Accurate delta hedging of european options using conformable calculus

Andres Olmos () and Nelson Muriel
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Andres Olmos: Universidad Iberoamericana, Ciudad de Mexico. Departamento de Fisica y Matemáticas. Mexico.
Nelson Muriel: Universiad Iberoamericana, Ciudad de Mexico. Departamento de Fisica y Matematicas. Mexico.

EconoQuantum, Revista de Economia y Finanzas, 2024, vol. 21, issue 1, 59-69

Abstract: Objective: we aim to develop a method for delta hedging portfolios of European options based on the theory of conformable calculus which improves accuracy of risk management of listed options in a first-order approximation. Methodology: we allow the time derivative in the classic Black-Scholes-Merton model to have a fractional order 0≤α≤1 and calculate the corresponding delta of a portfolio of listed options as a function of this conformable parameter. Results: applying this method to a portfolio consisting of eight European options on the SPX index, we find that conformable delta hedging offers more accurate average predictions than classical delta hedging. Limitations: this method is applicable for delta hedging in European options only. Originality: this is the first successful application of conformable calculus to delta hedging in European options. Conclusions: application of Conformable Calculus allows for a greater flexibility in the local approximation to price in delta-hedging European options and offers a new and more precise methodology to this objective

Keywords: option pricing; delta hedging; conformable calculus; risk management. (search for similar items in EconPapers)
JEL-codes: G12 G17 G19 (search for similar items in EconPapers)
Date: 2024
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