/EIE

Poisson intensity of limit order execution, calibration of parameters A and k using level 1 tick data

Primary LanguageJava

Poisson intensity of limit order execution, calibration of parameters A and k using level 1 tick data

Description

A limit order placed at a price St ± δ, has the instantaneous probability of execution λ(δ)dt where the intensity λ(δ) is given by:

λ(δ) = A e -kδ

λ - Poisson order execution intensity
δ - spread (distance from mid price St)
A - parameter, positively related to trading intensity
k - parameter, positively related to market depth

Package Execution Intensity Estimator (EIE) contains single and multi threaded calibration procedure of A and k parameters. Methods that calculate intensity λ(δ, A, k) and spread δ(λ, A, k) are provided as well. Algorithm operates on level 1 tick data, therefore it is suitable in a setting where liquidity is not fully observable (i.e. dark pools). Calibration is two step procedure performed separately for buy and sell limit orders.

Steps:

  • For each spread δk of N predefined spreads (δ0 , δ1 , δ2 , ... δN-1) estimate execution intensity λ(δk) using "waiting time" approach described in [1] 4.4.2.. Result of this step is set of N points (δk , λ(δk)) on empirical Spread Intensity Curve (SIC)
  • Estimate A and k based on N points from previous step. This can be achieved by various approaches. Code implements two approaches described in [2] 3.2:
    • LOG_REGRESSION performs OLS regression of log(λk) on δk. Finally k = -slope and A = e intercept
    • MULTI_CURVE from set of N points creates Ns = (N*(N-1))/2 unique pairs fo points ((δx , λx) , (δy , λy)). For each set of points solves the following set of equations for A' and k' :
      λx = A' e -k'δx
      λy = A' e -k'δy
      Final estimates are A = mean(A'1 , A'2 , ... A'Ns) and k = mean(k'1 , k'2 , ... k'Ns)

Once A and k are calibrated, depending on context of usage, user can specify:

  • spread δ to obtain corresponding intensity λ(δ)
  • intensity λ to obtain corresponding spread δ(λ)


    gamma-surface

Usage

  • Configuration parameters
    double spreadStep = 0.00001;  // increment of spread, greater than or equal to tick size
    int nSpreads  = 10; // number of spread increments, greater than 2
    long w = 3600000; // 60 min,  width of estimators sliding window
    long dt = 10000 //  10 seconds, time scaling
  • Create an instance of AkSolverFactory and specify SolverType
  • Create an instance of FillRateEstimator
    AkSolverFactory sf = new AkSolverFactory(SolverType.MULTI_CURVE);    
    IntensityEstimator ie = new IntensityEstimator(spreadStep, nSpreads, w, dt, sf);
  • Pass an instance of ExecutorService to EstimationExecutor. Ensure minimum number of 5 threads is available. This step is required only for multithreaded estimation.
    EstimationExecutor.setExecutor(executorService);
  • Pass data (bid, ask, timestamp) to the instance of FillRateEstimator with onTick/onTickAsync call
  • Run parameter estimates with estimate/estimateAsync call
    while(loop){
        ...
        // pass tick data to estimator
        Future<Boolean> tickResult = ie.onTickAsync(bid, ask, timeStamp);
        ...

        if (tickResult.get()) { // check if estimator can be called            
            Future<IntensityInfo> result = ie.estimateAsync(timeStamp);
            ...
            
            IntensityInfo intensityInfo =result.get();
            ...
  • Returned IntensityInfo instance gives access to parameters A and k for both buy and sell orders. Intensities λ(δ) and Spreads δ(λ) are returned by corresponding public methods.

Note:

  • More details on usage and configuration can be found in IntensityEstimatorTest and javadoc comments
  • Detailed test output is saved to target/intensity-log/ folder
  • Single threaded outperforms multithreaded execution when less complex configurations are used

References