The margining methodology enables a trustworthy clearing operation, given that reasonably conservative margins are required to avoid the risk of the clearing house incurring a loss in a default situation.
The margin requirement should theoretically be the market value of the account. However, under normal conditions, an account cannot be closed out at the instant a participant defaults at the prevailing market prices. It typically takes time to neutralize the account, and the value of the account can change during this period, which must be catered for in the margining methodology.
Genium Risk – The Margining System
The purpose of a margining system is to calculate accurate risk-based margin requirements for each counterparty account. Nasdaq Clearing uses a margining system called Genium Risk, which is integrated within the Genium INET clearing system, and is used to generate the daily counterparty margin requirements and intraday counterparty margin calculations.
Genium Risk is a multi-asset risk management system that integrates OTC and standardized products, hence generating risk offsets and efficiency for clearing house members. The margin methodologies, risk models and risk parameters are customized for different types of asset classes and credit risks, to generate accurate valuation and capital efficient calculations, in order to optimize the use of members’ collateral. The following sections describe the margin methodologies used for Equities, Fixed Income and Commodities.
Equities - OMS-II
OMS-II examines the portfolio as a whole to see how an adverse movement in the value of an underlying instrument would affect the value of the entire portfolio of a given counterparty. It uses a range of inputs in the margin calculation, some of which are specified below.
Market Price Models for Option Contracts
The market value of an option contract at each valuation point is calculated using industry-standard valuation models. The market price models used by Nasdaq Clearing to calculate margin requirements are based on the Black-Scholes or the binomial option valuation model for stock options and the Black-76 or Bachelier model for index and interest rate options.
Different values for the account must be calculated since the market often moves after collateral is pledged until Nasdaq Clearing can close a position in the event of a default situation. To do this, OMS-II stresses the price for the underlying security for each series to calculate the neutralization cost. In this way, OMS-II creates a “valuation interval” for each underlying security. The size of the valuation interval depends on the length of the liquidation period and the size of the historical price fluctuations over this liquidation period.
The upper and lower limits of the valuation points represent the worst expected movement (during the lead-time) for the margin calculation. However, the worst-case scenario for a portfolio with different options and forwards/futures based on the same underlying instrument can occur anywhere in the valuation interval. In order to reflect this, the valuation interval is divided into 31 valuation points for equity products.
OMS-II calculates the neutralization cost for each series with the same underlying security in each valuation point; the actual margin requirement is then based on the valuation point that rendered the highest margins, i.e. the worst-case scenario. This means that a portfolio that contains a series for which margins typically would be calculated at different ends of the valuation interval is calculated in the same valuation point. This methodology is justified since the market can only go in one direction at a time (see Correlations between Instruments below on this page).
Implied Volatility and Volatility Shifts
The risk of a change in implied volatility is taken into account by calculating the neutralization cost of an account by a higher and lower implied volatility than the market implied volatility. Therefore, the neutralization cost is calculated at each valuation point for three different implied volatility levels; low, market and high. Therefore, a typical valuation interval consists of 3x31 valuation points.
OMS-II produces a vector file for each contract cleared. A vector file consists of a data series that is shared by all positions in the series. There are primarily two reasons to produce a vector file. The first is to achieve computational efficiency, and the second is that the vector files can be externally distributed so that members can replicate the margin calculations in their own systems.
For full OMS-II model documentation, please see the Resource Center.
Fixed Income - CFM
Any margin methodology should mirror realistic circumstances, and at the same time, be capital efficient. When margining fixed income derivatives, it appears natural to utilize the correlation between different maturities along a yield curve. The Cash Flow Margin model (“CFM”) is a yield curve-based margin methodology that captures this correlation of fixed income instruments priced against the same curve.
Instead of stressing each instrument’s individual price, yield curves are stressed using their first three Principal Components (“PC”). All the instruments in an account are then evaluated against each stressed yield curve, and the margin requirement is determined as the combined value of these instruments calculated with the worst of the stressed yield curves. Each principal component (PC) explains part of the historical changes in yield curves. Nasdaq Clearing uses the first three PCs that explain around 90% – 95% of all historical changes to the yield curve.
PC1 is a parallel shift of the yield curve, PC2 is a change in slope, and PC3 is a change in curvature. The main steps of the margin model are:
- Bootstrap individual credit curves from prices of selected instruments;
- Change the entire yield curve to simulate possible future movements of the curve;
- Apply changes in the three first principal components (PC) as independent changes to the yield curve;
- A set of hypothetical future yield curves are constructed (the number of hypothetical future yield curves depends on how many subintervals each PC is divided into. With PC1 divided into 9 subintervals, PC 2 in 5 and PC 3 in 5 will 9*5*5 = 225 hypothetical future yield curves be constructed);
- For each hypothetical future yield curve, the market value of a portfolio is calculated;
- The hypothetical future yield curve that leads to the lowest market value for a portfolio is the ”margin curve” for that portfolio
For full CFM Model documentation, please see the Resource Center.
Commodities - SPAN®
The Commodities derivatives margin model represents a modification of CME SPAN® and takes into account special properties of traded commodities and features of delivery procedures. The model provides a possibility of 100% margin netting for some products within the same product group, depending on the delivery terms and volumes.
Price volatilities on the Commodities derivatives markets are crucially dependent on time to delivery. The volatility structure is formalized as a margin curve consisting of calculated volatilities as a function of time to delivery for a given market. The volatility of a contract with a given time to delivery and delivery period is then presented as an integral of a margin curve over the corresponding time period. Please see the Resource Center below for links to current margin curves.
The margin model possesses major properties of the generic SPAN® model and uses a scenario approach to determine margin levels sufficient to cover correspondent portfolio risks. The model considers possible price movements and changes in volatility, which are formalized in 16 standard scenarios. Features of the commodities derivatives markets and physical properties of delivery procedures assume special features for portfolio netting and provide dependencies between market prices that are included in the margining system.
For full SPAN ® documentation, please see the Resource Center.
Calculation of Risk Parameters for Underlying Instruments
Since neutralizing an account in a default situation can take time, there is a lead-time from the moment a default occurs to the time at which Nasdaq Clearing is able to close out the participant’s positions and, when necessary, liquidate the collateral that has been pledged.
For most financial products, it is assumed that it takes a maximum of two days (but up to five days for more illiquid products) to close a counterparty’s positions and liquidate related collateral in the event of a default. For commodity products, the liquidation period ranges between 2 to 5 days. Hence, the margin parameters are calculated with considerations taken to the assumed liquidation period.
Multiple analyses of the underlying instruments for financial products show that historical price movements are not normally distributed. Nasdaq Clearing uses a numerical method to calculate its risk parameters to avoid assumptions regarding a parametric distribution (e.g. normal). This method uses data over a one-year historical period to establish an approximation for the cumulative distribution for equity products. The third-largest movement is then used to determine the appropriate level of the risk parameters, equivalent to a 99.2 percent confidence interval for the one-year price history. For Fixed Income products, Nasdaq Clearing also uses data over a longer historical period, 10-year, to establish an approximation for the cumulative distribution. The movement corresponding to a 99.2 percentile movement is chosen (or 99.5 percent for OTC products) for the 10-year price history. Finally, the worst of the risk parameter based on one-year and 10-year look-back periods is applied.
Prices on commodities derivatives markets possess the same general properties as other financial instruments, including “heavy tails” and high excess. For margin calculations, Nasdaq Clearing applies contemporary statistical methods using stable distributions as a model for the tails of relative price increments distribution. The major part of the parameters is estimated within a one-year data horizon. The parameters of the margining model ensure that the member’s margin will cover any possible losses with 99.2 percent confidence.
Correlation Between Instruments
Cross margining is offered for instruments where fundamental economic rationale and statistical evidence of price dependencies exist, creating margin efficiencies for Clearing Participants. Below, we describe the methods used for modelling such dependencies.
For OMS-II, this is called the “window method”. In this method, the scanning range limits the individual movement for each series, but there is a maximum allowed difference between the scanning points of the two series. This range can be represented as a “window”, hence the name. The size of this window is estimated roughly by the same method used to estimate scanning ranges. Daily differences between the movements of the series are calculated using one year of data. These values are then used to build a cumulative numerical distribution from which the 99.2 percent confidence interval is applied.
Based on a given covariance, the window can display a spread demonstrating the maximum allowable difference in price variation between two underlying securities. In a narrow window, prices cannot vary as much as in a broad one. As a result, high covariance causes a narrow window and vice versa.
Fixed Income (CFM)
Yield curves with different credit risks can show a historical relationship. Calculations of allowed correlation between two or more yield curves are based on the strength of the historical relationship between the different yield curves. Each historical curve change can be represented in terms of movements in PC1, PC2 and PC3 by applying a method of least squares solution. The method gives historical time series in terms of movements in PC1, PC2 and PC3. From each curve, there will be a daily change in each Principal Components. The window size between each Principal Component is based on the maximum anticipated amount that the Principal Components can deviate from each other in terms of the number of valuation points in the valuation interval. Each day, the maximum difference of the changes will be calculated, resulting in a spread vector. The same numerical statistical approach when calculating the risk parameters is applied to this vector, i.e. the estimated window size is based on a 99.2% confidence interval. Instruments exposed to the same yield curve will have a logical correlation because only one stressed curve per margin account may be chosen in the margin calculations.
Due to economic and physical reasons, many commodities derivatives are correlated and show high statistical dependence in price dynamics. This dependence can decrease portfolio risks, which should result in lower margin requirements. The commodities derivatives margin model considers dependencies between prices on derivatives with the same underlying (time spread or intra-commodity spread) and dependencies between different groups of products (inter-commodity spread).
Dependence between price increments on the derivatives with the same underlying can be estimated based on statistical properties of price processes and features of delivery procedures. The latter defines additional restrictions on the price dynamics of commodities derivatives and results in the correlation coefficient being a significant factor in estimating the rate of dependence between correspondent price increments. The resulting decrease in margin is defined by the “window method” (see above), where the number of steps from the main scenario is defined by the correlation coefficient between price increments for correspondent derivatives (the higher correlation, the lower deviation from the main scenario). Correlation tables for each risk group are published daily in the parameter file (SPAN-file).
A margin simulation facility is provided in the Genium INET Clearing back-office application and over the open API.
Members can use this facility to get an indicative margin requirement on existing or fictive positions. The margin simulation calculations are based on the same methodology and parameters as the official evening margin calculations. However, it is important to note that the margin simulation is based on current real-time prices at the time of the simulation, and simulating the same position several times may thus give different results as market prices change. The result of the simulation should be seen as an indication of the official margin requirement.
Comprehensive, automated margin backtesting is a crucial element of the validation process. Back-testing, in general, aims to verify and validate that a model or method meets the requirements of its initial design.
The aim of Nasdaq Clearing’s automated margining backtesting functionality is to verify that the margining methodologies that Nasdaq Clearing relies upon are adequate, or in other words, that the margining results are in line with what the margining methodologies are designed to achieve.
Margin requirements are calculated each day by Nasdaq Clearing’s risk margining system Genium Risk. These calculations are based on several assumptions, and it is interesting to investigate how well these assumptions hold up during actual market events. From a risk management perspective, it is essential to verify that the margin requirements are not too low. The principle for Nasdaq Clearing’s margin backtesting is that for each account and margin date, the account's market value is calculated on the position from the margin date but using actual market prices over the assumed liquidation period following the margin date.
These calculations are performed automatically every day for a one-year reference period for all counterparty accounts and instruments. If the backtested market value of an account following the margin date is lower than the margin requirement, a margin breach is understood to have occurred. It should be noted that given the confidence level which Nasdaq Clearing applies in calculating risk interval parameters, margin breaches of counterparty portfolios are expected. But since risk interval parameters are calculated per underlying instrument, the diversity factor of a portfolio will determine if a margin breach occurs when a risk interval parameter is breached (a risk interval parameter breach occurs when an underlying price movement is larger than what the approved risk interval parameter accounts for). The margin backtesting data that is produced is analyzed more comprehensively monthly by Nasdaq Clearing, and the result is reported to the Risk Committee and the Swedish FSA.
In addition, Nasdaq Clearing performs daily backtesting and monitoring of risk parameters. Actual price movements of underlying instruments are compared each day to their corresponding margin parameters. Again, breaches are expected to happen. All breaches are logged, and the reason behind each breach is also noted. Based on the scale and number of breaches and the underlying cause, Risk Management decides if the risk parameter needs to be recalculated or not.
Appendix 13 - Parameter Value List Download Appendix 13 - Parameter Value List
Margin Parameters - Equity and Fixed Income Derivatives Download Margin Parameters - Equity and Fixed Income Derivatives
Commodities Margin Curves View Commodities Margin Curves