On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts

Avram, Florin; Chan, Terence; Usabel, Miguel

doi:10.1016/s0304-4149(02)00104-7

Cited by 43 publications

(26 citation statements)

References 22 publications

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“…Moreover with the advent of these new fluctuation identities and a better understanding of the analytical properties of the function W (q) came the possibility of revisiting and solving a number of classical and modern problems from applied probability, but now with the underlying source of randomness being a general spectrally negative Lévy processes. For example, in the theory of optimal stopping Avram et al (2002Avram et al ( , 2004; Alili and Kyprianou (2005) and Kyprianou (2006), in the theory of optimal control Avram et al (2007) and Loeffen (2007), in the theory of queuing and storage models Dube et al (2004) and Bekker et al (2008), in the theory of branching processes Bingham (1976) and Lambert (2007) Kyprianou and Surya (2007) and in the theory of fragmentation Krell (2007).…”

Section: Spectrally Negative Lévy Processes and Scale Functionsmentioning

confidence: 99%

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes

Hubalek

Kyprianou

2011

Seminar on Stochastic Analysis, Random Fields and Applications VI

102

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We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Lévy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussian Tempered Stable Convolution (GTSC) class. We give particular emphasis to special cases as well as cross-referencing their analytical behaviour against known general considerations. Spectrally negative Lévy processes and scale functionsLet X = {X t : t ≥ 0} be a Lévy process defined on a filtered probability space (Ω, F, F, P), where {F t : t ≥ 0} is the filtration generated by X satisfying the usual conditions. For x ∈ R denote by P x the law of X when it is started at x and write simply P 0 = P. Accordingly we shall write E x and E for the associated expectation operators. In this paper we shall assume throughout that X is spectrally negative meaning here that it has no positive jumps and that it is not the negative of a subordinator. It is well known that the latter allows us to talk about the Laplace exponent ψ(θ) := log E[e θX1 ] for (θ) ≥ 0 where in particular we have the Lévy-Khintchine representationwhere a ∈ R, σ ≥ 0 is the Gaussian coefficient and Π is a measure concentrated on (−∞, 0) satisfying (−∞,0) (1∧x 2 )Π(dx) < ∞. The, so-called, Lévy triple (a, σ, Π) completely characterises the process X. For later reference we also introduce the function Φ : [0, ∞) → [0, ∞) as the right inverse of ψ on (0, ∞) so that for all q ≥ 0 Φ(q) = sup{θ ≥ 0 : ψ(θ) = q}.(2)

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Section: Spectrally Negative Lévy Processes and Scale Functionsmentioning

confidence: 99%

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes

Hubalek

Kyprianou

2011

Seminar on Stochastic Analysis, Random Fields and Applications VI

102

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“…Boyarchenko and Levendorskiǐ (2002b, Chapter 6) generalized this method for wide classes of Lévy processes, and in Levendorskiǐ (2004), an efficient pricing procedure for the put under exponential jump-diffusion processes was suggested. A different generalization of Carr's randomization method for spectrally negative Lévy processes was used in Avram et al (2002).…”

Section: Carr's Randomizationmentioning

confidence: 99%

American options: the EPV pricing model

Boyarchenko

Levendorskiı̌

2005

Annals of Finance

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“…[2,3,13]) and may give rise to the existence of arrays of critical points in R + dividing the state space {0, 1, . .…”

Section: Note That Algebraic Calculations Show Thatmentioning

confidence: 99%

Time-Randomized Stopping Problems for a Family of Utility Functions

Perez¹,

Le²

2015

SIAM J. Control Optim.

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Abstract. This paper studies stopping problems of the form V = inf 0≤τ ≤T E[U ( max 0≤s≤T Zs Zτ )] for strictly concave or convex utility functions U in a family of increasing functions satisfying certain conditions, where Z is a geometric Brownian motion and T is the time of the nth jump of a Poisson process independent of Z. We obtain some properties of V and offer solutions for the optimal strategies to follow. This provides us with a technique to build numerical approximations of stopping boundaries for the fixed terminal time optimal stopping problem presented in

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On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts

Cited by 43 publications

References 22 publications

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes

American options: the EPV pricing model

Time-Randomized Stopping Problems for a Family of Utility Functions

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