An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration using Matlab

TL;DR

This paper explores the implementation and calibration of the Heston stochastic volatility model using Matlab, demonstrating efficient methods for option pricing and calibration with numerical examples.

Contribution

It provides a detailed Matlab-based approach for implementing and calibrating the Heston model, highlighting simple solutions for accurate option pricing.

Findings

Simple implementation methods yield fast, accurate vanilla option prices.

Calibration results are good with both local and global optimization techniques.

Numerical examples facilitate understanding of mathematical concepts.

Abstract

This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate vanilla option prices. We also perform several calibration tests, using both local and global optimization. Our analyses show that straightforward setups deliver good calibration results. All calculations are carried out in Matlab and numerical examples are included in the paper to facilitate the understanding of mathematical concepts.