Modeling Stock Market Prices in Excel

Modeling stock market prices is the process of using mathematical and statistical methods to describe and predict the behavior of stock prices over time. Stock prices are influenced by many factors, such as supply and demand, news, investor sentiment, economic conditions, and company performance. Therefore, modeling stock market prices is a complex and challenging task that requires a lot of data and computational power.

One of the common approaches to modeling stock market prices is to use stochastic models, which assume that stock prices follow random processes that can be described by probability distributions. Stochastic models can capture the uncertainty and volatility of stock prices, as well as the correlations between different stocks. Some examples of stochastic models are geometric Brownian motion, mean-reverting models, and jump-diffusion models.

Another approach to modeling stock market prices is to use deep learning models, which are artificial neural networks that can learn from large amounts of data and extract complex patterns and features. Deep learning models can handle nonlinear and high-dimensional data, as well as adapt to changing market conditions. Some examples of deep learning models are long short-term memory (LSTM), convolutional neural network (CNN), and hybrid models that combine LSTM and CNN.

Both stochastic models and deep learning models have their advantages and limitations, and there is no single best model for modeling stock market prices. The choice of the model depends on the data availability, the prediction objective, the evaluation criteria, and the trading strategy. Modeling stock market prices is an active and ongoing research area that aims to improve the accuracy and reliability of the predictions, as well as to provide insights and guidance for investors and traders.

Basic Theory

The fundamental principle behind modeling stock market prices is the efficient market hypothesis, which suggests that stock prices reflect all available information. While this hypothesis is a theoretical concept, various models attempt to predict future prices based on historical data and market trends. One common approach is to use historical stock prices and statistical methods to forecast future movements.

Procedures

Step 1: Data Collection

Begin by collecting historical stock prices for the asset you want to model. You can obtain this data from financial news websites, stock exchanges, or financial databases.

Step 2: Calculate Daily Returns

Calculate the daily returns by taking the percentage change in stock prices from one day to the next. The formula for daily returns (R) is:

$R_t = \left( \frac{P_t}{P_{t-1}} - 1 \right) \times 100$

Where:
– $R_t$ is the daily return at time $t$
– $P_t$ is the stock price at time $t$
– $P_{t-1}$ is the stock price at time $t-1$

Step 3: Calculate Average Daily Return

Compute the average daily return over the historical period. This will be used to estimate the expected return.

$\text{Average Daily Return} = \frac{\sum R_t}{N}$

Where:
– $\sum R_t$ is the sum of daily returns
– $N$ is the number of observations

Step 4: Calculate Standard Deviation of Daily Returns

Calculate the standard deviation of daily returns to measure the volatility of the stock. This is a key parameter in many pricing models.

$\text{Standard Deviation} = \sqrt{\frac{\sum (R_t - \text{Average Daily Return})^2}{N}}$

Step 5: Forecast Future Prices

Use the calculated average daily return and standard deviation to forecast future prices using models such as the Monte Carlo simulation or the Black-Scholes model.

Scenario: Modeling Stock Prices for Company XYZ

Let’s consider the historical daily stock prices for Company XYZ over the past 100 trading days. We’ll use this data to model the future stock prices for the next 10 days.

$P_{t-1}$	$P_t$	$R_t$
100	105	5%
105	102	-2.86%
102	110	7.84%

Using the data, we calculate the average daily return and standard deviation, which are 0.75% and 4.2%, respectively.

Now, let’s forecast the stock prices for the next 10 days using the Monte Carlo simulation.

Monte Carlo Simulation Formula

$P_t = P_{t-1} \times (1 + \text{Average Daily Return} + \text{Standard Deviation} \times \text{Random Number})$

Where the random number is generated using Excel’s RAND() function.

Excel Implementation

Data Table: Input the historical stock prices in an Excel table.
Daily Returns: Calculate daily returns using the formula mentioned earlier.
Average Daily Return and Standard Deviation: Use Excel functions like AVERAGE() and STDEV() to calculate these values.
Monte Carlo Simulation: Implement the simulation formula in Excel for each day.

Results

After running the Monte Carlo simulation, you’ll obtain a range of possible future stock prices. This provides a probabilistic forecast based on historical data and market volatility.