Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options

Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options

The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang, C. W. Oosterlee, 2008] and [F. Fang, C. W. Oosterlee, 2009]. In this paper, we extend the method to higher dimensions, with a multi-dimensional asset price process. The algorithm can be applied to, for example, pricing two-color rainbow options, but also to pricing under the popular Hes...

A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions

Abstract. Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computational complexity i...

Pricing early-exercise and discrete barrier options by fourier-cosine series expansions

We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C[a, b] ∈ R) transitional probability density functions. The computational complexity is O((M − 1)N logN) with N a (small) number...

On the Fourier cosine series expansion method for stochastic control problems

We develop a method for solving stochastic control problems under one-dimensional Lévy processes. The method is based on the dynamic programming principle and a Fourier cosine expansion method. Local errors in the vicinity of the domain boundaries may disrupt the algorithm. An extensive error analysis provides new insights based on which we develop an extrapolation method to deal with the propa...

Solving Inverse Scattering Problems Using Truncated Cosine Fourier Series Expansion Method