A study of American options under stochastic volatility and double exponential jumps

Document Type : Research Article

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box: 41938--1914, Rasht, Iran

Abstract

In this study, we introduce and validate a novel approach for pricing American-style options. Our model integrates stochastic volatility with a double exponential jump-diffusion process and incorporates a memory feature in the volatility component. We analyze the structure of the proposed model and demonstrate its accuracy and precision using real data from the $S\&P$ 500 index. Our results show that the model effectively captures market dynamics and provides a more accurate pricing of American options compared to traditional models.

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Journal of Mathematical Modeling
Volume 13, Issue 2
May 2025
Pages 467-484

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