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

By Søren Asmussen, Florin Avram, Martijn Pistorius. 2004

366 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/cfab433347ebc6292e1fef157f71c1f2933f6c71

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Citations in the corpus

Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, neutral): “…they are distinct) and solve the Cramér–Lundberg equation ψ( ) = 0, and Aj = lim s→ j ψ ′(0+)( j − s) ψ(s) with ψ(θ) = cCLθ + λCL(α(θI − T )−1t − 1), where t = −T 1 and 1 is the identity matrix; for details, see Lemma 1 of Asmussen et al. (2004) and Equation (13) of Kyprianou and Palmowski (2005).”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “[8] and Pistorius [84], while Wiener–Hopf factorization for a more general class of processes having positive jumps of rational transform was obtained by Lewis and Mordecki [74].”
Optimal dividends in the dual model under transaction costs (2013, methodology): “phase-type jumps with or without a Brownian motion (Asmussen et al., 2004). We shall confirm the existence of themaximizers 0 ≤ c 1 < c ∗ 2 < ∞ and examine the shape of the value function at c 1 and c ∗ 2 .We further compute for a sequence of unit transaction costs and confirm that, as β ↓ 0, the va”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, methodology): “In the setting of infinite activity Lévy processes with jumps in two directions, Cont and Voltchkova (2005) investigated discretization of the associated integro-differential equations, Boyarchenko and Levendorskiı̆ (2002a) employed Fourier methods to investigate barrier option prices for Lévy proce”
Some remarks on first passage of Levy processes, the American put and pasting principles (2005, neutral): “ar X iv :m at h/ 05 08 48 7v 1 [ m at h. PR ] 2 5 A ug 2 00 5 The Annals of Applied Probability 2005, Vol. 15, No. 3, 2062–2080 DOI: 10.1214/105051605000000377 c© Institute of Mathematical Statistics, 2005”
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes (2007, methodology): “[2] derived explicit expressions for the prices of perpetual Russian options in the dense class of Lévy processes with phase-type jumps in both directions by reducing the initial problem to the first passage time problem and solving the latter by martingale stopping and Wiener–Hopf factorization.”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “Howevery in recent years there is also a growing interest in applications of Wiener-Hopf factorization, for example in Mathematical Finance, where the above mentioned functionals are being used to describe the payoff of a contract and the corresponding probability distribution is used to compute its”
First Passage of a Markov Additive Process and Generalized Jordan Chains (2010, methodology): “Continuous-time Markov additive processes (MAPs) with one-sided jumps have proven to be an important modelling tool in various application areas, such as communications networking [19, Chapters 6–7] and finance [5], [14].”
A class of Lévy process models with almost exact calibration to both barrier and vanilla FX options (2010, positive): “In order to make for a more parsimonious calibration, we assumed that b31⁄4 b4 and b11⁄4 b61⁄4 3b4, b21⁄4 b51⁄4 2b4 (there was no special reason for choosing these multiples but, taking our lead from Asmussen et al. (2007), they seemed pragmatic choices).”
Fluctuations of spectrally negative Markov additive processes (2008, background): “…processes, on account of the robustness of their fluctuation theory; see for example Schmidli (1999), Asmussen (2000), Asmussen and Kella (2000), Asmussen et al. (2004), Avram et al. (2004), Klüppelberg et al. (2004), Pistorius (2003), Huzak et al. (2004), Chan (2005), Chiu and Yin (2005) and…”
Fluctuations of Lévy Processes with Applications (2014, methodology): “Recently, Mordecki (2002) and Asmussen et al. (2004) have used this property to establish another example of a Lévy process for which elements of the Wiener–Hopf factorisation can be expressed in more mathematical detail. See also Pistorius (2006) and Mordecki (2005). The process they consider takes”
First Passage Times for Markov Additive Processes with Positive Jumps of Phase Type (2008, methodology): “Recently, some results have been proven for Lévy processes with phase-type positive jumps as well; see [5], [11], [19], or [20].”
On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, methodology): “[1] by incorporating the joint LT of Gτa and Mτa .”