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This chapter introduces and elucidates several models for the valuation of European options. We explore two scenarios: first, when the interest rate is stochastic, and second, when volatility follows a stochastic process. The first case involves the utilization of the fractional Vasicek model, the fractional Cox-Ingersoll-Ross model, and, lastly, the fractional Heston model. The dependability, appropriateness of fit, and stability of our methodology are rigorously examined through theoretical studies conducted to validate our models. The outcomes of this study have been disseminated in (Arfaou and Kharrat in Filomat 37(9):2685–2697, 2023 [3], Kharrat in Filomat 35(10), 2021 [20], Kharrat and Arfaoui in Comput Econ 61:1745–1763, 2023 [21] and Kharrat in Methodol Comput Appl Probab 25(50), 2023 [22]).

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A Stable Relaxation Approach for Valuing European Options Across Diverse Time-Fractional Models

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  • 发表日期：

    2025年

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  • Mohamed Kharrat

摘要

This chapter introduces and elucidates several models for the valuation of European options. We explore two scenarios: first, when the interest rate is stochastic, and second, when volatility follows a stochastic process. The first case involves the utilization of the fractional Vasicek model, the fractional Cox-Ingersoll-Ross model, and, lastly, the fractional Heston model. The dependability, appropriateness of fit, and stability of our methodology are rigorously examined through theoretical studies conducted to validate our models. The outcomes of this study have been disseminated in (Arfaou and Kharrat in Filomat 37(9):2685–2697, 2023 [3], Kharrat in Filomat 35(10), 2021 [20], Kharrat and Arfaoui in Comput Econ 61:1745–1763, 2023 [21] and Kharrat in Methodol Comput Appl Probab 25(50), 2023 [22]).