quanteo 0.1.0

A quantitative options pricing and risk library.

QUANTEO: Quantitative Options Pricing & Risk

Quanteo is an Object-Oriented Python library for derivative pricing and risk sensitivity analysis. This project is developed as part of my learning journey during the MSc in Mathematical Engineering at Politecnico di Torino. The library implements stochastic models and variance reduction techniques to estimate option prices and Greeks, particularly for path-dependent derivatives.

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Author: Matteo Ientile
MSc Mathematical Engineering – Politecnico di Torino

Functionalities available at the moment

1. Simulation & Pricing Engines

• Monte Carlo: Path generation for Geometric Brownian Motion (GBM).
• Quasi-Monte Carlo: Sobol low-discrepancy sequences for improved convergence.
• Variance Reduction: Control Variates (anchored to analytical solutions) and Antithetic Sampling.
• Analytical Models: Closed-form Black-Scholes-Merton (BSM) for European and Geometric Asian options.

2. Risk Management (Greeks)

• Computation of $\Delta, \Gamma, \nu, \rho, \Theta$.
• Finite Differences: Central difference approximations for numerical sensitivities.
• CRN (Common Random Numbers): Epsilon caching to ensure stability in numerical derivatives.

3. Contract Types

• European Options: Standard Call/Put payoffs.
• Asian Options: Discrete Arithmetic and Geometric averages.

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Examples

The examples/ directory contains notebooks demonstrating the implementation:

• european_options_and_greeks.ipynb: Benchmarking BSM, MC, and QMC engines.
• asian_options_and_variance_reduction.ipynb: Statistical impact of Control Variates on Asian contracts.

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Usage

from quanteo.models import GBM
from quanteo.options import ArithmeticAsianOption, GeometricAsianOption
from quanteo.pricers import MonteCarloPricer, ControlVariateMC, GeometricAsianPricer

# 1. Market Data
model = GBM(S0=85.0, r=0.04, sigma=0.42)

# 2. Options (126 observations)
target = ArithmeticAsianOption(T=0.5, K=88.0, N=126)
control = GeometricAsianOption(T=0.5, K=88.0, N=126)

# 3. Analytical Anchor
exact_cv = GeometricAsianPricer().price(control, model).price

# 4. Monte Carlo with Control Variate
mc = MonteCarloPricer(n_paths=5000, n_steps=126)
cv_engine = ControlVariateMC(mc)

result = cv_engine.price(target, control, exact_cv, model)

print(f"Price: {result.price:.4f}")
print(f"95% CI: [{result.metrics['cv_lower_bound']:.4f}, {result.metrics['cv_upper_bound']:.4f}]")

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Roadmap

• Heston Model: Stochastic volatility integration.
• Jump Diffusion: Merton model for discontinuous price paths.
• American Options: Longstaff-Schwartz (LSM) implementation.
• Dashboard: Streamlit interface for visualization.