Russian and American put options under exponential phase-type Lévy models

Asmussen, Søren; Avram, Florin; Pistorius, Martijn

doi:10.1016/j.spa.2003.07.005

Cited by 339 publications

(343 citation statements)

References 31 publications

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“…Unfortunately, apart from a few special cases (such as the hyper-exponential Lévy processes [35,53,54]), no explicit formulas for φ ± q (ξ ) are known. Instead, one must use the integral formulas recalled in Section 4.2.…”

Section: Calculation Of the Wiener-hopf Factorsmentioning

confidence: 99%

Efficient Option Pricing Under Levy Processes, with CVA and FVA

2015

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We generalize the Piterbarg [1] model to include (1) bilateral default risk as in Burgard and Kjaer [2], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.

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Section: Calculation Of the Wiener-hopf Factorsmentioning

confidence: 99%

Efficient Option Pricing Under Levy Processes, with CVA and FVA

2015

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“…The representation in Eq. 9 can be proven along the lines of the proof of Proposition XI.2.2 in Asmussen (2003), by setting up a differential equation for…”

Section: Definitions and Assumptionsmentioning

confidence: 99%

“…To find an expression for this quantity, we directly apply the idea of Lemma VIII.5.1 of Asmussen (2003), as follows. Evidently, for j ∈ I, k ∈ I − , we have…”

Section: The Ladder Heights Of Smentioning

confidence: 99%

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Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications

Dieker¹,

Mandjes

2009

Methodol Comput Appl Probab

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Through Laplace transforms, we study the extremes of a continuoustime Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the extreme is 'attained'. For this, we investigate discrete-time Markov-additive processes and use an embedding to relate these to the continuous-time setting. The resulting Laplace transforms are given in terms of two matrices, which can be determined either through solving a nonlinear matrix equation or through a spectral method. Our results on extremes are first applied to determine the steady-state buffer-content distribution of several single-station queueing systems. We show that our framework comprises many models dealt with earlier, but, importantly, it also enables us to derive various new results. At the same time, our setup offers interesting insights into the connections between the approaches developed so far, including matrix-analytic techniques, martingale methods, the rate-conservation approach, and the occupation-measure method. We also study networks of fluid queues, and show how the results on single queues can be used to find the Laplace transform of the steady-state buffer-content vector; it has a matrix quasi-product form. Fluid-driven priority systems also have this property.

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“…Some other optimal stopping problems in such a model were solved, for example, in [9], [16]- [17], [13]- [14], [3]- [4] and [7]. The key point in solving optimal stopping problems for jump processes established in [18]- [19] is that the smooth fit at the optimal boundary may break down and then be replaced by the continuous fit (see also [2] for necessary and sufficient conditions for the occurrence of smooth-fit condition and references to the related literature, and [20] for an extensive overview).…”

Section: Introductionmentioning

confidence: 99%

The integral option in a model with jumps

Gapeev

2008

Statistics & Probability Letters

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To cite this version:Pavel V. Gapeev. The integral option in a model with jumps. Statistics and Probability Letters, Elsevier, 2009, 78 (16) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTThe integral option in a model with jumps Pavel V. Gapeev * Dedicated to the memory of Heiner ZieschangWe present a closed form solution to the considered in [15] optimal stopping problem for the case of geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The result can be interpreted as pricing perpetual integral options in a model with jumps.

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Russian and American put options under exponential phase-type Lévy models

Cited by 339 publications

References 31 publications

Efficient Option Pricing Under Levy Processes, with CVA and FVA

Efficient Option Pricing Under Levy Processes, with CVA and FVA

Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications

The integral option in a model with jumps

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