIBOR for interpolation when options expire less than 7 calendar das - Dissemination time change in the link 09:30:15 to 11:59:00 13:30:15 to 16:00:00.1 Jul 01 Updated Section 5 Index Maintenance & Dissemination

3 Table of Content Page 1. Overview. Management Responsibilit 3 3. Options Selection 4 4. Index Calculation 5 - Formula to Calculate Implied Volatilities - Deriving VHSI from ear-term & ext-term Implied Volatilities - Rolling Convention 5. Index Maintenance & Dissemination 7 6. Appendix 8 - Calculating Time to Expiration - Interpolating Risk-free Rates 7. Contact Information Disclaimer 11 1

4 1 Overview 1.1 The HSI Volatilit Index ( VHSI ) aims to measure the 30-calendar-da expected volatilit of the Hang Seng Index ( HSI ). The expected volatilit calculated is derived from the HSI option prices traded on Hong Kong Exchanges and Clearing Limited. 1. The methodolog of the VHSI is based on the CBOE Volatilit Index ( VIX ) in the US market. Modifications have been made to take into account trading characteristics of HSI options in the Hong Kong market. 1.3 The VHSI is derived from HSI put options and HSI call options in the two nearest-term expiration months in order to bracket a 30-calendar-da period. 1.4 In order to minimise pricing anomalies of expiring options, options are rolled from the 1st and nd contract months to the nd and 3rd contract months on the 3rd trading da prior to the expiration of the near-term options. 1.5 A flowchart illustrating the calculation of the VHSI is given below: ear-term ext-term Determine the Forward Index Level Determine the Forward Index Level Select Relevant Options for Inclusion in the Calculation Calculate Time to Expiration Select Relevant Options for Inclusion in the Calculation Calculate the ear-term Implied Volatilit Interpolate Risk-free Rate Calculate the ext-term Implied Volatilit Interpolate 30-calendar-da Expected Volatilit VHSI

5 Management Responsibilit Hang Seng Indexes Compan Limited ( HSIL ).1 HSIL is responsible for conducting regular reviews in accordance with the Index Methodolog.. HSIL is responsible for monitoring compan announcements and making ad hoc proposals which must be approved b the Chairman of the HSI Advisor Committee if constituent changes between the regular reviews are needed..3 HSIL is responsible for seeking the HSI Advisor Committee s endorsement of an special action in cases where, due to exceptional circumstances, an index review is not conducted according to the Index Methodolog..4 HSIL is responsible for seeking the HSI Advisor Committee s endorsement of changes to the Index Methodolog. HSI Advisor Committee.5 The Committee is responsible for ensuring index reviews are undertaken in accordance with the Index Methodolog..6 The Committee is responsible for reviewing an actions proposed b HSIL in the event that, due to exceptional circumstances, an index review is not conducted according to the Index Methodolog..7 The Committee is responsible for reviewing and endorsing all changes to the Index Methodolog as proposed b HSIL..8 The Committee is responsible for giving advice on an issues related to the Index Methodolog. 3

6 3 Options Selection 3.1 For both near-term and next-term, the forward index level, F, is calculated: F K e RT * (C K P K ) Where F = forward index level K = the strike price at which the absolute difference between mid- prices of the call and put options is the smallest T = time to expiration (see Appendix - 6.1) R = risk-free interest rate to expiration (see Appendix - 6.) C k = mid-price of the call option at strike K P k = mid-price of the put option at strike K 3. For each of the near-term and next-term options, out-of-mone call options with strike prices higher than or equal to F but lower than or equal to 10% of F are selected. 3.3 Out-of-mone put options with strike prices lower than F but higher than or equal to 80% of F are selected. 3.4 Options which are not good quotes will be excluded. A good quote is a quote with a bid price and an ask price available: Where 0 < bid price ask price. 1 Mid-price is an average of bid and ask prices 4

7 4 Index Calculation Formula to Calculate Implied Volatilities 4.1 The selected near-term and next-term options are used in the following generalised formula to calculate near-term implied volatilit, σ 1, and next-term implied volatilit, σ, respectivel. i i K i T K e RT Q K ( i ) Where σ = implied volatilit T = time to expiration (see Appendix - 6.1) K i = strike price of the i th out-of-the-mone option; a call if K i >= F and a pu if K i < F K i = interval between strike prices (see 4.) R = risk-free interest rate to expiration (see Appendix - 6.) Q(K i ) = mid-price of each option with strike K i 4. Generall, Ki is half the distance between the strike on either side of Ki and is calculated as: K i K i1 K i1 K for the lowest strike is the difference between the lowest strike and the next higher strike. K for the highest strike is the difference between the highest strike and the next lower strike. 5

8 Deriving VHSI from ear-term & ext-term Implied Volatilities 4.3 The near-term implied volatilit, σ 1, and the next-term implied volatilit, σ, are interpolated to derive a single value σ with a constant maturit of 30 calendar das to expiration. The VHSI is obtained b taking the square root of σ and multipling it b 100: Where VHSI * T1 1 T T 30 T1 T 30 T T1 T1 σ = σ 1 = σ = = 30 = T 1 = T = T1 = T = 30-calendar-da expected volatilit implied volatilit derived from the near-term options implied volatilit derived from the next-term options # of das in one ear 30 das time to expiration (in ears) of the near-term options time to expiration (in ears) of the next-term options # of das to expiration of the near-term options # of das to expiration of the next-term options Rolling Convention 4.4 In order to minimise pricing anomalies of expiring options, options are rolled from the 1st and nd contract months to the nd and 3rd contract months on the 3rd trading da prior to the expiration of the 1st contract month options for calculating the VHSI. 5 Index Maintenance & Dissemination 6

9 5.1 Options data are taken b snapshot at 15-second intervals for computation. 5. Please refer to the index dissemination time ( provided on our website for further details. 5.3 When good quotes are not sufficient due to an illiquid options market, there will be insufficient data to calculate σ 1 or σ. In such circumstances, the VHSI value will remain at the previous index value. This rule applies at all times, including opening, intrada and closing calculations (i.e. if there is insufficient data at 9:30am, the market opening, the VHSI value will remain at the previous close value until sufficient data to calculate the VHSI value becomes available). 5.4 When the bid price / ask price of the selected out-of-mone call option is greater than the bid price / ask price of the call option with good quote immediatel above the Forward Index Level, its pricing will be considered as unreasonable and will not be included for index calculation. 5.5 When the bid price / ask price of the selected out-of-mone put option is greater than the bid price / ask price of the put option with good quote immediatel below the Forward Index Level, its pricing will be considered as unreasonable and will not be included for index calculation. 5.6 Occasionall, the VHSI could jump up then down (or vice versa) in subsequent index ticks, due to volatile market situation. In case the calculated VHSI shows a tick-b-tick movement (either up or down) of more than 5% from the last disseminated index value, such calculated index value will be regarded as an abnormal index value and will not be disseminated, and the last disseminated index value will be used. If such abnormal index value persists for four consecutive ticks, it will be regarded as normal and will be disseminated. This treatment for abnormal index values will not be applied to the first and last index ticks of each trading session. 7

10 6 Appendix Calculating Time to Expiration 6.1 The time to expiration (T) is measured in ears. It is composed of three parts: 1 = fractional number of das remaining until midnight of the current da = number of das between current da and expir da 3 = fractional number of das from midnight of da prior to expir date to expiration time 1 3 T # of minutes remaininguntil midnight of the current da 4 * 60 # of minutes from midnight to the expiration time 4 * Where T T = # of das in one ear T = # of das to expiration of options ote: All the calendar das are counted for calculation. Interpolating Risk-free Rates 6. The HIBOR3 1-week rate (R 1 w), HIBOR 1-month rate (R 1 m), and HIBOR -month rate (R m) are used to interpolate the near-term (R 1 ) and next-term (R ) risk-free rates. R 1 T1 T R T1 T R T1 R T T R m m T T m R m T m The expiration time for HSI options is 4:00 pm on the expir da, the market close of expiring contract month 3 The latest HIBOR fixing provided b the Hong Kong Association of Banks 8

11 Where R 1 R R R R m = near-term risk-free rate = next-term risk-free rate = HIBOR 1-week rate = HIBOR 1-month rate = HIBOR -month rate = # of das in a week = # of das in the das between current da and one month later m = # of das in the das between current da and two months later T1 = # of das to expiration of the near-term options T = # of das to expiration of the next-term options = # of das in one ear T T T m m ote: The interpolation works when the near-term and next-term expirations are bracketed b the 1 week ~ 1 month and 1 month ~ month maturities of HIBOR rates, respectivel. When near-term options expire less than 7 calendar das, overnight and 1-week HIBOR rates are used for near-term interpolation. When the option expirations fall outside of the corresponding HIBOR rate expirations, most likel in the rolling period (see 3.4), it ma be necessar to choose longer-term HIBOR rates to interpolate the risk-free rates. For example, if the near-term expiration is between 1 month and months, the 1-month HIBOR and -month HIBOR will be used to interpolate the near-term risk-free rate R 1 ; if the next-term expiration is between months and 3 months, the -month HIBOR and 3-month HIBOR will be used to interpolate the next-term risk-free rate R. HIBOR Reuters Code Overnight HIHKDOD= 1 Week HIHKD1WD= 1 Month HIHKD1MD= Months HIHKDMD= 3 Months HIHKD3MD= 9

12 7 Contact Information Hang Seng Indexes Compan Limited Address : Website 83 Des Voeux Road Central, Hong Kong info@hsi.com.hk 10

13 8 Disclaimer All information contained herein is provided for reference onl. Hang Seng Indexes Compan Limited ( HSIL ) ensures the accurac and reliabilit of the above information to the best of its endeavours. However, HSIL makes no warrant or representation as to the accurac, completeness or reliabilit of an of the information contained herein and accepts no liabilit (whether in tort or contract or otherwise) whatsoever to an person for an damage or loss of an nature arising from or as a result of reliance on an of the contents of this document, or an errors or omissions in its contents and such contents ma change from time to time without notice. HSI Volatilit Index (the Index ) is published b HSIL, which has contracted with Standard & Poor s Financial Services LLC ( S&P ) to maintain and calculate the Index. Standard & Poor's" and "S&P" are trademarks of S&P and have been licensed for use b HSIL. VIX is a trademark of Chicago Board Options Exchange, Incorporated ( CBOE ) and S&P has granted a license to HSIL, with permission from CBOE, to use such mark for purposes relating to the Index. The Index is not owned, sponsored, endorsed or promoted b S&P or CBOE and neither S&P nor CBOE makes an representation regarding the advisabilit of investing in products that are based on such Index or otherwise reling on such Index for an purpose and neither S&P, CBOE nor HSIL shall have an liabilit for an errors or omissions in the Index or an values thereof. The information contained in this document is not intended to provide professional advice and should not be relied upon in that regard. Persons intending to use an information obtained from this document are advised to obtain appropriate professional advice. Hang Seng Indexes Compan Limited 015. All rights reserved. - End - 11