From 6f08326bdc90542e66d36cf8ece7604152349a53 Mon Sep 17 00:00:00 2001 From: "YiLung ( Dragon ) - Tsai" <147884721+DragonTsai@users.noreply.github.com> Date: Wed, 24 Dec 2025 14:31:04 +0000 Subject: [PATCH 1/5] Update README.md --- submissions/equityquant.dev/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/submissions/equityquant.dev/README.md b/submissions/equityquant.dev/README.md index 66a302d..931553c 100644 --- a/submissions/equityquant.dev/README.md +++ b/submissions/equityquant.dev/README.md @@ -1,7 +1,6 @@ # EquityQuant.dev Model **Team name:** equityquant.dev -**Contact:** Yi-Lung (Dragon) Tsai — ytsai@equityquant.dev **Model Description:** please see below --- @@ -174,3 +173,5 @@ automatically concatenates the split files when `dataset.parquet` is not present No data has been modified or filtered; the three files together form the complete submission dataset. +## Contact: +Thelonious Casey — theo.casey@marketcolor.co From ac6677baee969863c7035cd30437804cfec2420c Mon Sep 17 00:00:00 2001 From: "YiLung ( Dragon ) - Tsai" <147884721+DragonTsai@users.noreply.github.com> Date: Wed, 24 Dec 2025 14:31:44 +0000 Subject: [PATCH 2/5] Update README.md --- submissions/equityquant.dev/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/submissions/equityquant.dev/README.md b/submissions/equityquant.dev/README.md index 931553c..ff4ecdb 100644 --- a/submissions/equityquant.dev/README.md +++ b/submissions/equityquant.dev/README.md @@ -173,5 +173,5 @@ automatically concatenates the split files when `dataset.parquet` is not present No data has been modified or filtered; the three files together form the complete submission dataset. -## Contact: +## Contact Thelonious Casey — theo.casey@marketcolor.co From 247672d72998fe1f4f8c02a8a07b7caa8c3a1326 Mon Sep 17 00:00:00 2001 From: "YiLung ( Dragon ) - Tsai" <147884721+DragonTsai@users.noreply.github.com> Date: Wed, 24 Dec 2025 14:42:42 +0000 Subject: [PATCH 3/5] Update README.md --- submissions/equityquant.dev/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/submissions/equityquant.dev/README.md b/submissions/equityquant.dev/README.md index ff4ecdb..cabafc1 100644 --- a/submissions/equityquant.dev/README.md +++ b/submissions/equityquant.dev/README.md @@ -1,4 +1,4 @@ -# EquityQuant.dev Model +image# EquityQuant.dev Model **Team name:** equityquant.dev **Model Description:** please see below @@ -174,4 +174,4 @@ No data has been modified or filtered; the three files together form the complet submission dataset. ## Contact -Thelonious Casey — theo.casey@marketcolor.co +Thelonious Casey — tcasey@equityquant.dev From 1d7a0078b444a9641854c4ed35cda5edea439e08 Mon Sep 17 00:00:00 2001 From: "YiLung ( Dragon ) - Tsai" <147884721+DragonTsai@users.noreply.github.com> Date: Wed, 24 Dec 2025 14:43:03 +0000 Subject: [PATCH 4/5] Update README.md --- submissions/equityquant.dev/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/submissions/equityquant.dev/README.md b/submissions/equityquant.dev/README.md index cabafc1..8a521b5 100644 --- a/submissions/equityquant.dev/README.md +++ b/submissions/equityquant.dev/README.md @@ -1,4 +1,4 @@ -image# EquityQuant.dev Model +# EquityQuant.dev Model **Team name:** equityquant.dev **Model Description:** please see below From 5206ecd3eede1d8f8c666a169ed78b8b2903ce31 Mon Sep 17 00:00:00 2001 From: "YiLung ( Dragon ) - Tsai" <147884721+DragonTsai@users.noreply.github.com> Date: Wed, 24 Dec 2025 15:58:42 +0000 Subject: [PATCH 5/5] Add files via upload --- .../equityquant.dev/equityquant.dev_model.py | 142 + .../qvariance_simulation_100k.csv | 100001 +++++++++++++++ .../equityquant.dev/score_submission.py | 228 + 3 files changed, 100371 insertions(+) create mode 100644 submissions/equityquant.dev/equityquant.dev_model.py create mode 100644 submissions/equityquant.dev/qvariance_simulation_100k.csv create mode 100644 submissions/equityquant.dev/score_submission.py diff --git a/submissions/equityquant.dev/equityquant.dev_model.py b/submissions/equityquant.dev/equityquant.dev_model.py new file mode 100644 index 0000000..bf884f3 --- /dev/null +++ b/submissions/equityquant.dev/equityquant.dev_model.py @@ -0,0 +1,142 @@ +import numpy as np +import pandas as pd + +# ===================================================== +# Official horizons: 1–26 weeks +# ===================================================== +HORIZONS = 5 * (np.arange(26) + 1) + + +# ===================================================== +# CIR precision -> Poisson-weighted Gaussian mixture +# ===================================================== +def simulate_price_series( + n_days=300_000, + s0=100.0, + sigma0=0.25, + kappa=0.02, + c_int=15.0, + seed=1, + a_shape=1.5, + lam_cap=500.0 +): + rng = np.random.default_rng(seed) + dt = 1.0 / 252.0 + sqrt_dt = np.sqrt(dt) + + # --- CIR target + a = a_shape + beta = sigma0**2 + theta = a / beta + eta = np.sqrt(2.0 * kappa * theta / a) + + tau = theta + logP = np.empty(n_days) + logP[0] = np.log(s0) + r = np.empty(n_days - 1) + + # Typical lambda at long-run tau + lam_typ = min(lam_cap, c_int / theta) + lam_typ = max(lam_typ, 1e-8) + + # Calibrate mixture variance + s_unit2 = (sigma0**2 / 252.0) / lam_typ + s_unit = np.sqrt(s_unit2) + + for t in range(1, n_days): + # CIR step + dW_tau = rng.standard_normal() * sqrt_dt + tau_pos = max(tau, 0.0) + tau = tau + kappa * (theta - tau_pos) * dt + eta * np.sqrt(tau_pos) * dW_tau + tau = max(tau, 1e-10) + + # Shock intensity + lam = c_int / tau + if lam > lam_cap: + lam = lam_cap + + # Poisson-weighted Gaussian mixture + N = rng.poisson(lam) + r_t = rng.normal(0.0, s_unit * np.sqrt(N)) if N > 0 else 0.0 + + r[t - 1] = r_t + logP[t] = logP[t - 1] + r_t + + prices = np.exp(logP) + return prices, r + + +# ===================================================== +# Q-variance dataset builder (OFFICIAL, OVERLAPPING) +# ===================================================== +def build_qvariance_dataset_from_prices(prices, ticker="DRAGON"): + ret = np.diff(np.log(prices)) + scale = np.sqrt(252.0) + + rows = [] + for T in HORIZONS: + for i in range(0, len(ret) - T + 1): # OVERLAPPING + window = ret[i:i + T] + + x = window.sum() + sigma = np.std(window, ddof=0) * scale + z_raw = x / np.sqrt(T / 252.0) + + if not (np.isfinite(sigma) and sigma > 0 and np.isfinite(z_raw)): + continue + + rows.append({ + "ticker": ticker, + "date": int(i), + "T": int(T), + "z_raw": float(z_raw), + "sigma": float(sigma), + }) + + df = pd.DataFrame(rows) + + # Official de-meaning step + df["z"] = df.groupby("T")["z_raw"].transform(lambda g: g - g.mean()) + df = df.drop(columns="z_raw").dropna().reset_index(drop=True) + + return df[["ticker", "date", "T", "z", "sigma"]] + + +# ===================================================== +# Main +# ===================================================== +def main(): + prices, returns = simulate_price_series( + n_days=120_000, + sigma0=0.25, + kappa=0.02, + c_int=10.0, + seed=3 + ) + + # ------------------------------------------------- + # CSV (first 100K points) + # ------------------------------------------------- + n_out = 100_000 + + df_out = pd.DataFrame({ + "Day": np.arange(n_out), + "Price": prices[:n_out], + "y": np.concatenate([[0.0], returns])[:n_out] + }) + + df_out.to_csv("qvariance_simulation_100k.csv", index=False) + print("Saved qvariance_simulation_100k.csv") + + # ------------------------------------------------- + # Original outputs + # ------------------------------------------------- + pd.Series(prices, name="Price").to_csv("prices.csv", index=False) + + df_qv = build_qvariance_dataset_from_prices(prices) + df_qv.to_parquet("dataset.parquet", index=False) + print(f"Saved dataset.parquet with {len(df_qv):,} rows") + + +if __name__ == "__main__": + main() diff --git a/submissions/equityquant.dev/qvariance_simulation_100k.csv 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+99999,0.000713620537080284,0.0 diff --git a/submissions/equityquant.dev/score_submission.py b/submissions/equityquant.dev/score_submission.py new file mode 100644 index 0000000..5f83e98 --- /dev/null +++ b/submissions/equityquant.dev/score_submission.py @@ -0,0 +1,228 @@ +# score_submission.py - reads a parquet file and compares variance curve with baseline +# also divides data into 400 parts, if 5e6 time points this gives 5e6//400 days or about 50 years each part +# should see q-variance for each part, not just the total +# also checks distn for time invariance + +import pandas as pd +import numpy as np +from scipy.optimize import curve_fit +from scipy.stats import norm, poisson +from sklearn.metrics import r2_score +import matplotlib +matplotlib.use("module://matplotlib_inline.backend_inline") +import matplotlib.pyplot as plt +import matplotlib.cm as cm +import matplotlib.colors as mcolors +import os + +# load the parquet files from data_loader.py + +if os.path.isfile("dataset.parquet"): + df= pd.read_parquet("dataset.parquet") # READ SUBMISSION DATA +else: + df = pd.concat([pd.read_parquet("dataset_part1.parquet"),pd.read_parquet("dataset_part2.parquet"),pd.read_parquet("dataset_part3.parquet")]) + + +df["var"] = df.sigma**2 +TICKERS1 = np.unique(df["ticker"]) # use original tickers + +print(f"{len(df)} windows") +print(f"z has NaNs: {df['z'].isna().sum()}") # → 0 + +df_orig = df.copy() + +# divide dataframe into equal segments and rename 'ticker' column based on segment number +def assign_segmented_tickers(df,N_SEGMENTS): + nr = len(df) + + rows_per_segment = nr // N_SEGMENTS + nextra = nr % N_SEGMENTS + + # Drop extra rows if necessary + if nextra > 0: + df = df.iloc[:nr - nextra].copy() + nr = len(df) + + # Create an array of segment numbers + segment_ids = np.arange(1, N_SEGMENTS + 1).repeat(rows_per_segment) + + # Use list comprehension to handle string concatenation in standard Python, + # then convert back to a NumPy array if needed, or just assign directly. + new_tickers = ['V' + str(i) for i in segment_ids] + + # Assign the new ticker names to the 'ticker' column + df['ticker'] = new_tickers + + return df + +zmax = 0.6 #0.6 or 1 +delz = 0.025*2 +nbins = int(2*zmax/delz + 1) +bins = np.linspace(-zmax, zmax, nbins) # fixed bins +ymax = 0.35 + +# create data frame with e.g. zbin = (-0.601, -0.55], z_mid, sigma +binned = (df.assign(z_bin=pd.cut(df.z, bins=bins, include_lowest=True)) + .groupby('z_bin',observed=False) + .agg(z_mid=('z', 'mean'), var=('var', 'mean')) + .dropna()) + +def qvar(z, s0, zoff): # define q-variance function, parameter is minimal volatility s0 and zoff + return (s0**2 + (z - zoff)**2 / 2) + +def qvar2(z, s0, s1): # define q-variance function, parameter is minimal volatility s0 and qcoef + return (s0**2 + s1*z**2 ) + +# curve_fit returns a value popt and a covariance pcov, the _ means we ignore the pcov +popt = [0.2586, 0.0214] # same as optimized fit to data +popt, _ = curve_fit(qvar, binned.z_mid, binned["var"], p0=[0.2, 0]) # fit this data + +fitted = qvar(binned.z_mid, popt[0], popt[1]) # cols are z_bin, which is a range like (-0.601, -0.55], and qvar +r2 = 1 - np.sum((binned["var"] - fitted)**2) / np.sum((binned["var"] - binned["var"].mean())**2) + +print(f"σ₀ = {popt[0]:.4f} zoff = {popt[1]:.4f} R² = {r2:.4f}") + +# plot of all stocks +markfac = 1 # default is 1, can increase to 3 if less data points +plt.figure(figsize=(9,7)) +plt.scatter(df.z, df['var'], c='steelblue', alpha=markfac*0.1, s=markfac*1, edgecolor='none') +numeric_array = (1 - df["T"]/130) +string_array = [str(x) for x in numeric_array] +plt.plot(binned.z_mid, binned['var'], 'b-', lw=3) # label='binned' +plt.plot(binned.z_mid, fitted, 'red', lw=3, label=f'σ₀ = {popt[0]:.3f}, zoff = {popt[1]:.3f}, R² = {r2:.3f}') + +plt.xlabel('z (scaled log return)', fontsize=12) +plt.ylabel('Annualised variance', fontsize=12) +plt.title('Q-Variance: all data T=1 to 26 weeks', fontsize=14) + +plt.xlim(-zmax, zmax) +plt.ylim(0.0, ymax) + +plt.legend(fontsize=12) +plt.grid(alpha=0.3) +plt.tight_layout() +##plt.savefig("figure_1_1.png", dpi=300, bbox_inches='tight') + + +normcol = mcolors.Normalize(vmin=0, vmax=0.3) +cmap = cm.get_cmap('coolwarm') + + +# now change the fit for all and get coefficients qcopt +zmax = 1 # larger grid +ymax = 0.8 + +delz = 0.025*4 # wider bin for these noisy plots +nbins = int(2*zmax/delz + 1) +bins = np.linspace(-zmax, zmax, nbins) # fixed bins + +if len(np.unique(df_orig["ticker"])) >= 1: # set to >=1 to divide all data, or == 1 to divide model data only ### + print("dividing into 800 separate runs") + df = assign_segmented_tickers(df_orig,800) # divide and add tickers +else: + df = df_orig + +TICKERS = np.unique(df["ticker"]) +r2vec = np.zeros(len(TICKERS)) +q0vec = np.zeros(len(TICKERS)) +q1vec = np.zeros(len(TICKERS)) +i = 0 +fig, ax = plt.subplots(figsize=(9,7)) +for tickcur in TICKERS: + dfcur = df[(df["ticker"] == tickcur)].copy() + binned = (dfcur.assign(z_bin=pd.cut(dfcur.z, bins=bins, include_lowest=True)) + .groupby('z_bin',observed=False) + .agg(z_mid=('z', 'mean'), var=('var', 'mean')) + .dropna()) + + popt, _ = curve_fit(qvar, binned.z_mid, binned["var"], p0=[0.2, 0]) # custom fit + qopt, _ = curve_fit(qvar2, binned.z_mid, binned["var"], p0=[0.2, 0.5]) # custom fit to quadratic term + fitted = qvar(binned.z_mid, popt[0], popt[1]) # use fit for whole data set + r2vec[i] = 1 - np.sum((binned["var"] - fitted)**2) / np.sum((binned["var"] - binned["var"].mean())**2) + q0vec[i] = qopt[0] + q1vec[i] = qopt[1] + #print(f"ticker = {tickcur} σ₀ = {popt[0]:.4f} zoff = {popt[1]:.4f} R² = {r2:.4f}") + colcur = cmap(normcol(max(0,popt[0]))) # str(Tcur/100) + ax.plot(binned.z_mid, binned['var'], '-', c=colcur, alpha = 0.5, lw=2, label=f'σ₀ = {popt[0]:.3f}, zoff = {popt[1]:.3f}, R² = {r2vec[i] :.3f}') + i = i+1 + +r2mean = np.mean(r2vec) +r2median = np.median(r2vec) +ax.set_xlabel('z (scaled log return)', fontsize=12) +ax.set_ylabel('Annualised variance', fontsize=12) +ax.set_title(f'Mean R2 for individual stocks = {r2mean:4f}', fontsize=14) +#ax.legend(fontsize=12) + +ymax2 = 1.2 +ax.axis([-zmax+delz/2, zmax-delz/2, 0, ymax2]) # uses ymax2 for ensemble plot + + + +# now check for time-invariant distribution +data = df_orig.copy() + +# Quantum density function — returns plain array for curve_fit +def quantum_density(z, sig0, zoff=0.0): + ns = np.arange(0, 6) + qdn = np.zeros_like(z, dtype=float) + sigvec = sig0 * np.sqrt(2 * ns + 1) + means = zoff * np.ones_like(ns) - sigvec**2/2 # no drift term in pure Q-Variance + + for n in ns: + weight = poisson.pmf(n, mu=0.5) + qdn += weight * norm.pdf(z, loc=means[n], scale=sigvec[n]) + return qdn + +# Plot setup +zlim = 2 +zbins = np.linspace(-zlim, zlim, 51) +zmid = (zbins[:-1] + zbins[1:]) / 2 + +# Histogram +counts, _ = np.histogram(data["z"], bins=zbins, density=True) + +# Fit quantum model +p0 = [0.62, 0.0] # initial guess: sig0 ≈ 0.62 → σ₀ ≈ 0.079 after √2 scaling +popt, _ = curve_fit(quantum_density, zmid, counts, p0=p0, bounds=(0, [2.0, 0.5])) +sig0_fit, zoff_fit = popt + +# Predict on fine grid +z_fine = np.linspace(-zlim, zlim, 1000) +q_pred_fine = quantum_density(z_fine, *popt) + +# Predict on histogram bin centers for R² +q_pred_hist = quantum_density(zmid, *popt) +r2 = r2_score(counts, q_pred_hist) + +print(f"Fit: σ₀ = {sig0_fit:.4f}, zoff = {zoff_fit:.4f}, R² = {r2:.4f}") + +# obtain histogram bars +##counts, bin_edges, _ = plt.hist(data["z"], bins=zbins, density=True, visible=False) + +# now plot distn with periods +TVEC = [5, 10, 20, 40, 80] + +plt.figure(figsize=(9,7)) +plt.plot(z_fine, q_pred_fine, + color='red', lw=4, + label=f'Q-Variance fit: σ₀ = {sig0_fit:.3f}, R² = {r2:.4f}') + +for Tcur in TVEC: + datacur = data[(data["T"] == Tcur)].copy() + counts, bin_edges, _ = plt.hist(datacur["z"], bins=zbins, density=True, visible=False) + r2 = r2_score(counts, q_pred_hist) # use fit for whole data set + colcur = str(Tcur/(max(TVEC)+20)) + #plt.plot(zmid, counts, c=colcur, lw=2,label=f'T = {Tcur/5:.0f}') # , R² = {r2:.3f}' + plt.plot(zmid, counts, c=colcur, lw=2,label=f'T = {Tcur/5:.0f}, R² = {r2:.3f}' ) + +plt.title('Q-Variance: T dependence', fontsize=18, pad=20) +plt.xlabel('Scaled log-return z', fontsize=14) +plt.ylabel('Density', fontsize=14) +plt.xlim(-1.2, 1.2) +plt.legend(fontsize=10, loc='upper right') +plt.grid(alpha=0.3) +plt.tight_layout() + + +plt.show() +