Precise option pricing by the COS method--How to choose the truncation range

TL;DR

This paper introduces a new formula for selecting the truncation range in the COS method for option pricing, ensuring convergence and reducing mispricing compared to classical cumulant-based methods.

Contribution

A novel truncation range formula based on Markov's inequality is proposed, improving accuracy and convergence in the COS option pricing method.

Findings

The new truncation range guarantees convergence within a specified error.

Classical cumulant-based truncation can cause significant mispricing.

Computational time remains similar despite improved accuracy.

Abstract

The Fourier cosine expansion (COS) method is used for pricing European options numerically very fast. To apply the COS method, a truncation range for the density of the log-returns need to be provided. Using Markov's inequality, we derive a new formula to obtain the truncation range and prove that the range is large enough to ensure convergence of the COS method within a predefined error tolerance. We also show by several examples that the classical approach to determine the truncation range by cumulants may lead to serious mispricing. Usually, the computational time of the COS method is of similar magnitude in both cases.