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Russian and American put options under exponential phasetype Levy models

Summary: Russian and American put options under
exponential phase­type L´evy models
Søren Asmussen a
, Florin Avram b
, Martijn R. Pistorius c,
aDepartment of Mathematical Sciences, Aarhus University, Ny Munkegade, 8000
Aarhus C, Denmark
bD´epartement de Math´ematiques LMA, Universit´e de Pau, 64000 Pau, France
c Department of Mathematics, King's College London, Strand, London WC2R
Consider the American put and Russian option [46,47,22] with the stock price mod-
eled as an exponential L´evy process. We find an explicit expression for the price in
the dense class of L´evy processes with phase­type jumps in both directions. The
solution rests on the reduction to the first passage time problem for (reflected)
L´evy processes and on an explicit solution of the latter in the phase­type case via
martingale stopping and Wiener-Hopf factorisation. The same type of approach
is also applied to the more general class of regime switching L´evy processes with
phase-type jumps.
Key words: L´evy process, Markov additive process, first passage time, Wald


Source: Avram, Florin - Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour


Collections: Mathematics