• 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… 
pfadintegral.com
49 Citations
Highly Influential Citations
8
Background Citations
24
Methods Citations
20

49 Citations

Error Analysis in Fourier Methods for Option Pricing
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a…
Closed-Form Pricing of Two-Asset Barrier Options with Stochastic Covariance
Abstract Single and double barrier options on more than one underlying with stochastic volatility are usually priced via Monte Carlo simulation due to the non-existence of closed-form solutions for…
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
TLDR
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.
Option Pricing under Heston and 3 / 2 Stochastic Volatility Models : an Approximation to the Fast Fourier Transform
  • Economics
  • 2012
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…
Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models
TLDR
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
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…
Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results
TLDR
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
TLDR
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
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…
Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives
...
...

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…
...
...