# Margining

A key safeguard of CDCC's risk management process is the requirement that Clearing Members post collateral in the form of margin to guarantee the performance of their contract obligations. CDCC's risk-based margin is determined using industry-accepted methods and it is designed to provide the proper levels of protection to cover market movements on open positions and unsettled transactions.

The margin fund's provisions are defined by the initial margin and the variation margin. The initial margin covers the potential losses that may occur over a specified period of time (generally equal to two days) as a result of market fluctuations (this is also known as the Potential Future Exposure or PFE). The variation margin takes into account the portfolio's liquidating value (this is also known as the Replacement Cost or RC), which is managed through CDCC's mark to market daily process.

## Exchange-Traded Derivative Products Margin Calculation

### Initial Margin and Variation Margin

Initial margin deposits serve as collateral to cover the potential losses that may occur from a default as a result of fluctuations in a Clearing Member's portfolio value under normal market conditions.

The variation margin is literally equal to the Clearing Member's portfolio marked to market. At CDCC, each portfolio is marked to market daily. The variation margin for option contracts is collateralized, whereas the variation margin for futures contracts is settled every day.

CDCC uses a confidence level exceeding 99% under the Normal Distribution assumption. CDCC also considers a variable number of days (generally equal to two, for the most liquid product, and up to five days for the less liquid ones) as an acceptable liquidation period. The initial margin amount (also known as margin requirement or base margin) is calculated using the historical volatility of the daily price returns of the portfolio's underlying interests. The CDCC calculates a margin interval (MI) by specifying a critical value, a number of liquidation days and a volatility. The MI is the input parameter used by SPAN® software to calculate the initial margin.

### Margin Interval (MI) Calculation

The Margin Interval calculations are re-evaluated on a regular basis. However, the Corporation may use its discretion and update the Margin Intervals more frequently if necessary. The Margin Intervals are used to calculate the Initial Margin for each Derivative Instrument.

The Margin Interval (MI) is calculated using the following formula:

$$\dpi{100}MI = \alpha * \sqrt{n} * \sigma$$

Where α is equal to the critical value equivalent to 99.87% of the cumulative Normal distribution, n is the number of liquidation days1 and σ is the volatility estimator of the contract's returns and is computed using an exponentially weighted moving average (EWMA) approach.

The implemented formula for the volatility estimator based on the exponentially weighted moving average at any time t is:

$$\dpi{100}\sigma_{t} = \sqrt{(1-\lambda)*\sum_{i=1}^{260}\lambda^{i-1}*(R_{t-i}-\bar{R})^2/(1-\lambda^{260})}$$

Where R is the contract one day price's return, R is the mean return over the specified period and λ is the decay factor. CDCC uses a λ of 0.99.

In addition, CDCC considers a minimal floor for the EWMA volatility estimator defined above. The level of such floor is calculated as an average of daily EWMA volatility estimator observed over the last 10 years. In other words, the volatility estimator that will be used to calculate the MI cannot be lower than the calculated floor.

### Initial Margin Calculation

The initial margin represents the difference between the current market value of a derivative product and its most unfavourable projected liquidation value. This value is obtained by varying the values of the derivative product according to several scenarios representing adverse changes in market conditions.

Using the MI calculated with the above formula, the initial margin determination for options, futures and fixed income contracts is slightly different.

For option contract positions, SPAN® uses the MI to calculate the Price Scan Range (PSR). In order to calculate the most unfavourable projected liquidation value of the option, SPAN® runs several scenarios by varying the underlying value (using the PSR). The PSR used in SPAN® represents the potential variation of the product value. The PSR is calculated by the following formula:

$$\dpi{100}PSR=Underlying\ Price * MI * Contract\ Size$$

The contract size of an option is usually equal to 100.

For futures contract positions, SPAN® uses the MI to calculate the PSR. However, since the price of a futures contract is linear with respect to the price of its underlying, the initial margin for a futures contract is always equal to the PSR. Thus, the initial margin (IM) of a futures contract position is defined as follows:

$$\dpi{100}IM=MI * F * m * p$$

Where MI represents the margin interval, F is the futures contract price, m is the multiplier and p, the net position.

For example, if the price of the near-month Three-Month Canadian Bankers' Acceptance Futures contract (BAX) is \$99.20, its margin interval is 0.19% and its multiplier is 2500, then the margin requirement associated with a 100 contract long position will be:

$$\dpi{100}IM_{100\ BAX}=0.19\% * \99.20 * 2500 * 100=\47,120$$

## Additional Margin Surcharge to Comply with CPSS-IOSCO PFMI (Principle for Market Infrastructure)

### Additional Margin for Concentration Risk

If a Clearing Member defaults, CDCC might be in a situation to liquidate all its positions. In this case, if the defaulter's position is relatively large compared to the regular trading volume, the liquidation process will not necessarily be completed within the default Close-out Period of each product to prevent causing a non-ordinary market impact.

The Concentration Risk methodology will add a number of liquidation day(s) to the default Close-out Period that is applied only for the incremental positions that is above a certain threshold. The thresholds are determined based essentially on the regular trading volume of the product.

### Additional Margin for Wrong Way Risk

The Wrong-way risk is defined by the International Swaps and Derivatives Association (ISDA) as the risk that occurs when "exposure to counterparty is adversely correlated with the credit quality of that counterparty2". In short, it arises when default risk and credit exposure increase together.

For example, a Clearing Member has short put positions on his own company stocks. If this Clearing Member is forced into bankruptcy, his company stocks price will likely decrease significantly, therefore causing a big loss for his Short Put positions and triggering a significant margin call.

CDCC has identified two different situations where the specific wrong-way risk has to be addressed:

• Put Options: CDCC is not going to use SPAN® anymore to calculate the margin requirements for all the Short Options positions that are subject to the wrong-way risk and will charge the full strike value amount instead.
• Unsettled Items: Once the Option is Exercised or expired At-The-Money, it produces an unsettled item margin requirement. The latter is basically composed of the intrinsic value of the Option and the PFE on the option's underlying. In order to address the Specific Wrong-Way Risk, the margin requirement will be equal to the full strike value amount.

### Additional Margin for Mismatched Settlement

The mismatched settlement risk applies to Fixed Income transactions. The Mismatched Settlement Risk is the intraday risk arising from a lag between the settlement of positions that provide a margin offset with other positions and the next calculation of the margin requirement. More specifically, CDCC faces a risk that a Clearing Member settles a position that provides either an Initial Margin offset with other positions or a Variation Margin credit on the rest of the portfolio.

Operationally, the mitigation strategy will consist of a margin call specific to the Mismatched Settlement Risk done right after the 1:15 pm intraday margin run. The margin call amount will be determined so that it represents the worst potential exposure given the potential intraday settlements based on the positions cleared at that time.

Given the fact that margin offsets are granted when Fixed Income portfolios have both longs and shorts positions3, the additional margin charge will be calculated on a gross basis for the positions that could cause mismatched settlement exposure prior to the default.

CDCC considers the Intra-Day Variation Margin Risk as the intra-day risk arising in circumstances in which market volatility or surges in trading volumes produce unusually large Variation Margin (VM) exposures.

In order to address the Intra-Day Variation Margin Risk, CDCC will make punctual margin calls vis-à-vis each Clearing Member if it determines that its intra-day exposure to that Clearing Member exceeds a certain limit in relation to their respective Initial Margin and their Clearing Fund contribution. Thereby, CDCC will compare, on a daily basis: 1) the Clearing Member's Intra-day VM amount to its Initial Margin and 2) the Clearing Member's Intraday VM amount to its Clearing Fund contribution and require, if applicable, punctual margin calls.

The different futures contracts that belong to the same combined commodity generally have positively correlated returns. For example, a portfolio composed of a long position and a short position of two futures contracts that have the same underlying but different expiry dates will be less risky than the sum of the two positions taken individually. Margins on correlated positions aim to address this fact by reducing the initial margin amount for such a portfolio. Intra-commodity (Inter-month) spread charges on correlated futures positions are calculated by CDCC's Risk Management department each month for futures contracts only.

The margin calculation system SPAN® software automatically matches the long positions on futures maturing in a given month with the short positions on futures maturing in another month. The margin on such positions, which is a dollar amount based on the expected price variations between the maturity dates of different contracts, is applied for each combination. This dollar amount is less than the sum of the required margin for each individual position that composes the combination.

In order to determine the intra-commodity spread charge of a futures contract, CDCC performs a backtesting analysis of the historical profit and loss (P&L) for each combination (or portfolio) of a long and a short position of different futures with the same underlying. The backtesting analysis is performed over the last 260 business days and the 99th percentile of the absolute values of the portfolio's P&L is determined for each combination. This method gives the right dollar amount that should cover the potential P&L with a 99% confidence interval.

Because the P&L can be very different for each combination, the P&L that is compared to the margin for the backtesting exercise is weighted with the lowest open interest of the two contracts composing the combination over the total open interest of all contracts that have the same underlying. Hence, the P&L of the combinations with the higher open interest have a higher weight for the overall intra-commodity spread charge calculation.

Similarly, CDCC considers the correlation that exists between different classes of futures contracts when calculating the initial margin. For example, different interest rate futures contracts are likely to react to the same market indicators, but with different results. Accordingly, a portfolio composed of a long position and a short position on two different futures contracts will be less risky than the sum of the two positions taken individually. The CDCC will grant a margin relief according to the historical correlation of the daily returns of the two futures contracts.

When calculating the initial margin on a portfolio with several long and short futures positions, CDCC matches the positions in accordance with predefined steps. For example, if the first matching step consists of matching long or short positions of the front month with long or short positions of the second front month of the same futures contract, any contract that has not been matched will be available for the second matching step. This process is called the Priority Spread process and it is also used for fixed income transactions (cash buy or sell trades and repurchase transactions or repos).

CDCC regularly performs an analysis to determine the initial margin for a long position combined with a short position on two different classes of futures contracts that have a certain economic positive correlation.

To calculate an inter-commodity spread charge, CDCC uses the following method:

• A natural economic relation must exist between the futures contracts subject to an inter-commodity spread charge. For example, the market risk of a long position on a Ten-Year Government of Canada Bond Futures contract (CGB) can be offset partially with a short position on a Two-Year Government of Canada Bond Futures contract (CGZ).
• For each combination, CDCC calculates a hedge ratio between the two contracts. The hedge ratio is defined as a ratio that incorporates the contract size and the yield volatility of one futures position to the contract size and the yield volatility of the other futures position.
• The two-day liquidation period and the three standard deviations are the assumptions that are used to determine the inter-commodity spread charge.
• The margin relief is a percentage determined by the backtesting analysis, in which the daily portfolio's initial margin that is calculated with the formula below is compared to the daily portfolio's P&L. The percentage or the margin relief that covers 99% of the portfolio's P&L is set as margin relief.
• The initial margin (IM) for each combination is calculated as follows:
$$\dpi{100}IM_{Total}=(IM_{Position\ 1}+IM_{Position\ 2}) * (1-Margin\ Relief)$$
• If a futures contract is not matched under a specific hedge ratio, the remaining position is margined as an outright position.
• Inter-commodity spread charges are reviewed on a quarterly basis.

## Customized Derivative Instruments Margin Calculation (Converge®)

In essence, the method used to calculate margins for customized derivative instruments (other than fixed income transactions) and exchange-traded derivative products is identical. However, because customized derivative instruments are usually less liquid than exchange-traded derivative products, CDCC may use a different number of days of liquidation to calculate customized derivative instrument margins.

Also, when clearing physically settled OTC instruments, CDCC applies a liquidity-related risk premium, because the underlying interest of OTC instruments is usually less liquid. The liquidity risk premium is computed based on the historical bid/ask spreads of the underlying interest.

## Fixed Income Transactions Margin Calculation

### Conventional Repo Transactions

As for other products cleared by CDCC, Clearing Members are required to pledge collateral in favour of CDCC to cover the potential losses that could occur as a result of market movements with respect to their repurchase transactions. The margin requirement is valued at night and during the day using the SPAN® software. The margin requirement for repurchase transactions is comprised of various components to assure that fixed income clearing is supported by a sound risk management foundation. They are the following:

• Unsettled Items Margin (UI)
• Mark to market of the outstanding open position (MTM)
• Potential Future Exposure (PFE)

#### Unsettled Items Margin (UI)

Settlement of the first leg of a repurchase transaction occurs by an exchange of the purchase price against the purchased securities at CDS. CDCC is exposed on either side of the repurchase transaction with respect to the value of the purchased securities during the term of the repurchase transaction. It is exposed to the Reverse Repo Party if and when the value of the purchased securities increases, and to the Repo Party if and when the value of the purchased securities decreases.

The amount of the UI is the difference at any given time a valuation is made by CDCC between the market value of the purchased securities and the purchase price and shall be credited to the Repo Party's margin deposits (in the account where the relevant repurchase transaction resides) and debited from the Reverse Repo Party's margin deposits (in the account where the relevant repurchase transaction resides) if and when the current market value exceeds the purchase price, and the other way around if and when the purchase price exceeds the current market value.

#### Mark to Market of the Outstanding Open Position (MTM)

In order to minimize the credit risk borne by CDCC, the mark to market (MTM) process is used to ensure that the spread between the repo rate and the current Canadian Overnight Repo Rate (CORRA) is zero at the end of each trading day. The MTM repo rate payments essentially transfer any losses due to market movements in repo rates from one party to another. Each open position will need to be marked to market on a daily basis with the resulting net cash movements settling during the following morning settlement cycle (consistent with current processing).

The MTM repo rate payment calculation works as follows: during the term of a repurchase transaction, if the CORRA rate decreases, the Repo Party has to pay the difference of the initial (or previous) repo rate and the new CORRA rate; whereas if the CORRA rate increases, the Reverse Repo Party has to pay the difference of the new CORRA rate and the initial (or previous) repo rate. At the end of each business day, CDCC calculates with respect to each fixed income Clearing Member, the net MTM repo rate payment which is due or payable in accordance with Subsection D-606(5) of the CDCC Rules.

At the end of the business day preceding the repurchase date of a repurchase transaction, the net MTM Reversal Requirement is calculated in accordance with Subsection D-606(6) of the CDCC Rules, and the Net OCF MTM Payment (which compensates the Clearing Member that paid more MTM repo rate payments over the life of a given repurchase transaction) is calculated in accordance with Subsection D-606(7) of the CDCC Rules.

This MTM process serves to ensure that in the event a Clearing Member becomes non-conforming, CDCC will be able to replace the non-conforming Clearing Member's repurchase transaction(s) without incurring additional losses beyond the current valuation.

#### Potential Future Exposure (PFE)

In order to properly quantify the PFE (or margin requirement) with SPAN®, it is necessary to translate the repurchase transactions into their Futures contract equivalents. In order to accomplish this and obtain margin results which are representative of the net open position, the following process needs to be followed:

• Define the specifications of the "Virtual Futures Contract(s)" (VFC) that will be used to model the repurchase transaction;
• Use a "bucketing" process for the future cash flows on the repurchase transaction. In other words the repurchase transaction will be divided in one of more equivalent VFC, depending on the term of the repurchase transaction;
• Determine the forward rates that are consistent with the dates assigned to each VFC during the "bucketing process";
• Determine the net position in the VFC that will be sent to SPAN® on a daily basis.

After the futures contract equivalency has been determined for a repurchase transaction, the SPAN® records need to be created for the VFCxx, with xx being the month of the VFC. The business need is to be able to call for margin deposits on the following basis:

• Outright futures position on each created VFCxx;
• Intra-commodity spreads for VFCxx (spreads on long-short combinations for VFCxx positions on different days);
• Inter-commodity spreads for VFCxx – and other contracts listed at the Montréal Exchange, for example ONX or BAX.

These calculations will follow the same processes the CDCC currently has in place for Exchange transactions (margin intervals and the application to the margin deposits and Clearing Fund).

Besides the VFC valuations set forth above, CDCC will also calculate the risk associated to the security being exchanged. The procedure to calculate this risk will be the same used for Cash Buy or Sell Trades (refer to the "Potential Future Exposure" below).

Because settlement of cash buy or sell trades takes place on 1, 2 or 3 business days after the trade date, depending on the characteristics of the security being cleared through CDCC, there is a risk that one or both Clearing Members involved in the trade will default and wil not be able to fulfill their settlement obligations. To mitigate this risk, CDCC will ask the Clearing Members to deposit margin between the trade date and the relevant settlement time. The amount of margin is composed of two parts:

• Unsettled Items Margin (UI): The difference between the market value of the security and the purchase price needs to be collateralized.
• Potential Future Exposure (PFE): This is the SPAN component and it deals with potential movements in the fixed income security's price for the time it would take CDCC to liquidate the entire position in the market.

#### Unsettled Items Margin

The same process as set forth above in the "Unsettled Items Margin" section of the Conventional Repo Transactions part, the UI shall apply to cash buy or sell trades between the trade date and the date on which it settles (i.e., 1, 2 or 3 business days later). It shall be calculated daily as the difference between the purchase price and the current market value of the purchased securities and shall be payable by the seller to CDCC (which in turn shall credit such amount in favour of the buyer) if the market value goes up or by the buyer to CDCC (which in turn shall credit such amount in favour of the seller) if the market value goes down.

#### Potential Future Exposure

Potential Future Exposure (PFE) is used to mitigate the liquidation risk that exists with respect to the number of days it could take to liquidate a given position in the markets. To simplify calculations and allow margin offsets between securities, CDCC will create different buckets of securities that have similar characteristics. In other words if the buckets are defined as: Bucket 1: 0-1 year to maturity date, Bucket 2: 1-3 years to maturity date, Bucket 3: 3-7 years to maturity date, and Bucket 4: 7 and more years to maturity date, and the security underlying the repurchase transaction has a maturity of 3.5 years, then the security will belong to Bucket 3.

Therefore all the bonds within one bucket will share the same Margin interval. The PFE will be equal to the margin interval of the bucket, multiplied by the price, the duration and the contract size of the security. Moreover, CDCC uses a fixed duration set to 0.25, 0.5 and 1 for the securities that belong to the 3-month, 6-month and 1-year buckets respectively.

For fixed income clearing, every security will be assigned to one bucket. Thus, CDCC will calculate and give a spread (as a percentage) for any combination of a long position with a short position that belong to two different buckets. Therefore for one Clearing Member having a long position on Bucket 1 and a short position on Bucket 2 the margin requirement will be equal to:

$$\dpi{100}(PFE_{Bucket\ 1}+PFE_{Bucket\ 2}) * (1-Spread)$$

The spread is based on the correlation between the relevant buckets.