financial-stochastic-processes 0.1.6

A package for simulating financial stochastic processes.

FinancialStochasticProcesses Documentation

Installation

You can install the package via pip:

pip install financial_stochastic_processes

StochasticAssetPriceSimulator

The StochasticAssetPriceSimulator is a Python class designed to simulate various financial stochastic processes, such as Geometric Brownian Motion (GBM), Jump Diffusion, Heston Stochastic Volatility model, and Regime-Switching models. This class can be used to model and simulate asset price dynamics with optional control over randomness using a seed for reproducibility.

Features

• Geometric Brownian Motion (GBM): Simulates asset price movements under the GBM assumption.
• Jump Diffusion Model: Simulates asset price movements with both continuous price changes and discrete jumps, where jumps can be either upward or downward.
• Heston Model: Simulates asset price dynamics with stochastic volatility using the Heston model.
• Regime-Switching Model: Simulates asset prices under different market regimes using a regime-switching model.
• Seed Control: Optionally set a random seed to generate reproducible simulations.

1. Initialize the Simulator

You can initialize the simulator by providing the required parameters, including the initial stock price, time horizon, and time step size.

from financial_stochastic_processes import StochasticAssetPriceSimulator
simulator = StochasticAssetPriceSimulator(S0=100, T=1, dt=0.01, seed=42)

2. Simulate Geometric Brownian Motion (GBM)

Use the simulate_GBM method to generate asset prices under a GBM process.

gbm_simulation = simulator.simulate_GBM()

3. Simulate Jump Diffusion

Use the simulate_jump_diffusion method to generate asset prices under a Jump Diffusion process.

jump_diffusion_simulation = simulator.simulate_jump_diffusion()

4. Simulate Heston Model

Use the simulate_heston method to generate asset prices under the Heston stochastic volatility model.

heston_simulation, heston_volatility = simulator.simulate_heston()

5. Simulate Regime-Switching Model

Use the simulate_regime_switching method to generate asset prices under the regime-switching model.

regime_switching_simulation = simulator.simulate_regime_switching()

Example Code:

import matplotlib.pyplot as plt

# Initialize the simulator
simulator = StochasticAssetPriceSimulator(S0=100, T=1, dt=0.01, sigma1=0.2, sigma2=0.2, V0=0.05, seed=42)

# Simulate GBM
gbm_prices = simulator.simulate_GBM()

# Simulate Jump Diffusion
jump_diffusion_prices = simulator.simulate_jump_diffusion()

# Simulate Heston Model
heston_prices, heston_volatility = simulator.simulate_heston()

# Plot the results
plt.plot(gbm_prices, label="GBM")
plt.plot(jump_diffusion_prices, label="Jump Diffusion")
plt.plot(heston_prices, label="Heston Model")
plt.xlabel("Time")
plt.ylabel("Asset Price")
plt.legend()
plt.title("Stochastic Asset Price Simulation")
plt.show()

Parameters

The following parameters are available when creating a StochasticAssetPriceSimulator instance:

Parameter	Description	Default Value
S0	Initial stock price (Every Model)	Required
T	Time horizon (Every Model)	Required
dt	Time step size(Every Model)	Required
mu	Drift (expected return)(GBM, Jump Diffusion)	0.05
sigma	Volatility (GBM, Jump Diffusion)	0.2
lamb	Jump intensity (average number of jumps)(Jump Diffusion)	0.75
p	Probability of upward jumps(Jump Diffusion)	0.5
lambda1	Intensity of upward jumps(Jump Diffusion)	1.0
lambda2	Intensity of downward jumps(Jump Diffusion)	1.0
kappa	Mean reversion rate (Heston model)	0.15
theta	Long-term variance mean (Heston model)	0.05
V0	Initial variance for Heston model (Heston model)	0.05
sigma1	Volatility coefficient for W1 (Heston)	0.2
sigma2	Volatility coefficient for W2 (Heston)	0.2
P_tran	Transition matrix (regime-switching model)	np.array([[0.3,0.7], [0.4,0.6]])
mu_rs	Drift for the second regime (regime-switching model)	0.07
sigma_rs	Volatility for the second regime (regime-switching model)	0.4
seed	Seed for reproducibility	None

Requirements

• Python 3.6 or higher
• numpy

Install dependencies with:

pip install numpy

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Feel free to contribute to this project by submitting issues or pull requests. For major changes, please open an issue first to discuss what you would like to change.

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Happy simulating!