1 Introduction
Forecasting financial markets is a complex blend of quantitative precision and global economic nuance. In this exploration, Monte Carlo simulations emerge as the premier statistical tool to guide our understanding of future stock prices.
Named after the famous Monte Carlo Casino in Monaco, this approach does not rely on luck but is rooted in rigorous probabilistic models. Imagine orchestrating thousands of experiments in a controlled environment, each unfolding a different story of stock price movement. This is the power of Monte Carlo simulation. It allows us to visualize a range of outcomes based on historical data and probabilistic assumptions.
In this article, our approach is twofold: First, we delve into the complexities of historical and implied volatility, clarifying their differences, meanings, and correlations. While historical volatility measures stock price movements in the past, implied volatility provides a forward-looking perspective based on market sentiment and option pricing. Next, we employ a Monte Carlo simulation to use these two volatility measures to extrapolate the potential future path of our selected stocks.
Central to our analysis is the derivation of probabilities. By looking at the multiple potential outcomes of the simulation, we will calculate the likelihood that the stock price will fall within a specific range. For example, what is the probability that a stock's price exceeds a certain threshold or falls below another threshold? Thus, providing a quantifiable perspective on potential future scenarios.
2. Volatility analysis
2.1 Historical volatility
Historical volatility, often called statistical volatility or realized volatility, quantifies the variability in stock returns over a past period. It gives us an idea of how far a stock's price has deviated from its average value over that time frame.
After obtaining daily returns, the historical volatility (HV) of N days is calculated as follows
Describes the formula for calculating daily historical volatility. The calculation is based on a stock's price return and provides a measure of how volatile a stock has been on a daily basis.
Where: