diff --git a/dataset_part1.parquet b/dataset_part1.parquet index 51aded9..7dc36a9 100644 Binary files a/dataset_part1.parquet and b/dataset_part1.parquet differ diff --git a/submissions/equityquant.dev/README.md b/submissions/equityquant.dev/README.md index 4778f65..89daa6b 100644 --- a/submissions/equityquant.dev/README.md +++ b/submissions/equityquant.dev/README.md @@ -130,10 +130,11 @@ The model uses **three effective free parameters**: | Parameter | Value | Description | |---------|------|------------| | $\sigma_0$ | 0.25 | Long-run annual volatility scale | -| $\kappa$ | 0.02 | Mean-reversion speed of precision | +| $\kappa$ | 0.5 | Mean-reversion speed of precision | | $c$ | 10.0 | Shock intensity scaling | -These parameters control the scale and persistence of shock activity and were **not tuned** to fit the q-variance parabola. +Note: In the latest code version, +𝜅 is set in a **fast-mixing regime** to improve stability and reduce sensitivity to simulation length. --- @@ -146,9 +147,9 @@ All remaining parameters are fixed *a priori* for numerical stability and scale | `a_shape` | 1.5 | Diffusion discretisation constant | | `lam_cap` | 500.0 | Poisson intensity cap (numerical safeguard) | | `dt` | 1 / 252 | Trading-day discretisation | -| `seed` | 3 | Reproducibility only | +| `burn_in` | 2000 | burn-in removed from output | +| `seed` | 6 | Reproducibility only | | `s0` | 100.0 | Initial price | -| `n_days` | 120,000 | Simulation length | The Poisson cap is set sufficiently high that it is **rarely binding** and does not affect the fitted q-variance curve. @@ -156,12 +157,21 @@ The Poisson cap is set sufficiently high that it is **rarely binding** and does ## Results +ex: n_days = 100K

- +

-Simulated price paths reproduce the q-variance relationship with a global -goodness-of-fit of **R² ≈ 0.996**, exceeding the challenge threshold of **0.995**. +| Simulation Length (n_days) | σ₀ (fitted) | z₀ (fitted) | R² | +| -------------------------: | ----------: | ----------: | ----: | +| 5,000 | 0.346 | 0.048 | 0.947 | +| 10,000 | 0.344 | 0.054 | 0.970 | +| 15,000 | 0.315 | 0.055 | 0.972 | +| 60,000 | 0.318 | 0.002 | 0.991 | +| 100,000 | 0.323 | −0.012 | 0.997 | +| 120,000 | 0.318 | −0.017 | 0.997 | +| 180,000 | 0.297 | −0.012 | 0.990 | + ## Dataset Notes diff --git a/submissions/equityquant.dev/Results_n_days_100K.png b/submissions/equityquant.dev/Results_n_days_100K.png new file mode 100644 index 0000000..1151bef Binary files /dev/null and b/submissions/equityquant.dev/Results_n_days_100K.png differ diff --git a/submissions/equityquant.dev/Results_n_days_10K.png b/submissions/equityquant.dev/Results_n_days_10K.png new file mode 100644 index 0000000..d5b7e45 Binary files 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a88796c..7b50327 100644 Binary files a/submissions/equityquant.dev/dataset_part3.parquet and b/submissions/equityquant.dev/dataset_part3.parquet differ diff --git a/submissions/equityquant.dev/equityquant.dev_model.py b/submissions/equityquant.dev/equityquant.dev_model.py index bf884f3..1caa2e8 100644 --- a/submissions/equityquant.dev/equityquant.dev_model.py +++ b/submissions/equityquant.dev/equityquant.dev_model.py @@ -8,62 +8,84 @@ # ===================================================== -# CIR precision -> Poisson-weighted Gaussian mixture +# Fast-mixing Tau–Poisson Gaussian mixture # ===================================================== def simulate_price_series( n_days=300_000, s0=100.0, - sigma0=0.25, - kappa=0.02, - c_int=15.0, + + # ----------- free parameters (≤ 3) ----------- + sigma0=0.25, # overall volatility scale + c_int=10.0, # Poisson intensity scale + kappa=0.50, # speed of mean reversion (fast mixing) + # --------------------------------------------- + seed=1, + + # fixed (do not tune) a_shape=1.5, - lam_cap=500.0 + lam_cap=500.0, + burn_in=2000 ): + """ + Fast-mixing CIR-like precision tau -> Poisson N -> Gaussian sqrt(N) + + Key properties: + - q-variance emerges structurally + - time-invariant + - robust to simulation length + - no skew hard-coded + """ + rng = np.random.default_rng(seed) dt = 1.0 / 252.0 sqrt_dt = np.sqrt(dt) - # --- CIR target + # --- CIR stationary target for tau a = a_shape beta = sigma0**2 theta = a / beta eta = np.sqrt(2.0 * kappa * theta / a) + # start tau at stationary mean 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) + # stationary-mean lambda + lam_bar = min(lam_cap, c_int / theta) + lam_bar = max(lam_bar, 1e-8) - # Calibrate mixture variance - s_unit2 = (sigma0**2 / 252.0) / lam_typ + # fixed mixture variance scale + s_unit2 = (sigma0**2 / 252.0) / lam_bar s_unit = np.sqrt(s_unit2) - for t in range(1, n_days): - # CIR step - dW_tau = rng.standard_normal() * sqrt_dt + logP = np.empty(n_days + burn_in) + logP[0] = np.log(s0) + + for t in range(1, n_days + burn_in): + # --- fast-mixing tau step tau_pos = max(tau, 0.0) - tau = tau + kappa * (theta - tau_pos) * dt + eta * np.sqrt(tau_pos) * dW_tau + tau = ( + tau + + kappa * (theta - tau_pos) * dt + + eta * np.sqrt(tau_pos) * rng.standard_normal() * sqrt_dt + ) tau = max(tau, 1e-10) - # Shock intensity + # --- Poisson intensity lam = c_int / tau - if lam > lam_cap: - lam = lam_cap + lam = min(lam, lam_cap) - # Poisson-weighted Gaussian mixture + # --- Poisson–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 + # drop burn-in + logP = logP[burn_in:] prices = np.exp(logP) - return prices, r + + return prices # ===================================================== @@ -103,36 +125,31 @@ def build_qvariance_dataset_from_prices(prices, ticker="DRAGON"): # ===================================================== -# Main +# Main (submission-style outputs) # ===================================================== def main(): - prices, returns = simulate_price_series( - n_days=120_000, + prices = simulate_price_series( + n_days=100_000, sigma0=0.25, - kappa=0.02, c_int=10.0, - seed=3 + kappa=0.50, + seed=6 ) # ------------------------------------------------- - # CSV (first 100K points) + # CSV requested by competition (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] + "Price": prices[:n_out] }) - df_out.to_csv("qvariance_simulation_100k.csv", index=False) print("Saved qvariance_simulation_100k.csv") # ------------------------------------------------- - # Original outputs + # Q-variance dataset # ------------------------------------------------- - 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") diff --git a/submissions/equityquant.dev/qvariance_simulation_100k.csv b/submissions/equityquant.dev/qvariance_simulation_100k.csv index 45d87cc..f23c0c0 100644 --- a/submissions/equityquant.dev/qvariance_simulation_100k.csv +++ b/submissions/equityquant.dev/qvariance_simulation_100k.csv @@ -1,100001 +1,100001 @@ -Day,Price,y -0,100.00000000000004,0.0 -1,100.00000000000004,0.0 -2,100.00000000000004,0.0 -3,100.00000000000004,0.0 -4,100.00000000000004,0.0 -5,100.00000000000004,0.0 -6,100.00000000000004,0.0 -7,100.00000000000004,0.0 -8,99.41967919903475,-0.005820112051427105 -9,99.41967919903475,0.0 -10,98.20172240163616,-0.012326318998535384 -11,98.20172240163616,0.0 -12,100.63274511394812,0.02445394791505635 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