Evaluating Scale Functions of Spectrally Negative Lévy Processes

Budhi Surya

73 citations0/0 files storedJournal of Applied Probability

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

In this paper we present a robust numerical method to compute the scale function W(q)(x) of a general spectrally negative Lévy process (X, P). The method is based on the Esscher transform of measure Pν under which X is taken and the scale function is determined. This change of measure makes it possible for the scale function to be bounded and, hence, makes numerical computation easy, fast, and stable. Working under the new measure Pν and using the method of Abate and Whitt (1992) and Choudhury, Lucantoni, and Whitt (1994), we give a fast stable numerical algorithm for the computation of W(q)(x).

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References

1996Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads 2007On the optimal dividend problem for a spectrally negative Lévy process 2004Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options 2002Optimal capital structure and endogenous default 2010Smoothness of scale functions for spectrally negative Lévy processes 1994Multidimensional Transform Inversion with Applications to the Transient M/G/1 Queue 2004On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum 1994Martingale Approach to Pricing Perpetual American Options

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