stochastic-engine 0.1.0

A comprehensive, Pythonic quantitative finance library for stochastic processes, option pricing, and risk metrics

Stochastic Engine

A comprehensive, Pythonic quantitative finance library for stochastic processes, option pricing, and risk metrics.

No more Googling formulas. No more reimplementing Black-Scholes. Just clean, intuitive APIs.

Installation

pip install stochastic-engine

Or install from source:

git clone https://github.com/yourusername/stochastic-engine.git
cd stochastic-engine
pip install -e ".[dev]"

Quick Start

Simulate Stock Prices (GBM)

from stochastic_engine import GBM

# Simulate 1000 paths of stock prices over 1 year
gbm = GBM(S0=100, mu=0.05, sigma=0.2)
paths = gbm.simulate(T=1, steps=252, n_paths=1000)

# paths.shape = (1000, 253)  # 1000 paths, 253 time points

Price Options with Black-Scholes

from stochastic_engine import BlackScholes

# Price a European call option
option = BlackScholes(S=100, K=105, T=1, r=0.05, sigma=0.2)

print(f"Price: ${option.price:.2f}")      # $8.02
print(f"Delta: {option.delta:.4f}")       # 0.5462
print(f"Gamma: {option.gamma:.4f}")       # 0.0188
print(f"Vega:  {option.vega:.4f}")        # 0.3745
print(f"Theta: {option.theta:.4f}")       # -0.0180

# All Greeks at once
print(option.greeks)

Monte Carlo Pricing

from stochastic_engine import MonteCarloPricer

mc = MonteCarloPricer(S0=100, r=0.05, sigma=0.2, T=1)

# European call
result = mc.price_european_call(K=105, n_paths=100000)
print(f"Price: ${result.price:.2f} ± {result.std_error:.4f}")

# Asian call (average price option)
asian = mc.price_asian_call(K=100, n_paths=50000, steps=252)
print(f"Asian call: ${asian.price:.2f}")

Calculate Risk Metrics

from stochastic_engine import VaR, CVaR
from stochastic_engine.risk import sharpe_ratio, max_drawdown

# Historical VaR
returns = [...]  # Your return data
var = VaR(returns, confidence=0.95)
print(f"95% VaR: {var.historical():.2%}")
print(f"95% CVaR: {CVaR(returns, confidence=0.95).historical():.2%}")

# Performance metrics
print(f"Sharpe Ratio: {sharpe_ratio(returns):.2f}")
print(f"Max Drawdown: {max_drawdown(prices):.2%}")

Implied Volatility

from stochastic_engine import implied_volatility

# Find IV from market price
iv = implied_volatility(
    market_price=8.02,
    S=100, K=105, T=1, r=0.05
)
print(f"Implied Vol: {iv:.2%}")  # ~20%

Features

Stochastic Processes

• GBM - Geometric Brownian Motion (stock prices)
• OrnsteinUhlenbeck - Mean-reverting process (interest rates, pairs trading)

Option Pricing

• BlackScholes - Closed-form European options with all Greeks
• MonteCarloPricer - Flexible MC engine with variance reduction
  • European calls/puts
  • Asian options (arithmetic & geometric)
  • Custom payoff functions

Risk Metrics

• VaR - Historical, Parametric, Monte Carlo, Cornish-Fisher
• CVaR - Expected Shortfall
• Sharpe Ratio, Sortino Ratio, Calmar Ratio
• Max Drawdown
• Beta, Alpha, Information Ratio

Volatility

• Implied Volatility Solver - Newton-Raphson, Bisection, Brent's method
• IV Surface - Compute IV across strikes and maturities

Design Philosophy

1. Simple API: One-liners for common tasks
2. NumPy Native: Vectorized operations, array inputs
3. Stateless: Thread-safe, no global state
4. Type-Hinted: Full IDE/mypy support
5. Well-Documented: NumPy-style docstrings, tutorials, examples

API Reference

Processes

# Geometric Brownian Motion
gbm = GBM(S0=100, mu=0.05, sigma=0.2, seed=42)
paths = gbm.simulate(T=1, steps=252, n_paths=1000, method="exact")
samples = gbm.sample(t=1, n_samples=10000)
print(gbm.mean(1), gbm.variance(1))

# Ornstein-Uhlenbeck
ou = OrnsteinUhlenbeck(X0=0.1, mu=0.05, theta=0.5, sigma=0.02)
paths = ou.simulate(T=10, steps=2520, n_paths=100)
print(ou.half_life)  # Time to revert halfway to mean

Pricing

# Black-Scholes (vectorized)
strikes = np.array([95, 100, 105, 110])
bs = BlackScholes(S=100, K=strikes, T=1, r=0.05, sigma=0.2)
print(bs.price)   # Array of 4 prices
print(bs.delta)   # Array of 4 deltas

# Monte Carlo with custom payoff
def barrier_call(paths, K=100, barrier=120):
    """Knock-out call: worthless if price ever exceeds barrier."""
    knocked_out = (paths.max(axis=1) >= barrier)
    payoff = np.maximum(paths[:, -1] - K, 0)
    payoff[knocked_out] = 0
    return payoff

mc = MonteCarloPricer(S0=100, r=0.05, sigma=0.2, T=1)
result = mc.price_custom(barrier_call, n_paths=100000, steps=252)

Risk

# VaR methods
var = VaR(returns, confidence=0.95)
var.historical()          # Historical simulation
var.parametric()          # Variance-covariance (normal)
var.parametric("t")       # Student's t-distribution
var.monte_carlo()         # Monte Carlo
var.cornish_fisher()      # Adjusted for skewness/kurtosis

# Backtest VaR
results = var.backtest(window=250)
print(f"Violation rate: {results['violation_rate']:.2%}")

Examples

Monte Carlo Option Pricing vs Black-Scholes

from stochastic_engine import BlackScholes, MonteCarloPricer

# Analytical price
bs = BlackScholes(S=100, K=100, T=1, r=0.05, sigma=0.2)
print(f"BS Price: ${bs.price:.4f}")

# Monte Carlo price
mc = MonteCarloPricer(S0=100, r=0.05, sigma=0.2, T=1, seed=42)
result = mc.price_european_call(K=100, n_paths=100000)
print(f"MC Price: ${result.price:.4f} ± ${result.std_error:.4f}")

Portfolio VaR

import numpy as np
from stochastic_engine import VaR, CVaR

# Simulate portfolio returns
np.random.seed(42)
returns = np.random.normal(0.0005, 0.02, 252)  # 1 year of daily returns

var = VaR(returns, confidence=0.99)
cvar = CVaR(returns, confidence=0.99)

print(f"99% 1-day VaR:  {var.historical():.2%}")
print(f"99% 1-day CVaR: {cvar.historical():.2%}")
print(f"99% 10-day VaR: {var.scale_to_horizon(var.historical(), 10):.2%}")

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

MIT License - see LICENSE file for details.