A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes

@article{Lord2007AFA,
  title={A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes},
  author={R. Lord and Fang Fang and F. Bervoets and Cornelis W. Oosterlee},
  journal={Risk Management eJournal},
  year={2007}
}
A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognising that it is a convolution. The resulting convolution is dealt with numerically by using the Fast Fourier Transform (FFT). This novel pricing method, which we dub the Convolution method, CONV for… 
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161 Citations

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References

SHOWING 1-10 OF 59 REFERENCES
A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options
TLDR
Algorithms for the pricing of discretely sampled barrier, lookback, and hindsight options and discretely exercisable American options are developed using the double-exponential integration formula and the fast Gauss transform.
Numerical Valuation of European and American Options under Kou's Jump-Diffusion Model
Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model, which assumes the price of the underlying asset to behave like a geometrical Brownian…
Robust numerical valuation of European and American options under the CGMY process
We develop an implicit discretization method for pricing European and American options when the underlying asset is driven by an infinite activity Levy process. For processes of finite variation,…
Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly…
Accurate Evaluation of European and American Options Under the CGMY Process
TLDR
A finite-difference method for integro-differential equations arising from Le´vy driven asset processes in finance is discussed and the discretization is shown to be second-order accurate for a relevant parameter range determining the degree of the singularity in the Levy measure.
Lévy Processes in Finance: Theory, Numerics, and Empirical Facts
Preface Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible…
On American Options Under the Variance Gamma Process
American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon…
Wavelet Galerkin pricing of American options on Lévy driven assets
The price of an American-style contract on assets driven by a class of Markov processes containing, in particular, Lévy processes of pure jump type with infinite jump activity is expressed as the…
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…
Switching Levy Models in Continuous Time: Finite Distributions and Option Pricing
This paper introduces a general regime switching Levy process, and constructs the characteristic function in closed form. Correlations between the underlying Markov chain and the asset returns are…
...
...