From Discrete to Continuous: A High‐Accuracy Approximation for Pricing Arithmetic Asian Options Under Mixed Fractional Brownian Motion

In this paper, we focus on exploring an approximate solution for pricing arithmetic Asian option (AAO) in continuous form under the mixed fractional Brownian motion (MFBM). To achieve this, we use the AAO in discrete form and show that the error analysis for the approximation between discrete and continuous forms is of order . Since the discrete form follows the reciprocal gamma distribution for sufficiently large monitoring dates, we can extract the approximate analytical solution along with its sensitivity parameters like and , and show that the proposed solution is valid for a 95% confidence interval. Additionally, to enhance the accuracy of the option of AAO in continuous form, we use the reciprocal gamma distribution as well as the geometric Asian option (GAO) in discrete form as control variates. The results show that employing both control variates acts more efficiently than using each of them solely.