Stochastic Processes:
Stochastic processes model the behavior of stock prices over time. Examples include the Geometric Brownian Motion (GBM), a common model used in finance. GBM assumes that the returns of a stock are normally distributed and independent over
Monte Carlo Simulations:
Monte Carlo simulations use random sampling to model possible outcomes of a system. In finance, it's employed to simulate future stock price movements based on historical data and volatility. By running numerous simulations, you can estimate the probability of different price levels and potential portfolio values.
Stochastic Differential Equations (SDEs):
SDEs are used to model the continuous-time evolution of stock prices. They involve deterministic components, like drift (expected return), and stochastic components, such as volatility. The most common SDE used is the Black-Scholes model for option pricing.
Time Series Analysis:
1. Autoregressive Integrated Moving Average (ARIMA):
ARIMA is a popular time series model. It combines autoregressive (AR) and moving average (MA) components with differencing to make the series stationary. This model is useful in forecasting stock prices based on their past values.
2. Seasonal Decomposition of Time Series (STL):
STL decomposes time series into seasonal, trend, and remainder components, allowing for a better understanding of the underlying patterns and trends. It's beneficial in analyzing stock prices affected by seasonal factors.
3. Exponential Smoothing (ETS):
ETS methods, including Exponential Smoothing State Space Model, are useful in forecasting based on weighted averages of past observations, giving more weight to recent data. This is suitable for stock price prediction when recent prices are likely to have more relevance.
1. Machine Learning Algorithms:
Machine learning models like Random Forests, Support Vector Machines (SVM), and Neural Networks (e.g., Long Short-Term Memory - LSTM) can be utilized for stock price prediction. These models learn patterns and relationships in historical data to forecast future prices.
2. Reinforcement Learning:
Reinforcement learning, particularly in the context of Deep Q-Networks (DQNs) and Deep Deterministic Policy Gradients (DDPG), is gaining traction. These models learn optimal trading strategies by interacting with the environment (market) and maximizing a defined reward (profit).
3. Bayesian Networks:
Bayesian networks model the probabilistic relationships between variables. In finance, they can be used to model dependencies between various financial indicators and predict stock prices.