Accurate delta hedging of european options using conformable calculus

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 order0 ≤α≤ 1 and calculate the corresponding delta of a portfolio of listed options as a function of this conformableparameter. 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.