Commodity Rounding Discussion Outline

Commodity Rounding Discussion Outline

Prepared by Peter C. Stockman, DTCC

Draft as of August 13, 2008

The recommendations presented for discussion (Section 3) are not consistent with current market practice. They call for more precision in price inputs and intermediate calculations than is maintained by either the ICE eConfirm template or the LEAP rounding recommendations. One rationale for these recommendations is that counterparties agree price sources. The precision with which prices are published is a feature of price data themselves, not a feature of a particular transaction. A second rationale is that hedges and positions will eventually be formulated with greater precision that is reflected in settlement calculations in which inputs and intermediate results are rounded to a fixed precision. This will require change in settlement calculation rounding in the future. The proposal is to change the practice now, rather than latter, as doing so eliminates the negative impact on STP rates that current rounding practices create today.

1. Sources of Errors and Settlement Differences Due to “Rounding”
   
2. Inconsistent rounding of input data
   
3. Price data. Example: Market data provider or exchange publishes daily price with four digits to the right of the decimal. Prior to calculating a monthly average price Counterparty A rounds the daily prices to three decimal places and Counterparty B rounds the daily prices to two decimal places. When these two time series are averaged, slightly different monthly average prices result.

1.1.2.Quantity conversion factors. Example: Counterparty A rounds a quantity conversion factor (e.g. cubic feet to BBL) to four digits to the right of the decimal and Counterparty B rounds the same factor to three digits to the right of the decimal. When applied to quantity inputs with a large number of significant digits different converted quantity amounts result.

1.1.3.Currency conversion factors. Example: Counterparty A rounds a currency conversion factor (e.g. SGD per USD) to four digits to the right of the decimal and Counterparty B rounds the same factor to three digits to the right of the decimal. When the two converted prices are applied to a quantity input with a large number of significant digits different converted settlement amounts result.

1.2.Inconsistent rounding of intermediate calculation results. Example: Counterparty A rounds the monthly average price to four digits to the right of the decimal and Counterparty B rounds to five digits to the right of the decimal. The monthly average price is an intermediate calculation on the way to the final calculation result (a settlement amount). When applied to quantity inputs with a large number of significant digits the two monthly averages produce different settlement quantities.

1.3.Insufficient maintenance of significant digits in intermediate calculations to produce final calculation results that satisfy a standard for precision. Example: The ISDA standard for settlement amounts expressed as currencies calls for the settlement amount to be expressed to a precision equal to the smallest unit of currency available as legal tender[1] (e.g. two decimals or cents in the case of USD or Euro). One or both counterparties use a conversion factor in an intermediate calculation which has only on significant digit (e.g. 0.7). As this is the smallest number of significant digits in the calculation the final result can only be expressed accurately to a precision of one significant digit.

1.4.Inaccurate representation of the precision of input data, intermediate calculation results and final calculation results. Example: quantities are expressed with digits to the right of the decimal rather than as integer quantities (e.g. 10,000.00 BBL versus 10,000 BBL). Because integers carry unlimited significant digits an integer quantity figure will never reduce the number of signicant digits available in the final calculation result. In contrast, representing an integer quantity with decimal places imposes a fixed number of significant digits (seven significant digits in the case of 10,000.00 BBL). This number of significant digits will be the maximum number of significant digits for any calculation involving this quantity.

Example: Two prices are used to calculate a spread: 10.51 and 9.233. The differences between these numbers should be displayed as 1.28, not 1.277. If the difference is to be used in subsequent calculations then the difference is maintained electronically as 1.277 [In the case of addition and subtraction the maximum number of significant digits to the right of the decimal is the lowest number of digits to the right of the decimal in any component of the sum].

1. Target (i.e. More Desireable) Settlement Calculation Environment

The message of this section is that rounding and loss of precision are bad. Why is this the case? As energy derivative markets become more liquid and spreads collapse traders will position or hedge against smaller and smaller economic differences. Rounding numbers which figure in the settlement calculation will produce settlements which do not match the fine-grained economics of the trade. In parallel to this, trades will become larger in order to capture adequate P&L in a low spread environment. Larger trades mean more significant digits in quantity amounts. Large numbers of significant digits exacerbate rounding differences in settlements. We should adopt conventions relating to rounding and precision which accommodate these sorts of changes in the conduct of the markets.

2.1.Original precision of calculation inputs is maintained

2.1.1.Prices: when using price data in a calculation, the number of significant digits in which the price is available from the price source is maintained. For example, if a price (currency per unit of quantity) is available to an accuracy of four significant digits, then that level of precision is maintained whenever that price datum is used in a calculation.

Specifically, if a Commodity Reference Price is specified in the ISDA Commodities Definitions, then the number of significant digits for that commodity is the same as is use in publication specified in the Commodity Definitions.

2.1.2.Conversion factors: factors are expressed in a standard number of significant digits and this level of precision is maintained whenever the conversion factor is used in a calculation.

2.2.Significant digits in intermediate calculations support the final calculation result’s requirement for precision.

2.2.1.If the final settlement calculation result is expressed in a currency amount then the number of significant digits following the decimal maintained in all intermediate calculations and in all inputs is at least one digit greater than the ISDA standard number of digits after the decimal for that currency (that is, available as legal tender).
Ideally, no rounding of intermediate should occur. Only rounding of the final settlement calculation result to the number of digits following the decimal point standard for the particular currency.

2.2.2.If the final settlement calculation result is expressed as a quantity (e.g. BBL, MMBTU) then the number of significant digits maintained in intermediate calculations is at least one digit greater than the number of significant digits required for the quantity in the final settlement calculation result.
An implication of this practice is that conversion factors commonly applied to quantities or prices with a large number of significant digits must themselves be maintained electronically with a large number of significant digits if their use is not to erode the precision of settlement calculations.

2.3.Precision of inputs and final calculation results are accurately represented

2.3.1.Inaccurate representation of the precision of inputs and final calculation results introduces ambiguity regarding the number of significant digits to be maintained in intermediate calculations as well as the number of significant digits to be represented in the final calculation result

2.3.2.Trailing zeros to the right of the decimal should be included in an input only if all trailing zeros to the right of the decimal are significant digits. For example if prices are reported by market data providers to an precision of three decimal points then that input should be displayed and its value maintained electronically with three digits following the decimal: not four digits, not five digits, not rounded to two digits. Integer quantity inputs should be represented as integer numbers not rational numbers. Misrepresenting the number of significant digits in input data produce results in errors in representing output results.

2.3.3.For final calculation results, only significant digits are displayed. At least one extra significant digit is maintained electronically

1. Recommended Rounding and Settlement Calculation Approach [For Discussion]
   
2. Mathematical and scientific rules for maintenance of significant digits and accurately representing precision will be employed in intermediate calculations and final calculation results.
   

While this may appear to be a simple and desirable requirement, it will likely have broad implications for the display of intermediate and final calculation results. Where explicit rounding functions are employed there may be cases where the parameters passed to these existing rounding will need to be modified in order to produce compliant results. [SEE “Rounding LEAP (3) with PCS Comments.xls, the comments highlighted in yellow on select spreadsheet tabs]

3.2.Quantity Conversion Factor Inputs

3.2.1.The source of quantity conversion factors is standardized to [NAME APPROPRIATE TRADE HANDBOOK(S) or ISO standards]. The number of significant digits for the quantity conversion factor found in the standard source will be maintained whenever the factor is applied.

3.2.2.Where there is no standard source for a quantity conversion factor the factor will be confirmed between the counterparties. This factor will be represented and maintained electronically to a precision of six (6) digits to the right of any decimal. If the quantity conversion factor is an integer it will be represented and maintained as an integer.

3.3.Currency Conversion Factor Inputs. Currency conversion factors (currency prices) will be represented and maintained electronically to the same number of significant digits as these prices are published by [NAME OF MARKET DATA PROVIDER(S) and SCREEN NAME/NUMBER]

3.4.Commodity Price Inputs

3.4.1.If a Commodity Reference Price is specified in the ISDA Commodity Definitions, then the number of significant digits for that commodity is the same as is use in publication specified in the Commodity Definitions
This recommendation says that daily prices will not be rounded down to two digits to the right of the decimal prior to averaging. Both ICE eConfirm and the LEAP rounding recommendation call for such intermediate rounding in some cases.

3.4.2.If a Commodity Reference Price is not specified in the ISDA Commodity Definitions, then the counterparties will agree the number of significant digits. This precision will be maintained in all intermediate calculations.

3.5.Calculated Monthly Prices. Per Item 3.1, intermediate calculated prices (e.g. monthly average prices) will be maintained electronically with at least three digits to the right of the decimal.

3.6.Quantities. Unless measured to decimal precision, quantities will be represented as integer numbers. Unless quantity figures carry digits to the right of the decimal they will be assumed to be integer quantities.

1

[1] Article IX of he 2005 Commodity Definitions. It is worth noting that this rounding standard applies only Fixed Amounts, Floating Amounts and Cash Settlement amounts. It does not require all currency denominated quantities (e.g. prices) to be rounded.