R/simulate.R
In simonsays1980/bayespin: An R package for Bayesian estimation of the probability of informed trading
## Load the dynamic library
#' @useDynLib bayespin
#' @importFrom Rcpp sourceCpp
NULL
#' @details
#' `bayespin` implements the statistical methods for estimating the probability
#' of informed trading (PIN) with a Bayesian approach as proposed by Grammig et al.
#' (2015). This should simplify the usage of this rather complicated estimation
#' procedure and offers researchers an API that is easy to integrate, stable,
#' and fast in performance.
#'
#' The model by Grammig et al. (2015) comes along with some advantages in
#' comparison to the original model of Easley et al. (1996) and other Bayesian
#' approaches found in literature:
#' 1. It uses only the number of trades per day instead of the number of
#' seller- and buyer-initiated trades used by other approaches. This enables
#' the researcher to collect data more easily - also for historical horizons
#' and leads to less bias in case trade initiation must be estimated by
#' using the Lee and Ready (1991) algorithm.
#' 2. The Bayesian estimation of the PIN measure is found to be more stable
#' especially when it comes to very large trading volumes as they occur on
#' modern markets.
#' 3. Especially in settings where the rates of informed trading, `mu` and/or
#' the probability of information events are very small Bayesian estimation of
#' the underlying finite mixture distribution leads to more robust parameter
#' estimates.
#'
#' The package makes use of high-performance C++ algorithms for MCMC sampling
#' for finite mixture distributions offered by the
#' \href{https://github.com/simonsays1980/finmix}{`finmix`}
#' package. Model estimation with a simple `K-means` relabeling takes around
#' 4-6 seconds.
#'
#' ## Implementation of other estimation approaches
#' In addition to the Bayesian estimation approach from Grammig et al. (2015)
#' the `bayespin` package also implements several other methods to compute
#' the probability of informed trading:
#' * the original maximum likelihood procedure of the model by Easley et al.
#' (1996),
#' * the maximum likelihood procedure of the model by Jackson (2007) that also
#' uses solely the number of trades per trading day (this is similar to
#' Grammig et al. (2015))
#' These models were implemented to ease their use by researchers and to enable
#' comparisons between different models and estimation approaches.
#'
#' @references
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Jackson, D., 2007. Infering trader behavior from transaction data: A trade
#' count model. Journal of Computational and Graphical Statistics 12, 55-79.
#' * Lee, C., Ready, M. J., 1991. Inferring trade direction from intraday data.
#' The Journal of Finance 46, 733-746.
"_PACKAGE"
#' Simulates trades data
#'
#' @description
#' Simulates trades data from the model by Easley, Kiefer, O'Hara and Paperman
#' (1996). The simulation function is implemented in C++ and allows therefore
#' usage in specific performance-sensitive scenarios, like simulating huge
#' amounts of trade data or calling this function repeatedly in large
#' simulations.
#'
#' @details
#' The functions returns a `data.frame` with named columns `MisBuy`, `MisSell`,
#' `Buy`, `Sell`, and `Trades`. `Buy` and `Sell` are the number of buy and sell
#' trades per trading day and `Trades` defines the sum of these amounts.
#' `MisBuy` and `MisSell` are only added to allow for a standardization of
#' input data to the estimation functions of the `bayespin` package. The
#' corresponding simulation function [simulate_ekop_mis()] simulates
#' mis-specified trades data and returns in the fields `MisBuy` and `MisSell`
#' the number of mis-specified buy and sell trades per trading day respectively.
#'
#' @param size An integer specifying the number of trading days that should
#' be simulated.
#' @param alpha A double specifying the probability of an information event.
#' @param epsilon A double specifying the arrival rate of uninformed traders.
#' @param delta A double specifying the probability of information being good
#' or bad.
#' @param mu A double specifying the arrival rate of informed traders.
#' @param T A double defining the length of a trading day in minutes.
#' @return A `data.frame` containing the trades per day.
#' @export
#'
#' @examples
#' # Simulate trades data for 1000 trading dates with a trading day lasting
#' # 6.5 hours.
#' trades_data <- simulate_ekop(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5)
#' head(trades_data)
#'
#' @seealso
#' * [simulate_ekop_mis()] for simulating mis-specified trades data
#'
#' @references
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
"simulate_ekop" <- function(size = 1000, alpha = 0.2, epsilon = 0.2,
delta = 0.5, mu = 0.02, T = 60 * 6.5)
{
trade.sample <- simulateEKOP_cc(as.integer(size), as.double(alpha),
as.double(epsilon), as.double(delta),
as.double(mu), as.double(T))
cnames <- c("MisBuy", "MisSell", "Buy", "Sell", "Trades")
trade.sample <- data.frame(trade.sample)
colnames(trade.sample) <- cnames
return(trade.sample)
}
#' Simulates mis-specified trades data
#'
#' @description
#' Simulates mis-specified trades data from the model by Easley, Kiefer, O'Hara
#' and Paperman (1996). The simulation function is implemented in C++ and allows
#' therefore usage in specific performance-sensitive scenarios, like simulating
#' huge amounts of trade data or calling this function repeatedly in large
#' simulations.
#'
#' @details
#' The functions returns a `data.frame` with named columns `MisBuy`, `MisSell`,
#' `Buy`, `Sell`, and `Trades`. `Buy` and `Sell` are the number of buy and sell
#' trades per trading day and `Trades` defines the sum of these amounts.
#' `MisBuy` and `MisSell` define the number of mis-specified buy and sell
#' trades per trading day respectively.
#'
#' @param size An integer specifying the number of trading days that should
#' be simulated.
#' @param alpha A double specifying the probability of an information event.
#' @param epsilon A double specifying the arrival rate of uninformed traders.
#' @param delta A double specifying the probability of information being good
#' or bad.
#' @param mu A double specifying the arrival rate of informed traders.
#' @param T A double defining the length of a trading day in minutes.
#' @param mis A double specifying the mis-sepcification rate for trades.
#' @return A `data.frame` containing the trades per day.
#' @export
#'
#' @examples
#' # Simulate mis-specifed trades data for 1000 trading dates with a trading
#' # day lasting 6.5 hours.
#' trades_data <- simulate_ekop_mis(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5, mis = .1)
#' head(trades_data)
#'
#' @seealso
#' * [simulate_ekop()] for simulating trades data without mis-specification
#' * [correct_trades()] to reconstruct original trades data from mis-specified
#' ones
#'
#' @references
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
"simulate_ekop_mis" <- function(size = 1000, alpha = 0.2, epsilon = 0.2,
delta = 0.5, mu = 0.02, T = 60 * 6.5,
mis = 0.15)
{
trade.sample <- simulateEKOPMis_cc(as.integer(size), as.double(alpha),
as.double(epsilon), as.double(delta),
as.double(mu), as.double(mis),
as.double(T))
cnames <- c("MisBuy", "MisSell", "Buy", "Sell", "Trades")
trade.sample <- data.frame(trade.sample)
colnames(trade.sample) <- cnames
return(trade.sample)
}
#' Corrects mis-specified trades data
#'
#' @description
#' Calling [correct_trades()] on simulated mis-specified trades data corrects
#' the mis-specifications. This becomes handy when using simulated data in
#' comparison studies of e.g. estimators, etc.
#'
#' @details
#' Mis-specified trades are recorded in the columns `MisBuy` and `MisSell` for
#' buy and sell trades respectively. This information is used to re-construct
#' the well-specified trades data.
#'
#' @param trades A `data.frame` containing the trades data. This must have the
#' columns `MisBuy`, `MisSell`, `Buy`, and `Sell` specified.
#' @return A `data.frame` containing the re-constructed well-specified trades
#' data.
#' @export
#'
#' @examples
#' # Simulate mis-specifed trades data for 1000 trading dates with a trading
#' # day lasting 6.5 hours.
#' trades_data <- simulate_ekop_mis(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5, mis = .1)
#' trades_data_corr <- correct_trades(trades = trades_data)
#' head(trades_data_corr)
#'
#' @seealso
#' * [simulate_ekop_mis()] for simulating trades data with mis-specification
#' * [simulate_ekop()] for simulating trades data without mis-specification
"correct_trades" <- function(trades)
{
trades$Buy <- trades$Buy - trades$MisBuy + trades$MisSell
trades$Sell <- trades$Sell - trades$MisSell + trades$MisBuy
trades$MisBuy <- 0
trades$MisSell <- 0
return(trades)
}
simonsays1980/bayespin documentation built on Dec. 23, 2021, 2:25 a.m.
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## Load the dynamic library
#' @useDynLib bayespin
#' @importFrom Rcpp sourceCpp
NULL
#' @details
#' `bayespin` implements the statistical methods for estimating the probability
#' of informed trading (PIN) with a Bayesian approach as proposed by Grammig et al.
#' (2015). This should simplify the usage of this rather complicated estimation
#' procedure and offers researchers an API that is easy to integrate, stable,
#' and fast in performance.
#'
#' The model by Grammig et al. (2015) comes along with some advantages in
#' comparison to the original model of Easley et al. (1996) and other Bayesian
#' approaches found in literature:
#' 1. It uses only the number of trades per day instead of the number of
#' seller- and buyer-initiated trades used by other approaches. This enables
#' the researcher to collect data more easily - also for historical horizons
#' and leads to less bias in case trade initiation must be estimated by
#' using the Lee and Ready (1991) algorithm.
#' 2. The Bayesian estimation of the PIN measure is found to be more stable
#' especially when it comes to very large trading volumes as they occur on
#' modern markets.
#' 3. Especially in settings where the rates of informed trading, `mu` and/or
#' the probability of information events are very small Bayesian estimation of
#' the underlying finite mixture distribution leads to more robust parameter
#' estimates.
#'
#' The package makes use of high-performance C++ algorithms for MCMC sampling
#' for finite mixture distributions offered by the
#' \href{https://github.com/simonsays1980/finmix}{`finmix`}
#' package. Model estimation with a simple `K-means` relabeling takes around
#' 4-6 seconds.
#'
#' ## Implementation of other estimation approaches
#' In addition to the Bayesian estimation approach from Grammig et al. (2015)
#' the `bayespin` package also implements several other methods to compute
#' the probability of informed trading:
#' * the original maximum likelihood procedure of the model by Easley et al.
#' (1996),
#' * the maximum likelihood procedure of the model by Jackson (2007) that also
#' uses solely the number of trades per trading day (this is similar to
#' Grammig et al. (2015))
#' These models were implemented to ease their use by researchers and to enable
#' comparisons between different models and estimation approaches.
#'
#' @references
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Jackson, D., 2007. Infering trader behavior from transaction data: A trade
#' count model. Journal of Computational and Graphical Statistics 12, 55-79.
#' * Lee, C., Ready, M. J., 1991. Inferring trade direction from intraday data.
#' The Journal of Finance 46, 733-746.
"_PACKAGE"
#' Simulates trades data
#'
#' @description
#' Simulates trades data from the model by Easley, Kiefer, O'Hara and Paperman
#' (1996). The simulation function is implemented in C++ and allows therefore
#' usage in specific performance-sensitive scenarios, like simulating huge
#' amounts of trade data or calling this function repeatedly in large
#' simulations.
#'
#' @details
#' The functions returns a `data.frame` with named columns `MisBuy`, `MisSell`,
#' `Buy`, `Sell`, and `Trades`. `Buy` and `Sell` are the number of buy and sell
#' trades per trading day and `Trades` defines the sum of these amounts.
#' `MisBuy` and `MisSell` are only added to allow for a standardization of
#' input data to the estimation functions of the `bayespin` package. The
#' corresponding simulation function [simulate_ekop_mis()] simulates
#' mis-specified trades data and returns in the fields `MisBuy` and `MisSell`
#' the number of mis-specified buy and sell trades per trading day respectively.
#'
#' @param size An integer specifying the number of trading days that should
#' be simulated.
#' @param alpha A double specifying the probability of an information event.
#' @param epsilon A double specifying the arrival rate of uninformed traders.
#' @param delta A double specifying the probability of information being good
#' or bad.
#' @param mu A double specifying the arrival rate of informed traders.
#' @param T A double defining the length of a trading day in minutes.
#' @return A `data.frame` containing the trades per day.
#' @export
#'
#' @examples
#' # Simulate trades data for 1000 trading dates with a trading day lasting
#' # 6.5 hours.
#' trades_data <- simulate_ekop(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5)
#' head(trades_data)
#'
#' @seealso
#' * [simulate_ekop_mis()] for simulating mis-specified trades data
#'
#' @references
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
"simulate_ekop" <- function(size = 1000, alpha = 0.2, epsilon = 0.2,
delta = 0.5, mu = 0.02, T = 60 * 6.5)
{
trade.sample <- simulateEKOP_cc(as.integer(size), as.double(alpha),
as.double(epsilon), as.double(delta),
as.double(mu), as.double(T))
cnames <- c("MisBuy", "MisSell", "Buy", "Sell", "Trades")
trade.sample <- data.frame(trade.sample)
colnames(trade.sample) <- cnames
return(trade.sample)
}
#' Simulates mis-specified trades data
#'
#' @description
#' Simulates mis-specified trades data from the model by Easley, Kiefer, O'Hara
#' and Paperman (1996). The simulation function is implemented in C++ and allows
#' therefore usage in specific performance-sensitive scenarios, like simulating
#' huge amounts of trade data or calling this function repeatedly in large
#' simulations.
#'
#' @details
#' The functions returns a `data.frame` with named columns `MisBuy`, `MisSell`,
#' `Buy`, `Sell`, and `Trades`. `Buy` and `Sell` are the number of buy and sell
#' trades per trading day and `Trades` defines the sum of these amounts.
#' `MisBuy` and `MisSell` define the number of mis-specified buy and sell
#' trades per trading day respectively.
#'
#' @param size An integer specifying the number of trading days that should
#' be simulated.
#' @param alpha A double specifying the probability of an information event.
#' @param epsilon A double specifying the arrival rate of uninformed traders.
#' @param delta A double specifying the probability of information being good
#' or bad.
#' @param mu A double specifying the arrival rate of informed traders.
#' @param T A double defining the length of a trading day in minutes.
#' @param mis A double specifying the mis-sepcification rate for trades.
#' @return A `data.frame` containing the trades per day.
#' @export
#'
#' @examples
#' # Simulate mis-specifed trades data for 1000 trading dates with a trading
#' # day lasting 6.5 hours.
#' trades_data <- simulate_ekop_mis(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5, mis = .1)
#' head(trades_data)
#'
#' @seealso
#' * [simulate_ekop()] for simulating trades data without mis-specification
#' * [correct_trades()] to reconstruct original trades data from mis-specified
#' ones
#'
#' @references
#' * Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity,
#' information, and infrequently traded stocks. Journal of Finance 51,
#' 1405–1436.
#' * Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the
#' Probability of Informed Trading. Conference on Financial Econometrics &
#' Empirical Asset Pricing 2016, Lancaster University
"simulate_ekop_mis" <- function(size = 1000, alpha = 0.2, epsilon = 0.2,
delta = 0.5, mu = 0.02, T = 60 * 6.5,
mis = 0.15)
{
trade.sample <- simulateEKOPMis_cc(as.integer(size), as.double(alpha),
as.double(epsilon), as.double(delta),
as.double(mu), as.double(mis),
as.double(T))
cnames <- c("MisBuy", "MisSell", "Buy", "Sell", "Trades")
trade.sample <- data.frame(trade.sample)
colnames(trade.sample) <- cnames
return(trade.sample)
}
#' Corrects mis-specified trades data
#'
#' @description
#' Calling [correct_trades()] on simulated mis-specified trades data corrects
#' the mis-specifications. This becomes handy when using simulated data in
#' comparison studies of e.g. estimators, etc.
#'
#' @details
#' Mis-specified trades are recorded in the columns `MisBuy` and `MisSell` for
#' buy and sell trades respectively. This information is used to re-construct
#' the well-specified trades data.
#'
#' @param trades A `data.frame` containing the trades data. This must have the
#' columns `MisBuy`, `MisSell`, `Buy`, and `Sell` specified.
#' @return A `data.frame` containing the re-constructed well-specified trades
#' data.
#' @export
#'
#' @examples
#' # Simulate mis-specifed trades data for 1000 trading dates with a trading
#' # day lasting 6.5 hours.
#' trades_data <- simulate_ekop_mis(size = 1000, alpha = .3, epsilon = .4,
#' delta = .5, mu = .04, T = 60*6.5, mis = .1)
#' trades_data_corr <- correct_trades(trades = trades_data)
#' head(trades_data_corr)
#'
#' @seealso
#' * [simulate_ekop_mis()] for simulating trades data with mis-specification
#' * [simulate_ekop()] for simulating trades data without mis-specification
"correct_trades" <- function(trades)
{
trades$Buy <- trades$Buy - trades$MisBuy + trades$MisSell
trades$Sell <- trades$Sell - trades$MisSell + trades$MisBuy
trades$MisBuy <- 0
trades$MisSell <- 0
return(trades)
}
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