On the Interest Rate Derivatives Pricing with Discrete Probability Distribution and Calibration with Genetic Algorithm

Abstract

Bond prices and fixed-income derivatives intricately depend on the ever-evolving landscape of interest rates. This study introduces an exceptionally efficient semi-analytical pricing methodology designed for discretely updated path-dependent interest rate options. Our approach involves the derivation of an analytical solution for the characteristic function of the logarithm of the discretely discounted strike price, enabling the computation of coefficients for the Fourier-cosine series governing the path-dependent option pricing. The distinctive feature of our pricing method lies in the utilization of a modified Skellam probability distribution to model interest rate increments, resulting in a remarkably swift and precise calculation process. Unlike existing solutions for similar pricing challenges, our proposed formula considerably enhances computational efficiency. Moreover, we delve into the influence of central bank monetary decision probabilities on option prices via a comprehensive series of numerical experiments. In an effort to further fine-tune the calibration parameter values for the yield curve, we employ a genetic algorithm, thus contributing to the heightened precision of our pricing model. This research, with its innovative approach, not only refines pricing procedures but also offers valuable insights into the dynamic interplay between monetary policies and fixed-income derivatives.