The pricediscovery pacakge is used to conduct price discovery analysis
according to the Hasbrouck (1995)’s “one-security-many-markets” setting.
Current version can calculate Gonzalo and Granger (1995)’s component
shares (CSs), Hasbrouck (1995)’s information shares (ISs), and Putniņš
(2013)’s information leadership shares.
This package tries to implement such an empirical setting in an easy way. I would particularly focus on a case where the number of markets N > 2 as prior implementation is restrictive to bi-variable setting.
This package also helps to resample the price series. Raw financial data might be in tick level, or the data frequency between markets is not the same. Hence, a resampling is needed when conducting price discovery analysis.
Financial price discovery characterizes how information is incorporated into the fundamental values and many studies have suggested this process across multiple venues. The price discovery happens when the same security is traded among different venues, such as E-mini S&P 500 futures and SPY, the ETF. Knowing which market is informative to price formation process is important for market participants, especially for regulators, to understand the dynamics of market microstructure. This is also helpful for intraday arbitragers to understand better for lead-lag relationship.
For full methodological details, see the package vignette:
vignette("methodology", package = "pricediscovery")You can install the development version of pricediscovery like so:
#install.packages("devtools")
devtools::install_github("richie-ma/pricediscovery")
library(pricediscovery)I use a sample dataset for BTC-USD trade prices from five major cryptocurrecny exchanges: Kraken, Gemini, Coinbase, Bitstamp, and Bitfinex on January 5, 2026.
Let’s resample every market data to 1-second frequency and then merge all together.
### using the test datasets
library(ggplot2)
library(pricediscovery)
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
kraken <- readRDS(testthat::test_path("btcusd_kraken.rds"))[, .(time, kraken=price)]
gemini <- readRDS(testthat::test_path("btcusd_gemini.rds"))[, .(time, gemini=price)]
coinbase <- readRDS(testthat::test_path("btcusd_coinbase.rds"))[, .(time, coinbase=price)]
bitstamp <- readRDS(testthat::test_path("btcusd_bitstamp.rds"))[, .(time, bitstamp=price)]
bitfinex <- readRDS(testthat::test_path("btcusd_bitfinex.rds"))[, .(time, bitfinex=price)]
mkt_data <- list(kraken = resample(kraken, 'time', 'secs', 1, "00:00:00", "23:59:59"),
gemini = resample(gemini, 'time', 'secs', 1, "00:00:00", "23:59:59"),
coinbase = resample(coinbase, 'time', 'secs', 1, "00:00:00", "23:59:59"),
bitstamp = resample(bitstamp, 'time', 'secs', 1, "00:00:00", "23:59:59"),
bitfinex = resample(bitfinex, 'time', 'secs', 1, "00:00:00", "23:59:59"))
mkt_data_1s <- Reduce(
function(x, y) merge(x, y, by = "DT"),
mkt_data
)
mkt_data_1s
#> Key: <DT>
#> DT KRAKEN GEMINI COINBASE BITSTAMP BITFINEX
#> <POSc> <num> <num> <num> <num> <num>
#> 1: 2026-01-05 00:00:00 91507.0 91493.73 91489.03 91498 91463
#> 2: 2026-01-05 00:00:01 91507.0 91493.73 91488.63 91498 91463
#> 3: 2026-01-05 00:00:02 91507.0 91493.73 91489.73 91498 91463
#> 4: 2026-01-05 00:00:03 91507.0 91493.73 91486.62 91494 91463
#> 5: 2026-01-05 00:00:04 91507.0 91493.73 91503.93 91499 91463
#> ---
#> 86396: 2026-01-05 23:59:55 93866.9 93866.06 93870.07 93877 93758
#> 86397: 2026-01-05 23:59:56 93866.9 93866.06 93870.07 93876 93756
#> 86398: 2026-01-05 23:59:57 93866.9 93866.06 93870.07 93876 93756
#> 86399: 2026-01-05 23:59:58 93866.9 93866.06 93870.07 93876 93756
#> 86400: 2026-01-05 23:59:59 93866.9 93866.06 93870.06 93876 93756
ggplot(data = mkt_data_1s, aes( x = DT))+
geom_line(aes(y = KRAKEN, color='KRAKEN'))+
geom_line(aes(y = GEMINI, color='GEMINI'))+
geom_line(aes(y = COINBASE, color='COINBASE'))+
geom_line(aes(y = BITSTAMP, color='BITSTAMP'))+
geom_line(aes(y = BITFINEX, color='BITFINEX'))+
labs(
x = "Time",
y = "Price",
color = "Market"
)
One can see that prices in the five markets are close to each other and move together, suggesting that there should not be persistent deviations between one another.
Now, I calculate the price discovery shares. I select the lag based on SC with maximum lag 60, corresponding to 1 minute. In long-run equilibrium, I add a constant term to account for the price level differences between them. I use the standard cointgrating beta which is set to
price_discovery_measures <- pricediscovery::price_discovery(mkt_data_1s,
num_market = 5,
price_columns = c("KRAKEN",
"GEMINI",
"COINBASE",
"BITSTAMP",
"BITFINEX"),
log_price = TRUE,
lag_selection = TRUE,
vecm_max.lag = 60,
lag_select_ceritera = 'SC',
coin_const = TRUE,
coin_beta = TRUE)
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
price_discovery_measures
#> KRAKEN GEMINI COINBASE BITSTAMP BITFINEX type
#> <num> <num> <num> <num> <num> <char>
#> 1: 0.02587861 0.01578082 0.6346416 0.07312503 0.25057398 IS
#> 2: 0.01171890 -0.01217370 0.7226558 0.02202630 0.25577272 PT
#> 3: 0.25254256 0.08702411 0.0399411 0.57078844 0.04970378 ILS
#> 4: 0.01144035 0.01188435 0.7054792 0.02150276 0.24969334 CSGonzalo, J., and C. Granger. 1995. “Estimation of Common Long-Memory Components in Cointegrated Systems.” Journal of Business and Economic Statistics 13: 27–35.
Hasbrouck, J. 1995. “One Security, Many Markets: Determining the Contributions to Price Discovery.” Journal of Finance 50: 1175–99.
Putniņš, T. J. 2013. “What Do Price Discovery Metrics Really Measure?” Journal of Empirical Finance 23: 68–83.