This is a general overview of initial margin calculation with SPAN® for derivatives (futures and options).
The SPAN® method considers not only futures contracts and options on futures contracts but also other types of options. It estimates in a uniform manner all products having the same underlying instrument thus taking an overall view of the portfolio.
- SPAN® Derivatives Brochure - English Version
- Explanation related to the change in the feeding of the field Futures Price Scan Range of record 4B
- Option Valuation Formulas
The SPAN® method is based on the estimation of the balance liquidation value of a portfolio according to several scenarios representing changes in market conditions. This data is stored in risk arrays which are specific to each contract and updated on a daily basis.
The scenarios used by SPAN® consider the following :
Possible variation of underlying price,
Possible variation of underlying volatility,
Impact of time on option value.
The value of the futures contracts and options of the portfolio vary with changes in these factors. Through these scenarios, SPAN® determines the maximum loss incurred by a portfolio from one market day to the next. The clearing house then fixes a performance bond (initial margin) amount calculated to cover the repurchase of the portfolio while absorbing the loss.
SPAN® considers a total of 16 risk scenarios by using a scan range, or fluctuation range of the underlying instrument price and a volatility range defined for each combined commodity.
NOTE : The basic concept used for risk calculation is the combined commodity. This is a group of contracts having the same underlying instrument (futures contracts and the options on these contracts). SPAN® calculates the hedge using this concept.
The risk arrays integrate 7 price variation possibilities:
Price increase or decrease corresponding to 1/3 of the scan range,
Price increase or decrease corresponding to 2/3 of the scan range,
Price increase or decrease corresponding to 3/3 of the scan range.
For each of these price changes, an upward or downward variation in volatility is also considered.
Short option positions which are highly out of the money when reaching expiration represent a specific problem. It is true that should the underlying instrument vary sharply, these positions could then be in the money. SPAN® includes 2 scenarios to consider this risk, one for the fall in the underlying price, the other for a rise in price corresponding to two scan ranges. However, only a fraction of the total loss thus calculated is considered in the risk arrays.
Intermonth spreads (or calendar spreads)
SPAN® also takes into account reductions in risk due to the presence of opposite positions on different months within the same combined commodity.
The use of risk arrays implicitly assumes that price changes across months of a combined commodity are perfectly correlated, but this is not always so. In order to correct this aspect, SPAN® proceeds as follows :
The net delta for each month for which a position is held is considered. The long net deltas are totalled as also the short net deltas. The greatest number of possible spreads is formed. This number is then multiplied by the charge for each spread specified by the clearing house. The resulting amount is added to the amount calculated from the risk arrays (or "scanning risk").
Tiers are generally defined within the months in order to consider risks specific to a given quotation period. A spread within a tier (which, for example, groups together the first two months) results in a specific charge, whereas a spread calculated with another tier results in a different charge.
A priority table for spread calculation is therefore used.
In the case of deliverable contracts or special risk at maturity, an additional risk exposure may arise when the delivery date nears. In order to consider this risk, SPAN® adds two charges:
On spread positions including one delivery month,
On straight positions for the delivery month.
In the case of separate contracts having similar underlying instruments, the price variations may be correlated. Thus, opposite positions, in two different combined commodities, can lead to a decrease in the overall risk for the position. A decrease in the performance bond requirement (credit) is therefore calculated. A priority table is supplied for this purpose as well. For these spreads, SPAN® generates a credit expressed as a percentage of the performance bond called for the commodity group.
Short option minimum charge (short positions)
In event of a sharp variation in the underlying instrument price, short option positions can lead to considerable losses. SPAN® therefore includes an additional step. It calculates a minimum amount called for short positions in each combined commodity. This amount will be called if it is higher than the result obtained in the previous steps.
Performance bond calculation
The performance bond required for a given combined commodity is the result of the calculations in the steps described above from which the net option value is deducted, as the performance bond is the total of the net value of the portfolio and the risk. If the performance bond calculated is negative, it is considered as null and no amount is called.
Parameters adequacy is daily monitored with reference to implied or historical volatilities and actual markets movements.The ultimate responsibility for deciding upon parameters to be used rests with the Risk Committee.
Our methodology of parameters calibrating and monitoring is primarily based on two complementary approaches :
A probabilistic/statistical approach of Value-at-Risk type, with a general policy of a 2-day holding period and a 99.7 % 2-tail confidence interval (e.g. the equivalent of 3 standard deviations and a breach less than once a year, under normality assumption).
A deterministic approach of worst-case scenario type, based on observed market movements, especially regarding spread positions. SPAN® provides a flexible framework to take profit of both approaches while trying to avoid their weaknesses. For example, when margining a spread position between two assets, it would often be misleading to use a basic VaR approach only relying on their linear estimated correlation and assuming normality