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Russian and American put options under exponential phasetype Lévy models
, 2002
"... Consider the American put and Russian option [33, 34, 17] with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phasetype jumps in both directions. The solution rests on the reduction to the first passage ..."
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Cited by 41 (2 self)
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Consider the American put and Russian option [33, 34, 17] with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phasetype jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Lévy processes and on an explicit solution of the latter in the phasetype case via martingale stopping and WienerHopf factorisation. Also the first passage time problem is studied for a regime switching Lávy process with phasetype jumps. This is achieved by an embedding into a a semiMarkovian regime switching Brownian motion.
Optimal stopping and perpetual options for Lévy processes
, 2000
"... Solution to the optimal stopping problem for a L'evy process and reward functions (e x \Gamma K) + and (K \Gamma e x ) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and infimum of the process killed at this rate. Closed forms of this solution ..."
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Cited by 22 (2 self)
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Solution to the optimal stopping problem for a L'evy process and reward functions (e x \Gamma K) + and (K \Gamma e x ) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and infimum of the process killed at this rate. Closed forms of this solutions are obtained under the condition of positive jumps mixedexponentially distributed. Results are interpreted as admissible pricing of perpetual American call and put options on a stock driven by a L'evy process, and a BlackScholes type formula is obtained. Keywords and Phrases: Optimal stopping, L'evy process, mixtures of exponential distributions, American options, Derivative pricing. JEL Classification Number: G12 Mathematics Subject Classification (1991): 60G40, 60J30, 90A09. 1 Introduction and general results 1.1 L'evy processes Let X = fX t g t0 be a real valued stochastic process defined on a stochastic basis(\Omega ; F ; F = (F t ) t0 ; P ) that satisfy the usual conditions. A...
The distribution of the maximum of a Lévy process with positive jumps of phasetype
 Proceedings of the Conference Dedicated to the 90th Anniversary of Boris Vladimirovich Gnedenko (Kyiv
, 2002
"... Consider a Levy process with nite intensity positive jumps of the phasetype and arbitrary negative jumps. Assume that the process either is killed at a constant rate or drifts to 1. We show that the distribution of the overall maximum of this process is also of phasetype, and nd the distribu ..."
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Cited by 8 (0 self)
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Consider a Levy process with nite intensity positive jumps of the phasetype and arbitrary negative jumps. Assume that the process either is killed at a constant rate or drifts to 1. We show that the distribution of the overall maximum of this process is also of phasetype, and nd the distribution of this random variable. Previous results (hyperexponential positive jumps) are obtained as a particular case.
WienerHopf factorization for L'evy processes having negative jumps with rational transforms
, 2005
"... Abstract We give the closed form of the ruin probability for a L'evy processes, possibly killed at a constant rate, with completely arbitrary positive distributed jumps, and finite intensity negative jumps with distribution characterized by having a rational Laplace or Fourier transform. Abbreviated ..."
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Cited by 5 (0 self)
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Abstract We give the closed form of the ruin probability for a L'evy processes, possibly killed at a constant rate, with completely arbitrary positive distributed jumps, and finite intensity negative jumps with distribution characterized by having a rational Laplace or Fourier transform. Abbreviated Title: WHfactors of L'evy processes with rational jumps. 1 Introduction 1.1 L'evy processes and WienerHopf factorization Let X = {Xt}t>=0 be a real valued stochastic process defined on a stochasticbasis B = (\Omega, F, F = (Ft)t>=0, P). Assume that X is c`adl`ag, adapted, X0 = 0,and for 0 < = s < t the random variable Xt Xs is independent of the oefieldF