Lévy Processes in Finance: Pricing Financial Derivatives

By Wim Schoutens. 2003

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Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “Many applications of GH distributions, their subclasses, and related distributions are found in mathematical finance (Schoutens, 2003; Cont and Tankov, 2004; Barndorff-Nielsen and Halgreen, 1990; Madan et al., 1998; Barndorff-Nielsen, 1998; Barndorff-Nielsen and Prause, 2001; Carr et al., 2002) and…”
Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015, background): “These stochastic processes play an important role in probability and have been used in recent years to model prices in finance [26,59] and anomalous diffusions in physics [52,55], biology, and ecology [44, 56], among others.”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, unknown): “Meixner model (e.g., Schoutens 2003) The Lévy density of a Meixner Lévy process is given by kþðxÞ ¼ e x= xsinhðpx= Þ ¼ 2e xa pjxj= X1 n¼0 e 2pnjxj= jxj , x 6¼ 0, where , 40, 5 5 , so that we find þðduÞ ¼ 2 X1 n¼0 1fu ð2pnþp Þ= gdu: .”
Financial market models with Lévy processes and time-varying volatility. (2008, methodology): “log ( St St−1 ) = rt − dt + λtσt − L(σt) + σtεt, t ∈ N, (25)”
A multivariate jump-driven financial asset model (2006, unknown): “As concerns equities, this was one of the main reasons for the consideration of Lévy processes (see Schoutens (2003)).”
A Wiener–Hopf Monte Carlo simulation technique for Lévy processes (2009, background): “Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.”
Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type (2009, methodology): “This is based on (8) and a compound Poisson approximation of the BDLP Z at h̄ (see Schoutens 2003 for details).”
The Normal-Laplace Distribution and Its Relatives (2006, methodology): “…a Lévy process {Xt}t≥0, say for which the increments Xt+τ − Xτ have characteristic function (φGNL(s)) t where φGNL is the characteristic function of the GNL(µ, σ2, α, β, ρ) defined in (16) (such a construction is always possible for an infinitely divisible distribution - see e.g. Schoutens, 2003).”
Lévy Processes—From Probability to Finance and Quantum Groups (2004, background): “Readers who want to learn more about “Lévy finance” should consult [12], [4] , chapter 5 of [1], and references therein.”
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem (2018, unknown): “Just to cite a few we refer to [16,17,19,22,27,44] for some physical models, [1,23,34] for some applications in finances, [13] for applications in fluid dynamics, [21,26,32] for application in ecology and [20] for some applications in image processing.”
Analysis of Fourier Transform Valuation Formulas and Applications (2008, methodology): “te options on several assets, considering basket options, spread options and catastrophe insurance derivatives. In addition, the books of Cont and Tankov (2003),Boyarchenko and Levendorski (2002)andSchoutens (2003)are also discussing Fourier transform methods for option pricing. The aim of our artic”
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).”
Intraday pairs trading strategies on high frequency data: the case of oil companies (2017, methodology): “Concerning the normality assumption in the model, it is well known that stock prices as well as stock returns exhibit fat tails, especially on small scales such as the 5 min used in this paper (Cont 2001, Schoutens 2003, Leoni 2014), yet we used Brownian motion to describe the diffusions.”
GARCH option pricing: A semiparametric approach (2008, methodology): “We perform a short study using the European Call option data taken from Schoutens 2003).”