Heston vs. Black-Scholes Forecasting for Apple
Ansa Brew-smith
Heston Model vs. Black-Scholes Forecasting Using Real Apple Market Data
This project compares the Heston Model and the Black-Scholes Model for forecasting options prices using real market data from Apple Inc. (AAPL). The project involves data preprocessing, model implementation, and analysis of the results. Note: The predictions from the models have not yet been compared with real market data.
Table of Contents
Introduction
The goal of this project is to compare the effectiveness of the Heston Model and the Black-Scholes Model in forecasting options prices using real market data from Apple Inc. The project involves:
Downloading and preprocessing options and stock data
Implementing both pricing models
Analyzing and visualizing results
Important Note: The predictions from these models have not yet been validated against real market data.
Data Preprocessing
Data Collection
Downloaded historical options and stock data for AAPL using
yfinanceCollected multiple expiration dates and strike prices
Retrieved implied volatility surfaces
Data Cleaning
Handled missing values and outliers
Calculated time-to-expiration (T) in years
Filtered in-the-money (ITM) and out-of-the-money (OTM) options
Normalized and scaled relevant features
Key Features
Strike prices ranging from $50 to $450
Expiration dates from March 2025 to June 2027
Implied volatility surfaces
Daily historical stock prices
Models
Black-Scholes Model
Implements the classic options pricing formula
Assumes constant volatility
Calculates theoretical prices using:
Current stock price
Strike price
Risk-free rate
Time to expiration
Historical volatility
Heston Model
Stochastic volatility model
Accounts for volatility smile/skew
Parameters include:
Long-term volatility
Mean reversion rate
Volatility of volatility
Correlation between asset and volatility
Results
Current Status: Model predictions have been generated but not yet compared with real market data for validation.
Planned analysis will include:
Volatility surface comparisons
Pricing error metrics (RMSE, MAE)
Residual analysis
Model convergence tests
Acknowledgments
Yahoo Finance API for market data access Original authors of both financial models Contributors to Python scientific computing stack
Contact
For questions or collaborations: Email: brewsmith.a@northeastern.edu
Note: This is an ongoing research project. Validation against real market data and model calibration improvements are planned for future work.
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Posted May 7, 2025
Compared Heston and Black-Scholes models for Apple options pricing.
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Timeline
Jan 1, 2025 - Mar 1, 2025
