Efficient pricing of path‐dependent interest rate derivatives

Abstract

AbstractInterest rate derivative pricing is a critical aspect of fixed‐income markets, where efficient methods are essential. This study introduces a novel approach to pricing path‐dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier‐cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier‐cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed‐income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi‐closed and closed‐form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.