iStarPostTrade: The Kissell-Malamut _I-Star_ Market Impact model

In braverock/blotter: Tools for Transaction-Oriented Trading Systems P&L

The Kissell-Malamut I-Star Market Impact model

Description

The model is a cost allocation method to quantify the market impact of financial transactions, depending on an agent order size relative to the market volume; in the authors words is theoretically based on the supply-demand principle, although it may be rather difficult to express ourselves precisely in these terms and even so our interpretations may differ by the several possible scenarios that take place into the market in response to imbalances.

Usage

iStarPostTrade(MktData, sessions = NULL, yrBizdays = 250,
  horizon = 30, xtsfy = FALSE, grouping = FALSE, groupsBounds,
  minGroupDps, paramsBounds, paramsInit, OrdData, ...)

Arguments

MktData	A list of xts objects, each representing a security market data. See 'Details'
sessions	A character or a vector of character representing ISO time subsets to split each trading day in "sessions". If not specified, sessions will be assumed to be on a daily basis
yrBizdays	A numeric value, the number of business days in a given year data refers to. Default is 250 days
horizon	A numeric value, the number of sessions to compute the rolling variables over. Default is 30. See 'Details'
xtsfy	A boolean specifying whether the rolling variables computed should become xts object with consistent dates
grouping	A boolean or vector of booleans to specifying whether to group datapoints. Eventually, the second element specifies whether to average group values. Attention: the grouping may discard data. See 'Details'
groupsBounds	A vector with named elements being 'ImSize', 'POV', 'Vol'. They have to be increasing sequences expressing the respective variable bounds, which are used to build datapoints groups. See 'Details'
minGroupDps	A numeric value, the minimum number of datapoints a group should have to be included in the estimation process. Default is 25. See 'Details'
paramsBounds	A matrix providing model parameters bounds to pass to nls. Parameters are considered by row and columns represents lower and upper bounds, respectively. See 'Details'
paramsInit	A list providing model paramaters initial values to pass to nls. Elements should be named with the corresponding parameter, i.e. 'a_1', 'a_2', 'a_3', 'a_4' and 'b_1'. See 'Details'
OrdData	A data.frame providing custom order data specifics to estimate the impacts for, with required columns 'Side', 'Size', 'ArrPrice', 'AvgExecPrice', 'POV' and 'AnnualVol'. Or a list consisting of 'Order.Data' and 'Params' items. See 'Details'
...	Any other passthrough parameter

Details

Theoretically the I-Star model can be estimated using private order data for which one intends to estimate the impact costs. The main limitations of this approach are: on one hand the lack of data and the effect of neglecting the effect of wider market movements than the ones of the single security on which the order was placed, on the other it may include potential opportunistic trading biases. Based on these considerations we follow Kissell's main discussion line, focusing on the use of market "tic data" and derived quantities that represent proxies of the corresponding order-related variables.

The MktData input dataset must be a list, with items being market data by security considered. These items must be named to match the security they refer to. Each item is required to be an xts object having at least 'MktPrice' and 'MktQty' columns. For theoretical accuracy of the arrival price it is recommended to input 'Bid' and 'Ask' columns as well. Similarly, providing a 'Reason' column allows to have trades classified by your preferred criterion; when this data is not available the Lee-Ready tick test will be used to infer the trade direction. If the MktData list provided has items with different number of observations, then data considered will be only until to match the item with the smallest number of observations. Also, beware that to avoid strict restrictions on potentially mismatching intraday timestamps there is no timestamps complete matching, therefore: provide a dataset with securities included observed on the same number of unique days, consistently across the full dataset. Our best suggestion is to use a data set within the same timeframe and including the same number of days for each security involved in the analysis.

The horizon should be chosen according to the number of sessions a trading day is splitted into.

Parameters groupsBounds and minGroupDps regulate the grouping process. minGroupDps of each group has to be reached in order to let its datapoints be included in the estimation process. It dafaults to 25 datapoints, as suggested by the author. However, this appears to be a rule of thumb, as the parameter largerly depends on the given original dataset and on others parameters such as the sessions and horizon specifications. groupsBounds defaults to the following sequences:

Imbalance Size	0.005, 0.01, 0.02, ..., 0.3
Annualized volatility	0.1, 0.2, ..., 0.8
POV	0.01, 0.05, 0.1, ..., 0.65

Where each interval is considered to be left opened and right closed. Again, these values are suggested by the author and appear to come from empirical findings.

For the estimation we use nls, specifying the algorithm = 'port' in order to implement the constrained problem the author proposes. Parameters starting values are provided with paramsInit, if missing they are chosen to be their respective lower bound. Note that specified values must be included in the corresponding paramsBounds. If missing, default values for the bounds are:

100 <= a_1 <= 1000

0.1 <= a_2 <= 1

0.1 <= a_3 <= 1

0.1 <= a_4 <= 1

0.7 <= b_1 <= 1

Note that by definition 0 <= b_1 <= 1, however the author reports using 0.7 as an empirical value. Nonetheless, the user if left free to specify desired parameters bounds via paramBounds, where the rows must follow a_1, a_2, a_3, a_4 and b_1 order or be named accordingly.

OrdData can be a data.frame or list. When it is a data.frame, OrdData columns are required to be: 'Side', a numeric value being 1 ("buy") or -1 ("sell"); 'Size', the order size expressed in terms of , that is the ratio between the total number of traded units and that the ADV on the day the order was traded ; 'ArrPrice', a numeric value expressing the price of the traded security (for theoretical accuracy it is recommended to use the corresponding bid-ask spreads midpoint); 'AvgExecPrice', specifying the average execution price over the order lifetime; the 'POV' of and the 'AnnualVol', the order percentage of volume and annualized volatility respectively. Whereas, when OrdData is a list it has to contain two named elements: 'Order.Data', a data.frame with the same characteristics as above and 'Params', a vector consisting of named elements being the paramaters to use in the I-Star equations to compute the impact costs and the error measures. This is useful in cases one already has estimated parameters for the model or simply wants to see what I-Star model values would look like with different paramaters, perhaps those coming from the sensitivity analysis carried with iStarSensitivity.

Author(s)

Vito Lestingi

References

The Science of Algorithmic Trading and Portfolio Management (Kissell, 2013), Elsevier Science. A Practical Framework for Estimating Transaction Costs and Developing Optimal Trading Strategies to Achieve Best Execution (Kissell, Glantz and Malamut, 2004), Finance Research Letters. Inferring Trade Direction from Intraday Data (Lee and Ready, 1991), The Journal of Finance. Modern Applied Statistics with S (Venables and Ripley, 2002), Springer.

See Also

Return.calculate, sd.annualized, nls

braverock/blotter documentation built on Feb. 13, 2023, 1 p.m.