At1uri/stochastic-volatility-calibrator

⚡ Stochastic Volatility Calibrator & Heston Simulator

A quantitative modeling package developed by Ramprasad Atluri for continuous-time stochastic volatility simulation and calibration.

📌 Model Description

This model implements the bivariate continuous-time Heston Stochastic Volatility Model with full truncation discretization. It models the joint dynamics of an underlying asset price $S_t$ and its instantaneous variance $v_t$:

$$d{S}_t=\mu S_{t}dt+\sqrt{v_t}{S}_{t}d{W}_t^{S}dS\_t\; =\; \backslash mu\; S\_t\; dt\; +\; \backslash sqrt\{v\_t\}\; S\_t\; dW\_t^S$$

$$d{v}_t=\kappa (\theta -v_t)dt+\xi \sqrt{v_t}d{W}_t^{v}dv\_t\; =\; \backslash kappa\; (\backslash theta\; -\; v\_t)\; dt\; +\; \backslash xi\; \backslash sqrt\{v\_t\}\; dW\_t^v$$

$$\text{Cov}(d{W}_t^S,d{W}_t^v)=\rho dt\backslash text\{Cov\}(dW\_t^S,\; dW\_t^v)\; =\; \backslash rho\; \backslash ,\; dt$$

Parameters:

• $\kappa$ (Mean Reversion Speed): Rate at which variance pulls back towards its long-term average $\theta$.
• $\theta$ (Long-Term Variance): Long-run variance ceiling.
• $\xi$ (Vol of Vol): Volatility of the variance diffusion process.
• $\rho$ (Leverage Correlation): Asymmetric correlation capturing the financial leverage effect ($\rho < 0$).
• $v_0$ (Initial Variance): Instantaneous starting variance.

🚀 Quick Start

Download and run simulations directly in Python:

from huggingface_hub import hf_hub_download
import json

# Download weights
weights_file = hf_hub_download(
    repo_id="At1uri/stochastic-volatility-calibrator",
    filename="calibrator_weights.json"
)

with open(weights_file, "r") as f:
    config = json.load(f)

print("Calibrated Parameters:", config["calibrated_parameters"])

Full Simulation using calibrator.py:

from calibrator import HestonStochasticVolatilityModel

# Initialize pre-calibrated model
model = HestonStochasticVolatilityModel.load_pretrained()

# Simulate 500 Monte Carlo price and variance paths
price_paths, var_paths = model.simulate_paths(s0=100.0, t_days=252, n_paths=500)
print(f"Mean Terminal Price: {price_paths[:, -1].mean():.2f}")

📊 Diagnostics & Feller Condition

The pre-calibrated parameter set guarantees the Feller Condition: $$2\kappa \theta >{\xi }^{2}2\; \backslash kappa\; \backslash theta\; >\; \backslash xi^2$$ Ensuring the variance process $v_t$ remains strictly positive ($v_t > 0$) almost surely.

• Feller Ratio: $2\kappa\theta / \xi^2 = 2.012$ (Strictly satisfied)
• Calibration RMSE: $0.00318$

⚖️ License

MIT License. Free for academic, proprietary, and commercial quantitative development.