Enhanced Black-Scholes Option Pricing: Bit-Width Optimization with Automatic Differentiation and Lagrange Multipliers

This paper proposes a new method for bit-width optimization in the Black-Scholes option pricing model using auto-differentiation and Lagrange multipliers. The Black-Scholes model is a fundamental tool in financial markets for valuing options, but its computational efficiency and accuracy can be significantly enhanced through precise bit-width optimization. By applying automatic differentiation, accurate gradient calculations are ensured, facilitating an efficient optimization process. Additionally, using Lagrange multipliers introduces constraints that balance model accuracy with hardware resource utilization. Implementing this optimized model on the FPGA platform, specifically the PYNQ-Z2 board, demonstrates substantial improvements in computational efficiency and accuracy. Our results highlight the effectiveness of these advanced techniques in enhancing financial model computations, making it suitable for real-time financial applications requiring rapid computation.