Lévy Processes in Finance

By Wim Schoutens. 2003

388 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/d12935fef0a87d76250fd19a8dfac036ef860201

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

Citations in the corpus

The Normal-Laplace Distribution and Its Relatives (2006, methodology): “…{X t } t≥0 , say for which the increments X t+τ − X τ have characteristic function (φ GN L (s)) t where φ GN L is the characteristic function of the GNL(µ, σ 2 , α, β, ρ) defined in (16) (such a construction is always possible for an infinitely divisible distribution -see e.g. Schoutens, 2003).”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “After some elementary simplifications we obtain W (x) ∼ 1 κ (x→ ∞) (54) in agreement with the theory.”
PRICING OPTIONS ON VARIANCE IN AFFINE STOCHASTIC VOLATILITY MODELS (2010, methodology): “This recovers the formula obtained in Carr et al. (2005), where the integral w.r.t. the Lévy measure is computed in closed form for the CGMY Lévy process (cf., e.g., Schoutens 2003).”
Sato processes and the valuation of structured products (2009, neutral): “…addition to the Variance Gamma (VG) (Madan et al. 1998), the Normal Inverse Gaussian (NIG) (BarndorffNielsen 1998), and the Meixner (MXNR) process (Schoutens 2002, 2003) reported by Carr et al. (2007), are the CGMY (Carr et al. 2002) and the GH, the generalized hyperbolic model (Eberlein 2001,…”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, methodology): “[36]) The Lévy density of a Meixner Lévy process is given by k+(x) = δeβx/α x sinh(πx/α) = 2e ∞ ∑”
SMILE ASYMPTOTICS II: MODELS WITH KNOWN MOMENT GENERATING FUNCTIONS (2006, background): “In particular, the term-structure of the wings can be analytically understood.”
Pricing discretely monitored Asian options under Levy processes (2008, methodology): “See Schoutens (2003).”
Fractional Diffusion Models of Option Prices in Markets With Jumps (2007, background): “The literature proposes a number of ways of choosing an EMM under which pricing of instruments is performed.”
Fast deterministic pricing of options on Lévy driven assets (2002, methodology): “Meixner process The Meixner process was proposed in [40].”
Some explicit identities associated with positive self-similar Markov processes. (2007, background): “See for example Carr et al. [11], Boyarchenko and Levendorskii [8], Cont [14] or Schoutens [29].”
The application of continuous-time random walks in finance and economics (2006, background): “Conversely, for every infinite divisible distribution, there exists a corresponding Lévy process [56].”
Extremes of supOU Processes (2007, methodology): “We present here some important examples satisfying (17), which are also used for financial modelling; we refer to Schoutens [20] for an overview of these d.”