Evaluating first-passage probabilities for spectrally one-sided Lévy processes

By L. Rogers. Journal of Applied Probability, 2000

96 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4984ad200cb522f9a3d900c9830fef497df0e364

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In Atomic and Molecular Physics, and Optics

In Statistics and Probability

Citations in the corpus

Pricing Path-Dependent Options with Jump Risk via Laplace Transforms (2005, methodology): “…based on the Wiener-Hopf factorization for two-sided jump processes are given in Asmussen et al. (2004), Boyarchenko and Levendorskiı̆ (2002), and Kyprianou and Pistorius (2003); see also Avram et al. (2004) and Rogers (2000) for first passage times related to one-sided jump processes.”
Evaluating Scale Functions of Spectrally Negative Lévy Processes (2008, methodology): “To handle matrix multiplication, we use the approach of [22].”
First passage times of a jump diffusion process (2003, unknown): “[24].”
Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, background): “There are few examples for which the scale function is known in explicit form (although Rogers (2000) and Surya (2006) have developed methods to numerically invert the Laplace transform in (2)).”
Passage times for a spectrally negative Lévy process with applications to risk theory (2005, background): “The first passage time for Lévy processes has been well studied; see Doney (1991), Emery (1973), Prabhu (1970), Rogers (1990; 2000) and Zolotarev (1964).”
Break on Through to the Single Side (2008, unknown): “Indeed, the advantage of only allowing negative jumps in the driving Lévy process is the fact that we can calculate extremely fast the first passage time distributions (default probabilities) by exploiting the remarkable Wiener-Hopf factorization in combination with results by Rogers [5] and by per”
A class of Lévy process models with almost exact calibration to both barrier and vanilla FX options (2010, background): “Some simplification occurs (Rogers 2000) if the Lévy process is spectrally one-sided (i.e. jumps are either always up or always down).”
Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering (2007, background): “…and Kyprianou and Pistorius (2003) for some representations (though not explicit calculations) based on the Wiener–Hopf factorization related to the overshoot problems for general Lévy processes; and see also Avram et al. (2004) and Rogers (2000) for first passage times with one-sided jumps.”
Refracted Lévy processes (2008, methodology): “For the cases where no explicit formula is known for the scale function, [27] and [31] advocate simple methods of numerical Laplace inversion.”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, methodology): “For spectrally one-sided Lévy processes with a Gaussian component, Rogers (2000) derived a method to evaluate first-passage distributions.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “(Similar ideas can also be developed from the paper of Rogers [87]).”
Option Pricing Under a Double Exponential Jump Diffusion Model (2004, methodology): “However, for two-sided jumps, because of the laddervariable problems, generally speaking the renewal equations are not available and the fluctuation identities become too complicated for explicit computation; see, e.g., the discussion in Siegmund (1985) and Rogers (2000).”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “Rogers (2000) and Surya (2008) have provided robust methods for numerically computing scale functions.”