Calculations

Supposing that we have following information:

// copyright: www.idogicat.com

class MarketOrder {
    private String orderId;
    private String parentOrderId;
    private double price;
    private double qty;
    // ...
}

class ParentOrder {
    private String orderId;
    private String clientId;
    private String basketId; // in case we need to aggregate per basket...
    private Instrument instr;
    private String side;  // 'B', 'S', 'SS' (or use enumerate...)
    private double qty;
    private double limitPrice;
    private double execQty;  // sum of qty's of all market orders
    private double benchmark;

    private double notionalExecValue;
    private double notionalExecPrice;
    private double pl;
    private double plCps; // P & L in cps
    private double plBps; // P & L in bps

    // market orders
    private ArrayList<MarketOrder> marketOrders;

    // many methods are omitted

    private int getSideSign() {
        if(side.equals('B'))  return 1;
        else  return -1;
    }

    private void calcNotionalExecValue() {
        notionalExecValue= 0;
        for(MarketOrder order : marketOrders) {
            notionalExecValue+= order.getPrice() * order.getQty();
        }
    }

    private void calcNotionalExecPrice() {
        notionalExecPrice = notionalExecValue / execQty;
    }

    private void calcPL() {
        pl = getSideSign() * (benchmark * execQty - execValue);
    }

    private void calcPlInCps() {
        plCps = pl / execQty;
    }

    private void calcPlInBps() {
        plBps = pl * 10000 / (execQty * benchmark)
    }
    
}

class Instrument {
    private String ric;
    private double lotSize;
    private double adv;
    private double mktCap;

    // many methods omitted...

    public double getVwap(Date date);
    public double getTimedVwap(Date date, Time from, Time to);
}

Basic Calculations

Calculate deviation & standard deviation of all orders in a group (as described previously under 'Groups'):

All parent orders in the group form an order set O, any parent order in O is written as o(i):

Define two weights: w₁(i) and w₂(i): the former is for calc in cps; the latter is for bps:

where q_e(i) is executed quantities, and b(i) is benchmark of parent order o(i).

So we have average deviation of P & L of all orders in O:

where μ₁ is in cps, while μ₂ is in bps; d₁ is po.plCps, d₂ is po.plBps.

Standard deviations of P & L of all orders in O:

Performance Improvement

If we need to calculate for more than one order sets, as well as total orders, then we can use the following way to avoid repeated calculations:

Supposing that we have a collection of disjoint order sets:

then we can calculate total number of parent orders n_A, total weights w_A, population mean of all parent orders μ_A, and population standard deviation of all parent orders σ_A in following way:

First, calculate the values for each of the order set, and store the calculated results; then use the stored results and following formulas to calculate values for set A.