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Option Pricing with Levy Process [PDF]

open access: possibleSSRN Electronic Journal, 2001
In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices. This enables us to generate an implicit volatility surface implied by market data.
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Levy processes for image modeling

Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99, 2003
Nonhomogenous random fields are known to be well adapted to modeling a wide class of images. Their computational complexity generally causes their lack of appeal, we propose a more efficient model capable of capturing textures, shapes, as well as jumps typically encountered in infra-red images.
O.V. Poliannikov   +2 more
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Finite-size Lyapunov exponent for Levy processes

Physical Review E, 2007
The finite-size Lyapunov exponent (FSLE) is the exponential rate at which two particles separate from a distance of r to a x r (a>1) and provides a measure of dispersive mixing in chaotic systems. It is shown analytically that for particle trajectories governed by symmetric alpha -stable Levy motion, the FSLE is proportional to the diffusion ...
R, Parashar, J H, Cushman
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Mean Reverting Levy Based Processes

SSRN Electronic Journal, 2012
We investigate Stochastic Processes that are mean reverting (and have leptokurtic distributions. A new MR process is proposed which utilizes the infinitely divisible property of Levy process. The process itself can be calibrated and simulated easily using a small number of discrete time steps.
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Fast Simulation of Levy Processes

SSRN Electronic Journal, 2012
We present a robust method for simulating an increment of a Levy process, based on decomposing the jump part of the process into the sum of its positive and negative jump components. The characteristic exponent of a spectrally one-sided Levy process has excellent analytic properties, which we exploit to design a fast and accurate algorithm for ...
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