Retrieving Lévy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

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Retrieving Exponential Lévy Models from Option Prices: Regularization of an Ill-posed Inverse Problem

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

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Recovering exponential Lvy models from option prices: regularization of an ill-posed inverse problem

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

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Learning, Regularization and Ill-Posed Inverse Problems

Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we pro...

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Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

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Retrieving Lévy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem

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