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Bibliographic Details
Main Authors: Sidhu, Karmanpartap Singh, Saxena, Pranshi
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.06068
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author Sidhu, Karmanpartap Singh
Saxena, Pranshi
author_facet Sidhu, Karmanpartap Singh
Saxena, Pranshi
contents This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and continuous price movements. To overcome these limitations, we use Monte Carlo simulation alongside the GARCH model, Heston stochastic volatility model, and Merton jump-diffusion model. The Black-Scholes-Monte Carlo method simulates diverse stock price paths using geometric Brownian motion. The GARCH model forecasts time-varying volatility from historical data. The Heston model incorporates stochastic volatility to capture volatility clustering and skew. The Merton jump-diffusion model adds sudden price jumps via a Poisson process. Results show the Heston model consistently produces estimates closer to market prices, while the Merton model performs well for volatile assets with sudden price movements. The GARCH model provides improved volatility forecasts for future option price prediction. All experiments used live market data from November 2024.
format Preprint
id arxiv_https___arxiv_org_abs_2604_06068
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Beyond Black-Scholes: A Computational Framework for Option Pricing Using Heston, GARCH, and Jump Diffusion Models
Sidhu, Karmanpartap Singh
Saxena, Pranshi
Computational Finance
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and continuous price movements. To overcome these limitations, we use Monte Carlo simulation alongside the GARCH model, Heston stochastic volatility model, and Merton jump-diffusion model. The Black-Scholes-Monte Carlo method simulates diverse stock price paths using geometric Brownian motion. The GARCH model forecasts time-varying volatility from historical data. The Heston model incorporates stochastic volatility to capture volatility clustering and skew. The Merton jump-diffusion model adds sudden price jumps via a Poisson process. Results show the Heston model consistently produces estimates closer to market prices, while the Merton model performs well for volatile assets with sudden price movements. The GARCH model provides improved volatility forecasts for future option price prediction. All experiments used live market data from November 2024.
title Beyond Black-Scholes: A Computational Framework for Option Pricing Using Heston, GARCH, and Jump Diffusion Models
topic Computational Finance
url https://arxiv.org/abs/2604.06068