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Accurate delta hedging of european options using conformable calculus

Author

Listed:
  • 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.)

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

Suggested Citation

  • Andres Olmos & Nelson Muriel, 2024. "Accurate delta hedging of european options using conformable calculus," EconoQuantum, Revista de Economia y Finanzas, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 21(1), pages 59-69, January-J.
    • Handle: RePEc:qua:journl:v:21:y:2024:i:1:p:59-69
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    More about this item

    Keywords

    option pricing; delta hedging; conformable calculus; risk management.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G19 - Financial Economics - - General Financial Markets - - - Other

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