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

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  • Ricardo Crisostomo

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.

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  • Ricardo Crisostomo, 2015. "An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration using Matlab," Papers 1502.02963, arXiv.org, revised Mar 2015.
    • Handle: RePEc:arx:papers:1502.02963
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Farshid Mehrdoust & Idin Noorani, 2023. "Implied higher order moments in the Heston model: a case study of S &P500 index," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 477-504, December.
    2. Ricardo Crisóstomo, 2017. "Speed and biases of Fourier-based pricing choices: Analysis of the Bates and Asymmetric Variance Gamma models," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    3. Julien Hok & Tat Lung Chan, 2016. "Option pricing with Legendre polynomials," Papers 1610.03086, arXiv.org, revised Mar 2017.
    4. Dondukova Oyuna & Liu Yaobin, 2021. "Forecasting the Crude Oil Prices Volatility With Stochastic Volatility Models," SAGE Open, , vol. 11(3), pages 21582440211, July.
    5. Michael Kurz, 2018. "Closed-form approximations in derivatives pricing: The Kristensen-Mele approach," Papers 1804.08904, arXiv.org.
    6. Raj G. Patel & Chia-Wei Hsing & Serkan Sahin & Samuel Palmer & Saeed S. Jahromi & Shivam Sharma & Tomas Dominguez & Kris Tziritas & Christophe Michel & Vincent Porte & Mustafa Abid & Stephane Aubert &, 2022. "Quantum-Inspired Tensor Neural Networks for Option Pricing," Papers 2212.14076, arXiv.org, revised Mar 2024.

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    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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