Articlebronze2005

Some remarks on first passage of Lévy processes, the American put and pasting principles

206 citations0/0 files storedThe Annals of Applied Probability

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

Abstract

The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskiǐ [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100 (2002) 75–107], Mordecki [Finance Stoch. 6 (2002) 473–493], Asmussen, Avram and Pistorius [Stochastic Process. Appl. 109 (2004) 79–111] and Chesney and Jeanblanc [Appl. Math. Fin. 11 (2004) 207–225] to the American perpetual put optimal stopping problem. Furthermore, we make folklore precise and give necessary and sufficient conditions for smooth pasting to occur in the considered problem.

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References

2003Financial Modelling with Jump Processes 2003Lévy Processes in Finance 2000Ruin Probabilities 2003Russian and American put options under exponential phase-type Lévy models 2004Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options 2002Optimal stopping and perpetual options for Lévy processes 2002Non-Gaussian Merton-Black-Scholes Theory

Cited by

2005Integro-differential equations for option prices in exponential Lévy models 2011Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes 2012Exit problems for jump processes with applications to dividend problems 2011A Wiener–Hopf Monte Carlo simulation technique for Lévy processes 2011Nonparametric tests for pathwise properties of semimartingales 2010Pricing American options under stochastic volatility and stochastic interest rates 2009Fast and accurate pricing of barrier options under Lévy processes

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