• Corpus ID: 14684726

Option Pricing Formulae using Fourier Transform : Theory and Application

@inproceedings{Schmelzle2010OptionPF,
  title={Option Pricing Formulae using Fourier Transform : Theory and Application},
  author={Martin Schmelzle},
  year={2010}
}
Fourier transform techniques are playing an increasingly important role in Mathematical Finance. For arbitrary stochastic price processes for which the characteristic functions are tractable either analytically or numerically, prices for a wide range of derivatives contracts are readily available by means of Fourier inversion methods. In this paper we $rst review the convenient mathematical properties of Fourier transforms and characteristic functions, survey the most popular pricing algorithms… 
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References

SHOWING 1-10 OF 150 REFERENCES
Analysis of Fourier Transform Valuation Formulas and Applications
Abstract The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an
Optimal Fourier Inversion in Semi-Analytical Option Pricing
At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically
A Fourier Transform Method for Spread Option Pricing
TLDR
This paper introduces a new formula for general spread option pricing based on Fourier analysis of the payoff function that is found to be easy to implement, stable, efficient, and applicable in a wide variety of asset pricing models.
Spread Option Valuation and the Fast Fourier Transform
We investigate a method for pricing the generic spread option beyond the classical two-factor Black-Scholes framework by extending the fast Fourier Transform technique introduced by Carr & Madan
Fast Option Pricing Using Non Uniform Discrete Fourier Transform on Gaussian Discretization Grids
TLDR
The aim of this work is to offer for the first time an application in finance of a new tool that appears to have a great potential in terms of derivative pricing, which is valid under the hyphotesis of general processes for the underlying and easily extendable to any type of option pricing formulas.
Option Pricing by Transform Methods: Extensions, Unification, and Error Control
TLDR
In this general setting, the numerical pricing error of discretized transform computations, such as DFT/FFT, is bound to enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
TLDR
An option pricing method for European options based on the Fourier-cosine series and call it the COS method, which covers underlying asset processes for which the characteristic function is known and various types of option contracts.
Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform
  • Artur Sepp
  • Mathematics
    Acta et Commentationes Universitatis Tartuensis de Mathematica
  • 2004
We develop a general methodology for pricing European-style options under various stochastic processes via the Fourier transform. We generalize previous work in this field and present two approaches
Option Pricing Using the Fractional FFT
This paper shows how the recently developed fractional FFT algorithm (FRFT) can be used to retrieve option prices from the corresponding characteristic functions. The FRFT algorithm has the advantage
On a new approach to calculating expectations for option pricing
We discuss a simple new approach to calculating expectations of a specific form used for the pricing of derivative assets in financial mathematics. We show that in the ‘vanilla case’, the
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