Download Methodology of the Volatility Index Calculation

APPROVED
by the Order of CEO of
Open Joint Stock Company
‘Russian Trading System’ Stock Exchange
No. 97 as of 01.06.2011
Methodology of the Russian Volatility Index
1. General provisions
1.1.
Russian Volatility Index (hereinafter referred to as the “Index”) is calculated by Open Joint Stock
Company ‘Russian Trading System’ Stock Exchange (hereinafter referred to as the “Exchange”) in
accordance with the present Methodology (hereinafter referred to as the “Methodology”).
1.2.
The name of the Index in Russian is «Российский индекс волатильности», the name of the Index in
English is «Russian Volatility Index». Index symbol is «RTSVX».
2. Calculation of the Index:
2.1.
The Index is calculated every 15 seconds.
2.2.
The Index is calculated during the main trading session of the Exchange and during an additional
trading session (if any). While during the main trading session and additional evening trading session
the first Index value is calculated through 5 (five) minutes after the start of the trading session, the last
Index value is calculated at the moment of the session closing.
2.3.
Index value is expressed in index points and is calculated accurate to 4 decimal places.
2.4.
The Index is calculated in accordance with the following formula:
 ˆ 2 ,



RTSVX = 



ˆ1 ,
if
дни
ˆ12
T1
 n fut  nsmooth
nsmooth
дни
 n fut  nsmooth
T1
дни
 ˆ 22
n fut  T1
nsmooth
, if
дни
n fut  nsmooth  T1
if
 n fut
дни
T1
 n fut
where:
RTSVX – Index’s value;
T1days – time to expiration of options series with the nearby expiration date1
(hereinafter referred to
as “the nearby options series”) inclusive, fraction of a day:
T1
days
N exp iry

N
,
where
Nexpiry
– a number of seconds from the moment of Index calculation to
6:50:00 PM MSK at the expiration date of the nearby options series;
1
An expiration date is the last day of executing of given series options.
1
N – a number of seconds in a calendar day.
nfut – a number of calendar days from
the date of beginning of rollover2 to the expiration date of
nearby options series inclusive, the value is equal 8 (eight);
nsmooth – a number of calendar days for conducting the rollover, the value is equal 4 (four);
ˆ 1 – aggregated volatility of nearby options series, determined in accordance with clause 2.5 herein.
̂ 2 – aggregated volatility of options series with the expiration date following the expiration date of
nearby options series (hereinafter referred to as the “next options series”). The figure is determined in
accordance with clause 2.5 herein.
2.5.
The aggregated volatility is calculated in accordance with the following formula:
ˆ i 
 0
  P ( x )e  x
Fi Ti  10
2
10
Ti
dx   C ( x)e
 x Ti
0

dx  *100 ,

where
Fi –
price of a futures contract, which is an underlying asset for nearby/next options series
(hereinafter referred to as the “underlying futures contract”).
Ti – calendar period until an expiration date of nearby/next options series inclusive, fraction of a day:
days
T
Ti  i
365
C(x) – the function that specifies the price of call options3:
C( x)  FN (d1 )  KN (d2 ) ,
where:
N(d) – Gaussian distribution function 4,
1
N (d ) 
2
d1 
d
e

z2
2
dz

 x  0.5 ( x) 2 T
 x  0.5 ( x) 2 T
, d2 
,
 ( x)
 ( x)
K – option strike price;
σ(x) – option volatility value, determined in accordance with clauses 2.6-2.7
herein.
2
Rollover is a gradual transition from the settlements on nearby options series to the settlements on next options series.
3
Black-Scholes option pricing formula for futures-style options with futures as the underlying asset is applied.
4
Integration is made using Trapezoidal Rule with fixed step in
x
equal
dx  0.01 .
The Trapezoidal Rule for arbitrary integral
b
 f ( x)dx , where
f (x)
- a continuous function on
[a, b] , includes partitioning of [a, b] by points x0  a , x1  a  dx , ...,
a
xN  a  N  dx  b and the replacement of the integral by
N 1

i 0
f xi   f xi 1 
 dx .
2
2
x
1 K
ln   – a value that defines the moneyness of options.
T F
P(x) – the function that specifies the price of put options:
P( x)  C ( x)  F  K .
2.6.
Volatility curve is determined by the following function:


 ( x)  f ( x, s, a, b, c, d , e)  a  b * 1  e cy 
2
d * arctg (e * y )
e
where:
s, a, b, c, d, e
– volatility curve’s parameters, determined by the Exchange;
y xs
2.7. Function that specifies truncated volatility curve is determined based on the volatility curve in clause
2.6 herein.
The truncated volatility curve is calculated within the range of stable option’s quotes:
1


xdown  max   k down (0),
ln 1  rangedown  ,
T


1


xup  min  k up (0),
ln 1  rangeup  ,
T


where:
xdown – lower limit of the range of the stable option’s quotes;
xup – upper limit of the range of the stable option’s quotes;
kdown – a coefficient used for “at the money” option’s volatility in order to determine lower strike of the
volatility curve truncation. The coefficient’s value is 2 (two);
kup – a coefficient used for “at the money” option’s volatility in order to determine upper strike of the
volatility curve truncation. The coefficient’s value is 2 (two);
rangedown – maximum
range used to determine lower strike of the volatility curve truncation, the
value is 0.2 (two tenths);
rangeup – maximum range used to determine upper strike of the volatility curve truncation, the value
is 0.2 (two tenths).
The function that specifies the truncated volatility curve:
  ( xdown ) , if

 restricted ( x)   ( x),
if
  ( x ),
if
up

x  xdown
xdown  x  xup
xup  x
3. Information disclosure
3.1.
Information on the Index’s values is published in the Internet at www.rts.ru after 2 (two) minutes of
Index’s calculation.
3.2.
The text of the Methodology is subject to disclosure in the Internet at www.rts.ru.
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4.
Introduction of changes to the Methodology
4.1.
Amendments to the Methodology are made by the decision of Exchange’s CEO.
4.2.
The text of the Methodology with the changes made is published in the Internet at www.rts.ru not later
than one business day before the day such changes come into effect.
4