GARCH-BFGS

Fortran implementations of GARCH-family volatility models, distributional likelihoods, simulation programs, and command-line examples for fitting volatility models to close-to-close, OHLC, split overnight/intraday, and intraday return data.

The code is research-oriented. Most programs are small executable examples built from reusable modules, with model comparison based on log likelihood, AIC, BIC, and diagnostic summaries.

Features

• Symmetric GARCH, NAGARCH, GJR-GARCH, EGARCH, and related flexible GARCH variants.
• Innovation distributions including normal, Student t, GED, Laplace, logistic, hyperbolic secant, NIG, and Fernandez-Steel skewed t in the newer distribution-aware fitters.
• Simulation routines for stationary close-to-close GARCH models.
• Close-to-close return fitting with normal and non-normal innovations.
• Two-step fitting that fits the volatility model under normal noise and then fits distributions to standardized residuals.
• Split close-open/open-close models for daily OHLC data.
• Intraday OHLCV readers and intraday MCS-GARCH style models with diurnal volatility curves.
• Simple deterministic intraday diurnal variance baselines independent of GARCH estimation.
• Compact unformatted stream storage for intraday OHLCV tick data, useful when CSV parsing dominates runtime.
• Intraday models with overnight effects, prior-day range predictors, and prior-day open-to-close NAGARCH news impact predictors.
• Intraday ACF diagnostics for signed price changes, absolute price changes, and high-low ranges.
• Cross-asset intraday covariance/correlation matrices at multiple aggregation scales, with diagnostics for pairs whose correlations change unusually across frequencies.
• Daily realized-volatility forecast comparisons using close-to-close, OHLC, realized measures, HAR-style models, HEAVY/realized-GARCH-style models, and implied-volatility correlations.
• Calendar-day annual seasonal volatility tests.
• Iid distribution fitting/simulation and normal-mixture EM examples.
• Univariate value-at-risk estimators including empirical, Harrell-Davis, kernel, parametric, EVT, and Monte Carlo variants.
• Basic DCC/ADCC, GAS, and stochastic volatility examples retained from earlier experiments.

Requirements

• gfortran
• make

The Makefile currently uses:

FC      = gfortran
FFLAGS  = -Wall -Wextra -Werror -Wno-compare-reals -fbounds-check -O2

On Windows, the examples have been run from PowerShell/Git Bash style shells using MinGW gfortran.

Build

Build a specific executable:

make xfit_gen_garch_dist_returns.exe

Build all executable targets defined in the Makefile:

make all

Run a configured target:

make run_fit_gen_garch_dist_returns

Clean generated objects, modules, and executables:

make clean

Building all compiles all .exe targets currently defined in the Makefile and may take longer than building a specific executable.

Data

Some example programs use hard-coded default input files. Update the file name in the program or pass a command-line argument where supported.

Common expected inputs:

• Daily adjusted close price CSVs, such as spy_efa_eem_tlt_lqd.csv.
• Daily OHLC price CSVs for split close-open/open-close or range models.
• Intraday OHLCV CSVs, such as 1-second or 5-minute bars with timestamp, open, high, low, close, and volume.

The example files prices_ohlc.csv, spy_efa_eem_tlt_lqd.csv, and vix_spy.csv were obtained from Yahoo Finance. Intraday files referenced in source-code defaults, such as c:\python\databento\spy_1s_databento.csv and c:\python\intraday_prices\spy_5min_databento.csv, are Databento data files and are not included. Databento currently offers free signup credits for historical market data.

Large market data files are not necessarily included in this repository.

Main Modules

• garch.f90, nagarch.f90, gjr.f90, egarch.f90, fgarch.f90: model likelihood/filter logic.
• garch_types.f90: shared GARCH parameter/result types.
• garch_fit.f90: normal-noise fitting interface across GARCH model families.
• garch_fit_dist.f90: distribution-aware GARCH fitting.
• garch_sim.f90: simulation routines for stationary GARCH models.
• garch_split_fit_dist.f90: split close-open/open-close distribution-aware fitting.
• garch_mcsgarch.f90: reusable intraday MCS-GARCH filters and helpers.
• intraday_vol_baseline.f90: lagged/EWMA daily variance, deterministic diurnal multipliers, and simple intraday EWMA baseline forecasts.
• intraday_summary.f90: summary statistics and time-gap diagnostics for intraday OHLCV files.
• intraday_realized_measures.f90, realized_vol_forecast.f90, realized_garch.f90: daily realized-measure construction and realized-volatility forecast models.
• distributions.f90, special.f90, random.f90: distribution densities, special functions, and random variates.
• market_data.f90: intraday OHLCV containers, CSV and stream readers/writers, resampling, session filtering, and intraday transformations.
• intraday_returns.f90, intraday_correlation_report.f90, matrix_print.f90: intraday return alignment, cross-asset correlation reporting, and matrix printing.
• csv.f90, date.f90, strings.f90, path_utils.f90, glob.f90: data input and utility modules.
• stats.f90: sample statistics, correlations/covariances, autocorrelations, sorting, and ACF table printing.
• seasonal_vol.f90: calendar seasonal volatility regression helpers.
• normal_mixture_em.f90: normal-mixture EM code shared by the mixture examples.
• var_univariate.f90: univariate VaR estimators.

Selected Programs

Close-to-close examples:

• xfit_gen_garch_returns.f90: fit several GARCH models with normal noise to returns.
• xfit_gen_garch_dist_returns.f90: fit several GARCH models with several innovation distributions.
• xfit_garch_twostep_returns.f90: fit GARCH under normal noise, then fit distributions to standardized residuals.
• xsim_garch_fit.f90: simulate GARCH processes, fit them back, and compare true versus fitted parameters.
• xsim_garch_fit_dist.f90: simulate and fit GARCH models with non-normal innovations.

OHLC and split-return examples:

• xfit_split_garch_dist_returns.f90: fit GARCH models to close-open and open-close returns.
• xfit_split_range_garch_dist_returns.f90: fit split models using close-open, open-close, and high-low information.
• xfit_garch_ohlc_iv_returns.f90: fit OHLC-based models and compare volatility forecasts.

Intraday examples:

• xread_intraday_prices.f90: read and summarize intraday OHLCV data.
• xsummary_intraday.f90: print summary statistics for one or more intraday OHLCV CSV or .bin files, with wildcard expansion.
• xcsv_to_intraday_tick_stream.f90: convert one or more intraday OHLCV CSV files, or all CSV files in a directory, to compact .bin stream files.
• xroundtrip_intraday_tick_stream.f90: test CSV to stream to stream-read round trips for intraday tick data.
• xacf_intraday_measures.f90: compute ACFs for signed close changes, absolute close changes, and high-low ranges; reads .bin files directly when given one.
• xdiurnal_variance_baseline.f90: estimate a deterministic time-of-day variance multiplier from intraday returns using estimate_diurnal_variance_baseline.
• xfit_mcsgarch_intraday.f90: fit intraday MCS-GARCH models with diurnal volatility curves.
• xfit_mcsgarch_intraday_batch.f90: run intraday MCS-GARCH fits over multiple files.
• xfit_mcsgarch_on_intraday.f90: fit joint overnight/intraday MCS-GARCH models.
• xfit_mcsgarch_on_range_intraday.f90: fit overnight/intraday models with prior-day range and open-to-close predictors.
• xfit_mcsegarch_on_intraday.f90: fit an EGARCH-style intraday model with overnight effects.
• xcompare_intraday_ewma_ohlc.f90: compare simple intraday EWMA baselines using close-close, Parkinson, and Garman-Klass proxies.
• xcompare_intraday_ewma_freq.f90: compare EWMA predictors from higher-frequency bars for lower-frequency target volatility.
• xcorrel_intraday_assets.f90: compute realized volatilities plus covariance/correlation matrices for multiple assets at several intraday aggregation scales; accepts individual files or dir=....

Daily realized-volatility comparisons:

• xcompare_daily_realized_vol_forecasts.f90: compare daily volatility forecasts from realized measures, HAR-family models, realized-GARCH-style models, close-to-close GARCH/EWMA baselines, and optional implied-volatility correlations.
• xcompare_daily_intraday_garch.f90: compare daily forecasts from daily GARCH-style models and intraday MCS-GARCH-style models.
• xcompare_regular_allhours_rv.f90: compare regular-session and all-hours realized volatility as predictors of close-to-close volatility.

Diagnostics and utilities:

• xseasonal_vol_calendar.f90: test for annual calendar seasonal volatility.
• xcompare_nagarch_news.f90: compare NAGARCH news impact forms.
• xfit_dist_returns.f90: distribution fitting/testing utility for returns.
• xfit_dist.f90: fit iid distributions to numeric columns read from a CSV file.
• xsim_dist.f90: simulate iid distribution samples in the CSV format read by xfit_dist.f90.
• xcalibrate_dist_warm_starts.f90: calibrate distribution warm-start shape parameters.
• xmix.f90, xmix_ic.f90: normal-mixture EM simulation and information-criterion examples using normal_mixture_em.f90.
• xvar_univariate.f90: exercise the univariate VaR estimators on simulated returns.
• xf90_make_deps.py: report Makefile target dependencies by source file and audit x*.f90 executable coverage.
• xcompare_dirs.py: compare selected source file types across two directories.

Intraday Binary Stream Workflow

CSV parsing is slow for large intraday files. Convert a CSV once:

make xcsv_to_intraday_tick_stream.exe
./xcsv_to_intraday_tick_stream.exe c:\python\databento\spy_1s_databento.csv

This writes spy_1s_databento.bin in the current directory. Prices are stored as integer multiples of tick_size, which defaults to 0.001 dollars. Pass a second argument to use a different tick size, and a third argument to cap the number of data rows read:

./xcsv_to_intraday_tick_stream.exe c:\python\databento\spy_1s_databento.csv 0.005 100000

Named arguments are also supported and are clearer for batch conversion:

./xcsv_to_intraday_tick_stream.exe c:\python\databento\spy_1s_databento.csv tick_size=0.005 max_obs=100000

Convert all price CSV files in a directory and write the .bin files to a separate output directory:

./xcsv_to_intraday_tick_stream.exe dir=c:\python\intraday_prices\continuous out_dir=bin_dir tick_size=0.0000001

Programs can infer stream input from the .bin extension. For example:

make xacf_intraday_measures.exe
./xacf_intraday_measures.exe spy_1s_databento.bin

If spy_1s_databento.bin exists, xacf_intraday_measures.exe uses it by default; otherwise it falls back to the configured CSV path.

Summarize one or more intraday files:

make xsummary_intraday.exe
./xsummary_intraday.exe spy_1s_databento.bin
./xsummary_intraday.exe "c:\python\intraday_prices\continuous\*.csv"

The summary program reads CSV or .bin files, reports per-file OHLCV/return summaries, and can print time-gap diagnostics.

For cross-asset intraday correlations, pass files explicitly:

make xcorrel_intraday_assets.exe
./xcorrel_intraday_assets.exe ES.bin JY.bin TY.bin

or run on every .bin file in a directory:

./xcorrel_intraday_assets.exe dir=bin_dir

When a directory is supplied, xcorrel_intraday_assets.exe uses all .bin files if any are present; otherwise it uses all price CSV files in the directory. The output includes realized volatilities, covariance matrices, correlation matrices, and a final correlation-change diagnostic comparing lower-frequency correlations with the highest-frequency matrix using Fisher z differences.

Estimate a standalone deterministic intraday diurnal variance baseline:

make xdiurnal_variance_baseline.exe
./xdiurnal_variance_baseline.exe c:\python\intraday_prices\spy_5min_databento.csv diurnal_variance_baseline.csv

The program filters to regular-session bars, forms within-day log close-to-close returns, estimates lag-1 daily realized variance forecasts, calls estimate_diurnal_variance_baseline, prints the populated time-of-day bins, and writes the curve to CSV.

Source and Makefile Utilities

List .f90 files by how many Makefile targets depend on them:

python xf90_make_deps.py
python xf90_make_deps.py --show-targets

Audit x*.f90 program files against matching .exe targets and make all coverage:

python xf90_make_deps.py --audit-x

Compare selected source files in two directories:

python xcompare_dirs.py dir1 dir2

By default it compares *.f90, *.py, *.c, *.cpp, *.r, and *make*, grouped by pattern.

Intraday Range and OC Predictor Configuration

xfit_mcsgarch_on_range_intraday.f90 has explicit configuration arrays near the top of the file. For example, active innovation distributions are controlled by:

character(len=8), parameter :: fit_dist_names(*) = [character(len=8) :: &
    "NORMAL", "T"]

Add "FS_SKEWT" to restore Fernandez-Steel skewed-t fits:

character(len=8), parameter :: fit_dist_names(*) = [character(len=8) :: &
    "NORMAL", "T", "FS_SKEWT"]

The same program compares:

• R0: no prior-day range predictor.
• R5M: prior-day sum of 5-minute Parkinson ranges.
• RDAY: prior-day full regular-session Parkinson range.
• RBOTH: both range predictors.
• OC0: no prior-day open-to-close news impact.
• OCNAG: prior-day open-to-close NAGARCH-style news impact.

Current Notes

• The codebase contains many executable experiments. Prefer building one target at a time while developing.
• Some intraday model grids can be slow. Use normal-only distributions while developing model structure, then rerun a shortlist with Student t or skewed t.
• Several programs have default file paths from the local research environment. Treat these as examples and adjust them for your data layout.
• AIC and BIC comparisons are only directly meaningful when models are fit to the same observations and likelihood target.