@inbook{603040cd6f8345a2a10abab2dbc62b71,
title = "Forward evolution equations for knock-out options",
abstract = "We derive forward partial integrodifferential equations (PIDEs) for pricing up-and-out and down-and-out call options when the underlying is a jump diffusion. We assume that the jump part of the returns process is an additive process. This framework includes the Variance-Gamma, finite moment logstable, Merton jump diffusion, Kou jump diffusion, Dupire, CEV, arcsinh normal, displaced diffusion, and Black–Scholes models as special cases.",
keywords = "Forward equations, Jump diffusion, Knock-out options, L{\textquoteright}evy processes, Partial integrodifferential equation (PIDE)",
author = "Peter Carr and Ali Hirsa",
note = "Funding Information: We would like to thank participants of the ICBI Global Derivatives Conference 2003 in Barcelona, participants of Risk Europe 2003 in Paris, participants of the Control and Dynamical Systems Lecture Series at the Institute for Systems Research at the University of Maryland at College Park, and students at the Mathematics of Finance Programs at Courant Institute and Columbia University for their comments and discussions. We would also like to thank Robert Kohn and Pedro Judice of Courant Institute for their comments and suggestions. Errors are our own responsibility. Publisher Copyright: {\textcopyright} 2007, Birkh{\"a}user Boston.",
year = "2007",
doi = "10.1007/978-0-8176-4545-8_11",
language = "English (US)",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Springer International Publishing",
number = "9780817645441",
pages = "195--217",
booktitle = "Applied and Numerical Harmonic Analysis",
edition = "9780817645441",
}