Non-Gaussian Merton-Black-Scholes theory

By Svetlana Boyarchenko, Sergei Levendorskii. 2002

413 citations recorded by the source corpus.

Subfields: Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6b738fbbb57d699741bd265a783314f55ee2eb71

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Citations in the corpus

Fractional Diffusion Models of Option Prices in Markets With Jumps (2007, methodology): “Based on this work, Koponen [18] and Boyarchenko and Levendorskiǐ [19] proposed the use of modified LS (also known as Lévy-a-stable) processes to model the dynamics of securities.”
Fluctuations of Lévy Processes with Applications (2014, background): “…include generalised inverse Gaussian (see Good (1953) and Jørgensen (1982)), truncated stable (see Tweedie (1984), Hougaard (1986), Koponen (1995), Boyarchenko and Levendorskii (2002a) and Carr et al. (2003)), generalised hyperbolic (see Halgreen (1979)), Meixner (see Schoutens and Teugels…”
On the drawdown of completely asymmetric Lévy processes (2011, background): “try and excess kurtosis is that of exponential L´evy processes. This class has received considerable attention in the literature —we refer to Cont & Tankov [15] and Boyarchenko & Levendorskii [8] for background and references. By restricting ourselves to L´evy processes with jumps of a singl”
Symmetry and duality in Lévy markets (2006, methodology): “For the Lévy process in Finance see Boyarchenko and Levendorskii (2002), Schoutens (2003) and Cont and Tankov (2004).”
Optimal stopping of Hunt and Lévy processes (2006, background): “[3]).”
Some remarks on first passage of Levy processes, the American put and pasting principles (2005, background): “24 (1994) 195–220], Boyarchenko and Levendorskǐi [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim.”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, background): “ssian [6] and generalised hyperbolic processes [18]. This class of models has been extensively studied and we refer for background and further references to the books by Boyarchenko and Levendorski˘ı [13], Cont and Tankov [16] and Schoutens [36]. In this paper we consider barrier options driven by L”
Tempered stable distributions and processes in finance: numerical analysis (2010, methodology): “The KoBol [4], the CGMY [5], the Inverse Gaussian (IG) and the tempered stable of Tweedie [23] are only some parametric examples in this class, that have an infinite dimensional parametrization by a family of measures [25].”
Jump-diffusion Models: a Practitioner's Guide (2009, methodology): “In diffusion models their prices are usually expressed as solutions of the Black-Scholes partial differential equation ∂P ∂t + 1 2 σ(2)S(2) ∂(2)C ∂S2 = rC − rS ∂C ∂S (10) (4)Fourier-transform based methods for pricing single-barrier options can be found in the literature [24, 5, 18] but except for s”
VALUATION OF CONTINUOUSLY MONITORED DOUBLE BARRIER OPTIONS AND RELATED SECURITIES (2009, neutral): “Boyarchenko and the second author [9, 10, 11, 35, 36, 12, 13].”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, neutral): “, [64], [89], [23], [24], [25], [34], [106].”
WIENER-HOPF FACTORIZATION FOR LEVY PROCESSES HAVING POSITIVE JUMPS WITH RATIONAL TRANSFORMS (2008, background): “stopping problem related to the pricing of a perpetual call and put option, respectively, in a market model generated by a Lévy process (see [7] and [18]).”
Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes (2007, background): “Tempered stable processes have been studied by many authors including [2, 3, 6, 10] under different names.”
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 EIGENFUNCTION EXPANSION METHOD IN MULTI‐FACTOR QUADRATIC TERM STRUCTURE MODELS (2007, neutral): “Subordination with ν = 0.05 is close to Variance Gamma subordination, whereas the one with ν = 0.95 is close to the one-sided version of KoBoL process of order ν = 1: Φ(λ) = (p− λ) log(p− λ) − p log p (see equation (3.5) in Boyarchenko and Levendorskǐi (2002)).”