
The objective of SPAN is to identify overall risk in a portfolio of futures and
options contracts for each member. The system treats futures and options
contracts uniformly, while at the same time recognizing the unique exposures
associated with options portfolios like extremely deep outofthemoney short
positions, intermonth risk and intercommodity risk.
Because SPAN is used to determine performance bond requirements (margin
requirements), its overriding objective is to determine the largest loss that a
portfolio might reasonably be expected to suffer from one day to the next day.
In standard pricing models, three factors most directly affect the value of
an option at a given point in time:
1. Underlying market price
2. Volatility (variability) of underlying instrument 3. Time to expiration
As these factors change, so too will the value of futures and options maintained
within a portfolio. SPAN constructs scenarios of probable changes in underlying
prices and volatilities in order to identify the largest loss a portfolio might
suffer from one day to the next. It then sets the margin requirement at a level
sufficient to cover this oneday loss.
The complex calculations (e.g. the pricing of options) in SPAN are executed by
the Clearing Corporation. The results of these calculations are called Risk
arrays. Risk arrays, and other necessary data inputs for margin calculation are
then provided to members on a daily basis in a file called the SPAN Risk
Parameter file.
Members can apply the data contained in the Risk parameter files to their
specific portfolios of futures and options contracts to determine their SPAN
margin requirements.
Hence members need not execute complex option pricing calculations which are
performed by NSCCL. SPAN has the ability to estimate risk for combined futures
and options portfolios and revalue the same under various scenarios of changing
market conditions.
The SPAN risk array represents how a specific derivative instrument (for
example, an option on NIFTY index at a specific strike price) will gain or lose
value from the current point in time to a specific point in time in the near
future (typically it calculates risk over a one day period called the ‘look
ahead time’), for a specific set of market conditions which may occur over this
time duration.
The specific set of market conditions evaluated are called the risk scenarios,
and these are defined in terms of :
(a) how much the price of the underlying instrument is expected to change over
one trading day and
(b) how much the volatility of that underlying price is expected to change over
one trading day.
The results of the calculation for each risk scenario – i.e. the amount by which
the futures and options contracts will gain or lose value over the lookahead
time under that risk scenario  is called the risk array value for that
scenario. The set of risk array values for each futures and options contract
under the full set of risk scenarios, constitutes the Risk Array for that
contract.
In the Risk Array losses are represented as positive values and gains as
negative values. Risk array values are typically represented in the currency
(Indian Rupees) in which the futures or options contract is denominated.
SPAN further uses a standardized definition of the risk scenarios defined in
terms of
(i) the underlying ‘price scan range’ or probable price change over a one day
period,
(ii) and the underlying price ‘volatility scan range’ or probable volatility
change of the underlying over a one day period.
These two values are often simply referred to as the ‘price scan range’ and the
‘volatility scan range’. There are sixteen risk scenarios in the standard
definition. These scenarios are listed as under:
1. Underlying unchanged; volatility up
2. Underlying unchanged; volatility down
3. Underlying up by 1/3 of price scanning range; volatility up
4. Underlying up by 1/3 of price scanning range; volatility down
5. Underlying down by 1/3 of price scanning range; volatility up
6. Underlying down by 1/3 of price scanning range; volatility down
7. Underlying up by 2/3 of price scanning range; volatility up
8. Underlying up by 2/3 of price scanning range; volatility down
9. Underlying down by 2/3 of price scanning range; volatility up
10. Underlying down by 2/3 of price scanning range; volatility down
11. Underlying up by 3/3 of price scanning range; volatility up
12. Underlying up by 3/3 of price scanning range; volatility down
13. Underlying down by 3/3 of price scanning range; volatility up
14. Underlying down by 3/3 of price scanning range; volatility down
15. Underlying up extreme move, double the price scanning range (cover 35% of
loss)
16. Underlying down extreme move, double the price scanning range (cover 35% of
loss)
SPAN uses the risk arrays to scan probable underlying market price changes and
probable volatility changes for all contracts in a portfolio, in order to
determine value gains and losses at the portfolio level. This is the single most
important calculation executed by the system.
As shown above in the sixteen standard risk scenarios, SPAN starts at the last
underlying market settlement price and scans up and down three even intervals of
price changes (‘price scan range’).
At each ‘price scan point’, the program also scans up and down a range of
probable volatility from the underlying market's current volatility (‘volatility
scan range’). SPAN calculates the probable premium value at each price scan
point for volatility up and volatility down scenario. It then compares this
probable premium value to the theoretical premium value (based on last closing
value of the underlying) to determine profit or loss.
Deepoutofthemoney short options positions pose a special risk identification
problem. As they move towards expiration, they may not be significantly exposed
to "normal" price moves in the underlying. However, unusually large underlying
price changes may cause these options to move intothemoney, thus creating
large losses to the holders of short option positions. In order to account for
this possibility, two of the standard risk scenarios in the Risk Array (sr. no.
15 and 16) reflect an "extreme" underlying price movement, currently defined as
double the maximum price scan range for a given underlying. However, because
price changes of these magnitudes are rare, the system only covers 35% of the
resulting losses.
After SPAN has scanned the 16 different scenarios of underlying market price and
volatility changes, it selects the largest loss from among these 16
observations. This "largest reasonable loss" is the ‘Scanning Risk Charge’ for
the portfolio  in other words, for all futures and options contracts.
The price scan range, as explained above, is the probable price change over a
oneday period. In case of index products and stock products the price scan
range is taken as three standard deviations (3 sigma ) and three and a half
standard deviations (3.5 sigma) respectively as calculated for VaR purpose for
the underlying index and underlying security or other price scan range as may be
prescribed. The price scan range for options and futures on individual
securities is also linked to liquidity. This is measured in terms of impact cost for an order size of Rs 5 lakh
calculated on the basis of order book snapshots in the previous six months as
per defined methodology.
Accordingly if the mean value of the impact cost exceeds 1%, the price scanning
range is scaled up by square root of three. This is in addition to the
requirement on account of look ahead period as may be applicable.
The mean impact cost as stipulated by SEBI is calculated on the 15th of each
month on a rolling basis considering the order book snap shots of previous six
months. If the mean impact cost of a security moves from less than or equal to
1% to more than 1%, the price scan range in such underlying is scaled by square
root of three and scaling is dropped when the impact cost drops to 1% or less.
Such changes are made applicable on all existing open positions from the third
working day from the 15th of each month.
SPAN uses delta information to form spreads between futures and options
contracts. Delta values measure the manner in which a future's or option's value
will change in relation to changes in the value of the underlying instrument.
Futures deltas are always 1.0; options deltas range from 1.0 to +1.0. Moreover,
options deltas are dynamic: a change in value of the underlying instrument will
affect not only the option's price, but also its delta.
In the interest of simplicity, SPAN employs only one delta value per contract,
called the "Composite Delta." It is the weighted average of the deltas
associated with each underlying ‘price scan point’. The weights associated with
each ‘price scan point’ are based upon the probability of the associated price
movement, with more likely price changes receiving higher weights and less
likely price changes receiving lower weights. Please note that Composite Delta
for an options contract is an estimate of the contract's delta after the
lookahead  in other words, after one trading day has passed.
As SPAN scans futures prices within a single underlying instrument, it assumes
that price moves correlate perfectly across contract months. Since price moves
across contract months do not generally exhibit perfect correlation, SPAN adds a
Calendar Spread Charge (also called the Intermonth Spread Charge) to the
Scanning Risk Charge associated with each futures and options contract. To put
it in a different way, the Calendar Spread Charge covers the calendar
(intermonth etc.) basis risk that may exist for portfolios containing futures
and options with different expirations.
For each futures and options contract, SPAN identifies the delta associated with
each futures and option position, for a contract month. It then forms spreads
using these deltas across contract months. For each spread formed, SPAN assesses
a specific charge per spread which constitutes the Calendar Spread Charge.
The margin for calendar spread shall be calculated on the basis of delta of the
portfolio in each month. Thus a portfolio consisting of a near month option with
a delta of 100 and a far month option with a delta of –100 would bear a spread
charge equivalent to the calendar spread charge for a portfolio which is long
100 near month futures contract and short 100 far month futures contract.
The calendar spread position shall be granted calendar spread treatment till the
expiry of the near month contract.
Short options positions in extremely deepoutofthemoney strikes may appear to
have little or no risk across the entire scanning range. However, in the event
that underlying market conditions change sufficiently, these options may move
intothemoney, thereby generating large losses for the short positions in these
options. To cover the risks associated with deepoutofthemoney short options
positions, SPAN assesses a minimum margin for each short option position in the
portfolio called the Short Option Minimum charge, which is set by the NSCCL. The
Short Option Minimum charge serves as a minimum charge towards margin
requirements for each short position in an option contract.
For example, suppose that the Short Option Minimum charge is Rs. 50 per short
position. A portfolio containing 20 short options will have a margin requirement
of at least Rs. 1,000, even if the scanning risk charge plus the inter month
spread charge on the position is only Rs. 500.
In the above scenario only sell positions are margined and offsetting benefits
for buy positions are given to the extent of long positions in the portfolio by
computing the net option value.
The total margin requirements for a member for a portfolio of futures and
options contract are computed as follows:
(i) SPAN will add up the Scanning Risk Charges and the Intracommodity Spread
Charges.
(ii) SPAN will compare this figure (as per i above) to the Short Option Minimum
charge
(iii) It will select the larger of the two values between (i) and (ii)
(iv)Total SPAN Margin requirement is equal to SPAN Risk Requirement (as per iii
above), less the ‘net option value’, which is mark to market value of difference
in long option positions and short option positions.
The options price for a Call, computed as per the following Black Scholes formula:
C = S * N (d_{1})  X * e^{ rt} * N (d_{2})
and the price for a Put is :
P = X * e^{ rt} * N (d_{2})  S * N (d_{1})
where :
d_{1} = [ln (S / X) + (r + σ^{2} / 2) * t] / σ * sqrt(t)
d_{2} = [ln (S / X) + (r  σ^{2} / 2) * t] / σ * sqrt(t)
= d_{1}  σ * sqrt(t)
C = price of a call option
P = price of a put option
S = price of the underlying asset
X = Strike price of the option
r = rate of interest
t = time to expiration
σ = volatility of the underlying
N represents a standard normal distribution with mean = 0 and standard deviation
= 1
ln represents the natural logarithm of a number. Natural logarithms are based on
the constant e (2.71828182845904).
Rate of interest may be the relevant MIBOR rate
or such other rate as may be specified.
SPAN® is a registered trademark of the Chicago Mercantile Exchange, used herein
under License. The Chicago Mercantile Exchange assumes no liability in
connection with the use of SPAN by any person or entity.
Liquid Assets 
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