# 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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## 49 Citations

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- 2022

An eﬃcient numerical method for pricing European multi-asset options based on two complementary ideas that smooth the Fourier integrand via an optimized choice of damping parameters based on a proposed heuristic optimization rule and uses the adaptive sparse grid quadrature based on sparsiﬁcation and dimension-adaptivity techniques to accelerate the convergence of the numerical quadratures in high dimensions.

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The purpose of this thesis is to build a fast and accurate technique for computing option prices under stochastic volatility assumption. Currently, the methodology based on the fast Fourier transform…

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- Computer ScienceInt. J. Comput. Math.
- 2020

A fast regime switching algorithm is proposed that tells if it is sufficient to evaluate the integrand in standard double arithmetic or if a higher precision arithmetic has to be used and compared and recommended numerical quadratures for typical SV models and different parameter values.

A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk

- Business
- 2012

We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with…

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- Computer Science
- 2013

This paper uses the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develops a closed-form series expansion in powers of correlation, to propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas.

Robust High-Precision Option Pricing by Fourier Transforms: Contour Deformations and Double-Exponential Quadrature

- Computer Science
- 2018

Two new methods to evaluate semi-infinite Fourier style integrals, both relying on double-exponential quadrature are proposed, both efficient, accurate, and robust, and significantly outperform standard methods.

Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results

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Exponential Levy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives…

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