Metadata-Version: 2.4
Name: stochvolmodels
Version: 2.0.0
Summary: Fourier-transform pricing, Monte Carlo validation, and calibration of European options under stochastic-volatility models in Python.
Author-email: Artur Sepp <artursepp@gmail.com>
Maintainer-email: Artur Sepp <artursepp@gmail.com>, Parviz Rakhmonov <ParvizRZ@gmail.com>
License-Expression: MIT
Project-URL: Homepage, https://github.com/ArturSepp/StochVolModels
Project-URL: Documentation, https://stochvolmodels.readthedocs.io/en/latest/
Project-URL: Repository, https://github.com/ArturSepp/StochVolModels.git
Project-URL: Issues, https://github.com/ArturSepp/StochVolModels/issues
Keywords: stochastic volatility,volatility modeling,option pricing,heston model,log-normal stochastic volatility,monte carlo simulation,fourier transform,quantitative finance,derivatives pricing,implied volatility,volatility surface
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Financial and Insurance Industry
Classifier: Intended Audience :: Science/Research
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: 3.13
Classifier: Topic :: Office/Business :: Financial :: Investment
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Software Development :: Libraries :: Python Modules
Requires-Python: >=3.10
Description-Content-Type: text/markdown
License-File: LICENSE.txt
Requires-Dist: numba>=0.60.0
Requires-Dist: numpy>=2.0
Requires-Dist: scipy>=1.12.0
Requires-Dist: pandas>=2.2.0
Requires-Dist: matplotlib>=3.8.0
Requires-Dist: seaborn>=0.13.0
Provides-Extra: research
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Requires-Dist: qis>=5.11.0; extra == "research"
Provides-Extra: visualization
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Provides-Extra: numerical
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Provides-Extra: all
Requires-Dist: stochvolmodels[jupyter,numerical,research,visualization]; extra == "all"
Dynamic: license-file

# StochVolModels (`stochvolmodels`)

`stochvolmodels` provides Fourier-transform pricing, Monte Carlo validation, and calibration of
European options under stochastic-volatility models in Python.

It is a focused research and practitioner library, not a general derivatives platform: the stable
workflows cover European vanilla and related variance analytics under Heston and the
Karasinski-Sepp log-normal stochastic-volatility model.

[![PyPI](https://img.shields.io/pypi/v/stochvolmodels?style=flat-square)](https://pypi.org/project/stochvolmodels/)
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[![CI](https://github.com/ArturSepp/StochVolModels/actions/workflows/ci.yml/badge.svg)](https://github.com/ArturSepp/StochVolModels/actions)
[![Downloads](https://static.pepy.tech/badge/stochvolmodels)](https://pepy.tech/project/stochvolmodels)
[![Monthly](https://static.pepy.tech/badge/stochvolmodels/month)](https://pepy.tech/project/stochvolmodels)
[![Open LogSV quickstart in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ArturSepp/StochVolModels/blob/main/examples/getting_started/quickstart_colab.ipynb)

**Paper:** Sepp, A. and Rakhmonov, P. (2023), *Log-normal stochastic volatility model with quadratic drift*, [International Journal of Theoretical and Applied Finance, 26(8)](https://www.worldscientific.com/doi/10.1142/S0219024924500031). See [Citation](#citation) for the full BibTeX list.

**Documentation:** [stochvolmodels.readthedocs.io](https://stochvolmodels.readthedocs.io/en/latest/) ·
[offline quickstart](examples/getting_started/quickstart.py) ·
[LogSV quickstart in Colab](https://colab.research.google.com/github/ArturSepp/StochVolModels/blob/main/examples/getting_started/quickstart_colab.ipynb)

---

## Why stochvolmodels

`stochvolmodels` is the reference implementation of the Karasinski-Sepp log-normal beta stochastic volatility model, maintained by one of the model's originators, with the Heston model implemented alongside as a benchmark. The design goal is a single generic interface for a stochastic volatility model — a closed-form moment generating function for Fourier-transform pricing on one side, Monte Carlo dynamics on the other — so that analytic prices, simulated prices, and calibrated implied volatilities are directly comparable model to model.

The same analytics power the research: the `papers` module reproduces the computations and figures of five papers, from the quadratic-drift log-normal SV model (IJTAF) to cryptocurrency inverse options (Quantitative Finance), robust stochastic volatility modelling, impermanent-loss hedging in DeFi, and stochastic volatility for the factor HJM framework — see [Supporting Illustrations](#papers).

## Overview

The StochVol package provides:
1) Analytics for Black-Scholes and Normal vols
2) Interfaces and implementation for stochastic volatility models,
including Karasinski-Sepp log-normal SV model and Heston SV model 
using analytical method with Fourier transform and Monte Carlo simulations
3) Visualization of model implied volatilities

For the analytic implementation of stochastic volatility models, the package provides interfaces for a generic volatility model with the following features.
1) Interface for analytical pricing of vanilla options 
using Fourier transform with closed-form solution for moment generating function
2) Interface for Monte-Carlo simulations of model dynamics


[Illustrations](#papers) of using package analytics for research 
work is provided in top-level package ```papers``` 
which contains computations and visualisations for several papers


## When to use it — and when not

Use `stochvolmodels` for European vanilla pricing and implied-volatility analytics under stochastic volatility, for model calibration to option chains (a calibration example to Bitcoin options data is included), and for replicating the papers above.

It is not a general derivatives platform: no American or path-dependent payoffs, no local-volatility or term-structure models. For fast Black-Scholes-Merton and Bachelier array pricing without stochastic volatility, use [`vanilla-option-pricers`](https://github.com/ArturSepp/VanillaOptionPricers); for strategy backtesting and reporting, use [`qis`](https://github.com/ArturSepp/QuantInvestStrats).

## Installation
Install using
```python 
pip install stochvolmodels
```
Upgrade using
```python 
pip install --upgrade stochvolmodels
```
Clone using
```python 
git clone https://github.com/ArturSepp/StochVolModels.git
```


### Core Dependencies
- `python >= 3.10`
- `numba >= 0.60.0`
- `numpy >= 2.0`
- `scipy >= 1.12.0`
- `pandas >= 2.2.0`
- `matplotlib >= 3.8.0`
- `seaborn >= 0.13.0`

### Optional extras

| Extra | Installs | Needed for |
|---|---|---|
| `research` | `qis >= 5.11.0`, `option-chain-analytics >= 4.0.0` | scripts in `papers/` and option-chain research |
| `visualization` | `plotly >= 5.0.0` | interactive figures |
| `numerical` | `scikit-learn >= 1.3.0`, `statsmodels >= 0.14.0` | statistical fits |
| `jupyter` | `jupyter`, `notebook`, `jupyterlab`, `ipykernel`, `ipywidgets` | notebooks |
| `dev` | `build`, `pytest`, `pytest-cov`, `pytest-regressions`, `ruff` | builds, tests, and linting |

Install an extra using
```python
pip install stochvolmodels[research]
```
The library itself imports none of these: `import stochvolmodels` needs the core dependencies only.

### API stability

The names listed by `stochvolmodels.__all__` are the stable high-level API. Historical package-root
names remain available lazily for compatibility, but names not in `__all__` should be treated as
advanced interfaces.

The rough-LogSV Monte Carlo and Factor HJM implementations are experimental research surfaces.
Their characterized pricing paths are tested, but deep imports under
`stochvolmodels.pricers.rough_logsv` and `stochvolmodels.pricers.factor_hjm` may evolve between
minor releases. The legacy `Gaussian_interval` quadrature path requires unsupported `orthopy` and
`quadpy` packages and now raises a precise `ImportError`; the incomplete rough-Heston kernel raises
`NotImplementedError` until a characterized Mittag-Leffler backend is provided.


# Table of contents
1. [Model Interface](#introduction)
    1. [Log-normal stochastic volatility model](#logsv)
    2. [Heston stochastic volatility model](#hestonsv)
2. [Running log-normal SV pricer](#paragraph1)
   1. [Computing model prices and vols](#subparagraph1)
   2. [Running model calibration to sample Bitcoin options data](#subparagraph2)
   3. [Comparison of model prices vs MC](#subparagraph3)
   4. [Analysis and figures for the paper](#subparagraph4)
3. [Running Heston SV pricer](#heston)
4. [Supporting Illustrations for Public Papers](#papers)


Running model calibration to sample Bitcoin options data

## Implemented Stochastic Volatility models <a name="introduction"></a>
The package provides interfaces for a generic volatility model with the following features.
1) Interface for analytical pricing of vanilla options using Fourier transform with closed-form solution for moment generating function
2) Interface for Monte-Carlo simulations of model dynamics
3) Interface for visualization of model implied volatilities

The model interface is in `src/stochvolmodels/pricers/model_pricer.py`.

### Log-normal stochastic volatility model <a name="logsv"></a>

The analytics for Karasinski-Sepp log-normal stochastic volatility model is based on the paper

[Log-normal Stochastic Volatility Model with Quadratic Drift](https://www.worldscientific.com/doi/10.1142/S0219024924500031) by Artur Sepp and Parviz Rakhmonov


The dynamics of the log-normal stochastic volatility model:

$$dS_{t}=r(t)S_{t}dt+\sigma_{t}S_{t}dW^{(0)}_{t}$$

$$d\sigma_{t}=\left(\kappa_{1} + \kappa_{2}\sigma_{t} \right)(\theta - \sigma_{t})dt+  \beta  \sigma_{t}dW^{(0)}_{t} +  \varepsilon \sigma_{t} dW^{(1)}_{t}$$

$$dI_{t}=\sigma^{2}_{t}dt$$

where $r(t)$ is the deterministic risk-free rate; $W^{(0)}_{t}$ and $W^{(1)}_t$  are uncorrelated Brownian motions, $\beta\in\mathbb{R}$ is the volatility beta which measures the sensitivity of the volatility to changes in the spot price, and $\varepsilon>0$ is the volatility of residual volatility. We denote by $\vartheta^{2}$, $\vartheta^{2}=\beta^{2}+\varepsilon^{2}$, the total instantaneous variance of the volatility process.


Implementation of Lognormal SV model is contained in 
```python 
src/stochvolmodels/pricers/logsv_pricer.py
```

### Heston stochastic volatility model <a name="hestonsv"></a>

The dynamics of Heston stochastic volatility model:

$$dS_{t}=r(t)S_{t}dt+\sqrt{V_{t}}S_{t}dW^{(S)}_{t}$$

$$dV_{t}=\kappa (\theta - V_{t})dt+  \vartheta  \sqrt{V_{t}}dW^{(V)}_{t}$$

where  $W^{(S)}$ and $W^{(V)}$ are correlated Brownian motions with correlation parameter $\rho$

Implementation of Heston SV model is contained in 
```python 
src/stochvolmodels/pricers/heston_pricer.py
```

## Running log-normal SV pricer <a name="paragraph1"></a>

Basic features are implemented in 
```python 
examples/calibration/run_lognormal_sv_pricer.py
```

### Loading cached SPX/VIX chains for experiments

Empirical CBOE chains remain owned and normalized by OptionChainAnalytics. Install the optional
packages separately, set `OCA_DATA_PATH` to the ignored OCA data directory containing
`cboe_options/`, and request only the observation window needed by the experiment:

```bash
pip install "stochvolmodels[research]" "option-chain-analytics[cboe]>=4.0.0"
```

```python
import pandas as pd

from stochvolmodels.data.fetch_option_chain import load_cboe_option_chain

option_chain = load_cboe_option_chain(
    ticker='SPX',
    value_time=pd.Timestamp('2023-11-08 22:00:00+00:00'),
    days_map={'1w': 7, '1m': 21, '3m': 63},
    delta_bounds=(None, None),
)
```

The adapter reads OCA's ignored per-underlying Parquet cache and returns SVM's existing lightweight
`OptionChain`; it does not copy the dataset or add provider metadata to the calibration object. See
`examples/calibration/load_cboe_option_chain.py` for SPX and VIX cases.

Imports:
```python
import numpy as np 
import stochvolmodels as sv
from stochvolmodels import LogSVPricer, LogSvParams, OptionChain
```


### Computing model prices and vols <a name="subparagraph1"></a>

```python 
# instance of pricer
logsv_pricer = LogSVPricer()

# define model params    
params = LogSvParams(sigma0=1.0, theta=1.0, kappa1=5.0, kappa2=5.0, beta=0.2, volvol=2.0)

# 1. compute the price
model_price, vol = logsv_pricer.price_vanilla(params=params,
                                             ttm=0.25,
                                             forward=1.0,
                                             strike=1.0,
                                             optiontype='C')
print(f"price={model_price:0.4f}, implied vol={vol: 0.2%}")

# 2. prices for slices
model_prices, vols = logsv_pricer.price_slice(params=params,
                                             ttm=0.25,
                                             forward=1.0,
                                             strikes=np.array([0.9, 1.0, 1.1]),
                                             optiontypes=np.array(['P', 'C', 'C']))
print([f"{p:0.4f}, implied vol={v: 0.2%}" for p, v in zip(model_prices, vols)])

# 3. prices for option chain with uniform strikes
option_chain = OptionChain.get_uniform_chain(ttms=np.array([0.083, 0.25]),
                                            ids=np.array(['1m', '3m']),
                                            strikes=np.linspace(0.9, 1.1, 3))
model_prices, vols = logsv_pricer.compute_chain_prices_with_vols(option_chain=option_chain, params=params)
print(model_prices)
print(vols)
```


### Running model calibration to sample Bitcoin options data  <a name="subparagraph2"></a>
```python 
btc_option_chain = sv.get_btc_test_chain_data()
params0 = LogSvParams(sigma0=0.8, theta=1.0, kappa1=5.0, kappa2=None, beta=0.15, volvol=2.0)
btc_calibrated_params = logsv_pricer.calibrate_model_params_to_chain(option_chain=btc_option_chain,
                                                                    params0=params0,
                                                                    constraints_type=sv.ConstraintsType.INVERSE_MARTINGALE)
print(btc_calibrated_params)

logsv_pricer.plot_model_ivols_vs_bid_ask(option_chain=btc_option_chain,
                               params=btc_calibrated_params)
```
The full fitted-surface figure is generated by the paper workflow and is not committed as a build
artifact.



### Comparison of model prices vs MC  <a name="subparagraph3"></a>
```python 
btc_option_chain = sv.get_btc_test_chain_data()
uniform_chain_data = OptionChain.to_uniform_strikes(obj=btc_option_chain, num_strikes=31)
btc_calibrated_params = LogSvParams(sigma0=0.8327, theta=1.0139, kappa1=4.8609, kappa2=4.7940, beta=0.1988, volvol=2.3694)
logsv_pricer.plot_comp_mma_inverse_options_with_mc(option_chain=uniform_chain_data,
                                                  params=btc_calibrated_params,
                                                  nb_path=400000)
                                           
```
The full analytic-versus-Monte-Carlo figure is generated by the paper workflow.


### Analysis and figures for the paper <a name="subparagraph4"></a>

The paper figures and equation-mapped analysis live in
```python 
papers/logsv_model_with_quadratic_drift
```


## Running Heston SV pricer <a name="heston"></a>

Examples are implemented here
```python 
examples/pricing/run_heston_sv_pricer.py
examples/pricing/run_heston.py
```

Content of run_heston.py
```python 
import numpy as np
import matplotlib.pyplot as plt
from stochvolmodels import HestonPricer, HestonParams, OptionChain

# define parameters for bootstrap
params_dict = {'rho=0.0': HestonParams(v0=0.2**2, theta=0.2**2, kappa=4.0, volvol=0.75, rho=0.0),
               'rho=-0.4': HestonParams(v0=0.2**2, theta=0.2**2, kappa=4.0, volvol=0.75, rho=-0.4),
               'rho=-0.8': HestonParams(v0=0.2**2, theta=0.2**2, kappa=4.0, volvol=0.75, rho=-0.8)}

# get uniform slice
option_chain = OptionChain.get_uniform_chain(ttms=np.array([0.25]), ids=np.array(['3m']), strikes=np.linspace(0.8, 1.15, 20))
option_slice = option_chain.get_slice(id='3m')

# run pricer
pricer = HestonPricer()
pricer.plot_model_slices_in_params(option_slice=option_slice, params_dict=params_dict)

plt.show()
```


## Supporting Illustrations for Public Papers <a name="papers"></a>

As illustrations of different analytics, this package includes module ```papers``` 
with codes for computations and visualisations featured in several papers
for 

1) "Log-normal Stochastic Volatility Model with Quadratic Drift" by Artur Sepp 
and Parviz Rakhmonov: https://www.worldscientific.com/doi/10.1142/S0219024924500031
```python 
papers/logsv_model_with_quadratic_drift
```


2) "What is a robust stochastic volatility model" by Artur Sepp and Parviz Rakhmonov, SSRN:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4647027
```python 
papers/volatility_models
```


3) "Valuation and Hedging of Cryptocurrency Inverse Options" by Artur Sepp
and Vladimir Lucic, 
SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4606748 
```python 
papers/inverse_options
```

4) "Unified Approach for Hedging Impermanent Loss of Liquidity Provision" by 
Artur Sepp, Alexander Lipton and Vladimir Lucic, 
SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4887298 
```python 
papers/il_hedging
```

5) "Stochastic Volatility for Factor Heath-Jarrow-Morton Framework" by Artur Sepp and Parviz Rakhmonov,
Review of Derivatives Research, 2025, 28(3), article 12: https://doi.org/10.1007/s11147-025-09217-4
(preprint: http://ssrn.com/abstract=4646925)
```python 
papers/sv_for_factor_hjm
```

6) "Jump risk premia in the presence of clustered jumps" by Francis Liu, Natalie Packham and
Artur Sepp, SSRN: https://ssrn.com/abstract=4735365. The repository folder contains related
development code and is not an exact replication package.
```python
papers/jump_risk_premia_clustered_jumps
```

## Project Structure

```
StochVolModels/
├── src/
│   └── stochvolmodels/
│       ├── data/                 # option-chain containers and sample data
│       ├── pricers/              # analytic, transform, and Monte Carlo models
│       ├── utils/                # quadrature, payoff, plotting, and rate helpers
│       └── tests/                # shipped pytest suite and regression data
├── examples/                     # repository-only runnable workflows
│   ├── getting_started/
│   ├── pricing/
│   ├── calibration/
│   ├── monte_carlo/
│   └── advanced/
├── papers/                       # paper replications and labelled development code
├── docs/                         # documentation sources and figures
└── README.md
```

## Ecosystem

This package is part of an open-source Python stack for quantitative finance — full catalogue at [github.com/ArturSepp](https://github.com/ArturSepp):

| Package | Purpose |
|---|---|
| [`qis`](https://github.com/ArturSepp/QuantInvestStrats) | Performance analytics, factsheets, and visualisation |
| [`optimalportfolios`](https://github.com/ArturSepp/OptimalPortfolios) | Portfolio construction and backtesting |
| [`factorlasso`](https://github.com/ArturSepp/factorlasso) | Sparse factor models and factor covariance estimation |
| [`bbg-fetch`](https://github.com/ArturSepp/BloombergFetch) | Bloomberg data fetching |
| [`trendfollowing`](https://github.com/ArturSepp/TrendFollowingSystems) | Trend-following systems: closed-form theory and replication |
| [`goal-based-allocation`](https://github.com/ArturSepp/GoalBasedAllocation) | Dynamic MV allocation under regime-switching jump-diffusions |
| [`stochvolmodels`](https://github.com/ArturSepp/StochVolModels) *(this package)* | Stochastic volatility pricing analytics |
| [`vanilla-option-pricers`](https://github.com/ArturSepp/VanillaOptionPricers) | Vectorised vanilla option pricers and implied volatility fitters |

Dependency links within the stack: `optimalportfolios` builds on `qis` and `factorlasso`; `trendfollowing` builds on `qis`.

## Contributing

Contributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.

## License

This project is licensed under the MIT License - see the [LICENSE.txt](LICENSE.txt) file for details.

## Citation

If you use this package in your research, please cite the relevant papers:

```bibtex
@misc{sepp2024stochvolmodels,
  title={StochVolModels: Python Implementation of Stochastic Volatility Models},
  author={Sepp, Artur},
  year={2024},
  howpublished={\url{https://github.com/ArturSepp/StochVolModels}},
  note={Python package for pricing analytics and Monte Carlo simulations}
}

@article{sepprakhmonov2023,
title={Log-normal stochastic volatility model with quadratic drift},
author={Sepp, Artur and Rakhmonov, Parviz},
journal={International Journal of Theoretical and Applied Finance},
volume={26},
number={8},
year={2023},
url={https://www.worldscientific.com/doi/epdf/10.1142/S0219024924500031}
}

@article{sepprakhmonov2023b,
title={What is a robust stochastic volatility model},
author={Sepp, Artur and Rakhmonov, Parviz},
year={2023},
note={Working paper},
url={http://ssrn.com/abstract=4647027}
}

@article{lucicsepp2024,
title={Valuation and hedging of cryptocurrency inverse options},
author={Lucic, Vladimir and Sepp, Artur},
journal={Quantitative Finance},
volume={24},
number={7},
pages={851--869},
year={2024},
url={https://www.tandfonline.com/doi/full/10.1080/14697688.2024.2364804}
}

@article{sepprakhmonov2025,
title={Stochastic volatility for factor Heath-Jarrow-Morton framework},
author={Sepp, Artur and Rakhmonov, Parviz},
volume={28},
number={3},
pages={12},
year={2025},
journal={Review of Derivatives Research},
doi={10.1007/s11147-025-09217-4},
note={Preprint: http://ssrn.com/abstract=4646925}
}
```

## Acknowledgments

Special thanks to co-authors and collaborators:
- Parviz Rakhmonov  
- Vladimir Lucic
- Alexander Lipton

For additional research and advanced analytics, see the companion modules and papers included in this package.
