Risk Arrays
The specific set of market conditions evaluated, are called the risk scenarios, are defined in terms of (a) how much the price of the underlying instrument is expected to change over the look-ahead time, and (b) how much the volatility of that underlying price is expected to change over the look-ahead time. The results of the calculation for each risk scenario, the amount by which the specific derivative instrument will gain or lose value over the look-ahead time under that risk scenario, is called the risk array value for that scenario. The set of risk array values for that contract (derivative instrument) under the full set of risk scenarios, constitutes the risk array. By convention, risk array values are calculated for a single long position. "Long" here means long the instrument, not long the market: buying a put and buying a call both yield long positions for the purposes of SPAN. Also by convention, since SPAN is more interested in potential losses than potential gains, losses are represented as positive values, and gains as negative values. Risk array values are typically represented in the performance bond currency in which the specific contract is denominated. Since its inception, SPAN has used a standardized definition of the risk scenarios, defined, as indicated above, in terms of the underlying price scan range, and the underlying price volatility scan range. These two values are often simply referred to as the price scan range and the volatility scan range. There are 16 risk scenarios in the standard definition. Here's an example of a typical options risk array:
June Euro FX Call at $0.70 Strike; Futures Settlement = $0.6966
For example, the fourth risk array value given above, negative $120, means that a long position in this specific option will experience a gain of $120 over the next trading day, if the price of the underlying future goes up by one-third of the price scan range, and if the volatility of that underlying futures price decreases by the full amount of the volatility scan range. These values are calculated using an options pricing model to evaluate (1) the theoretical value of the option today, and (2) the hypothetical theoretical value of the option (a) after the look-ahead time has passed and (b) if the price of the underlying future and the volatility of that price, move as specified. The difference between these two values yields the risk array value itself.
Scanning Risk Charge
As shown above in the 16 standard risk scenarios, SPAN starts at the current underlying market settlement price and scans up and down three even intervals of price changes. At each underlying market price, the program also scans up and down a range from the underlying market's current volatility. As noted above, the individual exchanges and clearing organizations using SPAN determine the magnitude of these scan ranges for each underlying instrument. At CME®, these scan ranges are determined by its Board of Directors and Performance Bond Sub Committee. Deep-out-of-the-money short options positions pose a special risk identification problem. As they move toward expiration, they may not be significantly exposed to "normal" price moves in the underlying instrument. However, unusually large underlying price changes may cause these options to move into the money, thus creating large losses to the holders of short positions. In order to account for this possibility, two of the standard risk scenarios reflect an "extreme" underlying price movement, currently defined as double the maximum scan range for a given underlying instrument. However, because price changes of these magnitudes are rare, the program only covers a fraction 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 combined commodity, in other words, for all contracts represented in the portfolio that have the same underlying instrument.
Composite Delta
In the interest of simplicity, SPAN employs only one delta value per contract, called the "Composite Delta." It is derived as the weighted average of the deltas associated with each underlying price scan point. The weights associated with each 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. You can think of the Composite Delta for an options contract as the best estimate of what the contract's delta will be after the look ahead time has passed, in other words, after one trading day has passed. Like the risk arrays, the Composite Delta for each contract is calculated by each exchange and clearing organization using SPAN, and is included together with the risk arrays in the SPAN risk parameter file transmitted daily to outside users.
Short Option Minimum Charge
For example, suppose that the Euro FX Short Option Minimum rate is $40 per position. A portfolio containing 20 short Euro FX options will have a risk requirement of at least $800, irrespective of the outcomes of the other SPAN calculations.
Intra-commodity Spread Credits
For each futures contract or other underlying instrument in which the portfolio has positions, SPAN identifies the net delta associated with that underlying. It then forms spreads using these net deltas according to patterns (a table of required spreads) specified in the SPAN risk parameter file. As an example of one such required spread, SPAN could form spreads between all Treasury bill futures contract months with net long delta, and all contract months with net short delta. SPAN is completely flexible in how the required spreads are defined for each combined commodity. As spreads are formed, SPAN keeps track for each tier (a set of consecutive futures contracts) of how much delta has been consumed by spreading for the tier, and how much remains. For each spread formed, SPAN assesses a charge per spread at the specified charge rate for the spread. The total of all of these charges for a particular combined commodity, constitutes the Intracommodity Spread Charge for that combined commodity.
Delivery Charges
Putting it all Together
For each underlying instrument (each combined commodity) in which a portfolio has positions, SPAN will add up the Scanning Risk Charges, the Intra-Commodity Spread Charges and any Delivery Month Charges. The program then subtracts any Inter-Commodity Spread Credits that it has calculated for the combined commodity. SPAN compares this figure to the Short Option Minimum charge for the combined commodity, selects the larger of these two values, and multiplies the result by the Maintenance Requirement Adjustment Factor (typically set to one.) The result is the Maintenance Risk Requirement for the combined commodity. This value is then multiplied by the Initial to Maintenance Ratio for this combined commodity to yield the Initial Risk Requirement. (The adjustment factors and initial to maintenance ratios are set by the exchange or clearing organization using SPAN for each type of customer account, member, hedger, and speculator, and are contained in the SPAN risk parameter file. The adjustment factors are typically all one, and the initial to maintenance ratios are typically all one except for speculative public customers, for whom they may be greater than one.) The Maintenance Risk Requirements for all of the combined commodities in the portfolio are then converted to a common currency and summed, as are the Initial Risk Requirements. These values are then compared to the total portfolio Net Liquidating Value, including the current net value of all premium-style options, to determine if a performance bond excess or deficiency exists. Sometimes the term total performance bond requirement is used to refer to the SPAN risk requirement, less the net value (net option value) of all premium-style options in the portfolio. If the total performance bond requirement is calculated in this way, then it is compared to the total equity, that is, everything that constitutes the net liquidating value except the net option value. We sometimes say that the total performance bond requirement has two components: the risk component, in other words, the SPAN risk requirement and the equity component. Whether you compare the SPAN risk requirement to the portfolio net liquidating value, or the total requirement to the total equity, the result is the same; the only difference lies in which side of the comparison the net option value is put. Note that SPAN is done when the portfolio SPAN risk requirement has been calculated. All other aspects of the performance bond calculation process, the determination of whether a performance bond excess or deficiency exists, and any call for more performance bond collateral or release of excess collateral, are outside the scope of SPAN.
Intra-commodity Spreading (Inter-month) Risk Charge
For each futures contract or other underlying instrument in which the portfolio has positions, SPAN identifies the net delta associated with that underlying. It then forms spreads using these net deltas according to patterns (a table of required spreads) specified in the SPAN risk parameter file. As an example of one such required spread, SPAN could form spreads between all Treasury bill futures contract months with net long delta, and all contract months with net short delta. SPAN is completely flexible in how the required spreads are defined for each combined commodity. As spreads are formed, SPAN keeps track for each tier (a set of consecutive futures contracts) of how much delta has been consumed by spreading for the tier, and how much remains. For each spread formed, SPAN assesses a charge per spread at the specified charge rate for the spread. The total of all of these charges for a particular combined commodity, constitutes the Intracommodity Spread Charge for that combined commodity.
About Initial and Maintenance Requirements
It's important to note that, with a portfolio-approach system such as SPAN, the meaning of an initial and maintenance requirement differs from its meaning in older, less-efficient systems. For example, "strategy-based" margins, or "delta-based" margins. With these older systems, individual positions were tracked as to whether they were "new" or not; new positions were assessed the higher, "initial" requirements and non-new positions were assessed the lower, "maintenance requirement." But because SPAN uses a portfolio approach, it evaluates the risk associated with the entire portfolio independently of when and how the positions in that portfolio were put on. Therefore, instead of looking at whether individual positions are new or not, we look at whether the entire portfolio is new or not. A portfolio that had any positions in it on the prior trading day is considered to be not new. US futures exchanges have adopted the following rule: when a customer portfolio for
which a higher initial requirement exists is new, the customer must meet the initial requirement.
Thereafter, so long as the net liquidating value for the account does not fall below the
maintenance risk requirement, only the maintenance requirement need be met. If, on the other hand,
the net liquidating value falls below the maintenance requirement, additional collateral must be
deposited to bring the net liquidating value up to the level of the initial requirement.
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