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 $0\le \alpha \le 1$ 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.