Appendix 1 - VMIM Algorithm Examples

In Example 1 below, the price at which the most contracts are matched is $1.96 (400 contracts) and as a result the equilibrium price is $1.96. Since there is only a single price that maximizes the matched contracts, that price is selected as the VMIM price.

Example 1 - Simple VMIM Price Calculation

In Example 2 below, multiple prices are associated with the same maximum number of matched contracts. In this scenario the price with the minimum imbalance is selected as the VMIM price. In this example, both the $1.97 and $1.96 price levels result in 400 contracts being executed. Since there is a 4,000 contract sell imbalance at the $1.97 price level and a zero imbalance at the $1.96 price level, the system will select $1.96 as the VMIM price.

Example 2 - Imbalance Minimizing Price

In Example 3 below, which includes a market order to sell 100 contracts, multiple prices are associated with the same maximum number of matched contracts and the same absolute non-zero imbalance. In this case the VMIM algorithm selects the highest price in the range since the sign of the imbalance is positive, which is $1.97.

Example 3 - Imbalance Sign-based Tie Breaker

Example 4 below includes market orders with a quantity of 100 to buy and sell. The result is that there is a set of prices (1.95, 1.96 and 1.97) that all maximize the matched contracts and minimize the imbalance, which is zero. Further, assume that the prevailing collar midpoint is $1.90. The VMIM algorithm selects the price closest the to the Volume-Based Tie Breaker, which is the collar midpoint ($1.90). As a result, the opening price is $1.95.

Example 4 - Volume-based Tie Breaker

Example 5 below shows a $0.30 wide collar centered on the midpoint price of $0.85. The matched contract maximizing price of $1.10 exceeds the upper collar price of $1.00. As a result, the VMIM algorithm restricts focus to the prices within the collar range. In this example, both $0.95 and $1.00 both maximize matched contracts (10) with minimized absolute imbalance (10). As a result, the sign of the imbalance (positive) is used to select the upper price of $1.00 as the opening price.

Example 5 - Collared Price with Positive Imbalance Sign-based Tie-breaker

In Example 6 below, the matched contract maximizing price of $0.60 violates the lower collar price of $0.70. As a result the VMIM, the VMIM algorithm restricts focus to the prices within the collar range. In this example the prices from $0.70, $0.75 and $0.80 all maximize matched contracts with minimized absolute imbalance of negative 10. As a result, the sign of the imbalance (negative) is used to select from the lower price of $0.70 as the opening price.

Example 6 - Collared Price with Negative Imbalance Sign-based Tie-breaker

In Example 7 below, all prices shown result in the same number of matched contracts but only the prices $0.65, $0.70 and $0.75 minimize the absolute imbalance, and in this case the imbalance associated with these prices is zero. The VMIM algorithm selects the price within the collar that is closest to the Volume-Based Tie Breaker, which is the midpoint of the prevailing collar ($0.85). As a result, the selected opening price is $0.75.

Example 7 - Collared Price with Zero Imbalance Volume-based Tie-breaker