NUFFT for the Fast COS Method

2025-07-17

AI Summary

This paper addresses the batch pricing of European options with identical maturities but multiple strikes under Lévy processes and affine stochastic volatility models. We propose an efficient algorithm that integrates the Fourier cosine (COS) expansion with the non-uniform fast Fourier transform (NUFFT). The method constructs the COS series using the model’s characteristic function and—novelty—the first incorporation of NUFFT into the COS framework, thereby lifting the conventional FFT requirement for uniformly spaced strike grids and enabling rapid evaluation at arbitrary, non-uniform strike sets. Compared to the standard COS method, our approach achieves order-of-magnitude speedup in multi-strike scenarios, significantly enhancing both computational efficiency and flexibility. The algorithm is particularly suited for high-frequency risk management, model calibration, and derivatives bookkeeping in practice.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Matrix & Tensor Methods

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The COS method is a very efficient way to compute European option prices under Lévy models or affine stochastic volatility models, based on a Fourier Cosine expansion of the density, involving the characteristic function. This note shows how to compute the COS method formula with a non-uniform fast Fourier transform, thus allowing to price many options of the same maturity but different strikes at an unprecedented speed.

Problem

• Speeding up European option pricing with NUFFT
• Enhancing COS method efficiency for multiple strikes
• Applying non-uniform FFT to characteristic function calculations

Innovation

• NUFFT accelerates COS method
• Pricing multiple options simultaneously
• Efficient for same maturity different strikes