The Variance Gamma Process and Option Pricing

By Dilip B Madan 5, Peter P. Carr, Eric C. Chang. 1998

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Citations in the corpus

Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “The GH, NIG, and VG distributions are well-known in mathematical finance and risk management (Schoutens, 2003; Cont and Tankov, 2004; Barndorff-Nielsen and Halgreen, 1990; Madan et al., 1998; Barndorff-Nielsen, 1998; Barndorff-Nielsen and Prause, 2001).”
Multivariate asset models using Lévy processes and applications (2012, unknown): “In particular, if α = 0, expression (8) is to be understood in a limiting sense and G(t) is a Gamma process so that X(t) is a (asymmetric) VG process (see Madan et al., 1998, for example). If, instead, α = 1/2, the subordinator follows an Inverse Gaussian process and X (t) is the NIG process introdu”
Wavelet Galerkin pricing of American options on Lévy driven assets (2005, methodology): “We mention here the Variance Gamma (VG) (Madan and Seneta 1990, Madan et al. 1998), the extended Koponen family (Boyarchenko and Levendorski 2000) (also referred to as KoBoL, tempered or truncated tempered stable processes or truncated Lévy flights in physics and later used in Carr et al. (2000)…”
On The Expected Discounted Penalty function for Lévy Risk Processes (2006, methodology): “This process has been used in finance as well as in insurance [see Dufresne et al. (1991) and Madan et al. (1998)].”
The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing (2011, unknown): “Ritchey (1990) and Gemmill and Saflekos (2000) use two lognormals, and Melick and Thomas (1997) use three lognormals.”
An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums (2009, unknown): “This case is very important in financial applications for the asymptotic validation of such popular models of the evolution of financial indexes as variance-gamma Lévy processes (VG processes; Madan & Seneta (1990)) or two-sided gamma processes (Carr et al. (1998)).”
From local volatility to local Lévy models (2004, unknown): “We recognize in equation ( 18 ) the inverse of our convolution transform operator as in general an integro-di®erential operator.”
Pure jump L'evy processes for asset price modeling (2002, unknown): “The normality of distributions has been augmented with the assumption of continuity of trajectories when Samuelson introduced in 1965 the geometric Brownian motion, then used in the seminal papers by Black-Scholes (1973) and Merton (1973). As documented in a considerable number of papers written by ”
Pricing Credit Default Swaps Under Levy Models (2007, background): “In [14], the general case with skewness is treated.”
Time Changes for Lévy Processes (2001, background): “The search for such a formulation began in earnest with Clark (1973), and has been pursued more recently by Geman and Ané (1996), Ané and Geman (2000), Madan, Carr, and Chang (1998), and Bakshi and Madan (1999).”
Self-Exciting Jumps, Learning, and Asset Pricing Implications (2015, background): “A recent survey has been provided by Pastor and Veronesi (2009). One of the key implications is that Bayesian learning generates persistent and long-term changes to the agents’s beliefs, which have important influence on stock valuation, risk measures, and time series predictability.”
Calibration of Jump-Diffusion Option Pricing Models: A Robust Non-Parametric Approach (2002, methodology): “Double exponential [23] : ν(x) = [1x>0pα1e−α2x + (1− p)α2e−α2x1x<0] • Variance Gamma [24] ν(x) = A|x|−1 exp(−η±|x|) • Tempered stable(1) processes [22, 12]: ν(x) = A±|x|−(1+α) exp(−η±|x|) • Normal inverse gaussian process [6] • Hyperbolic and generalized hyperbolic processes [14, 13] • Meixner proce”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “…independent increments property of Lévy processes, if Z∗u, t =Zt −Zu and G∗u, t =Gt −Gu are the increments of Zt and Gt, then we obtain by theorem 1 of Madan et al. (1998): p(z∗u, t | )= ∫ p(z∗u, t |g∗u, t, , J )p(g∗u, t) d(g∗u, t) = 2 exp{ (z ∗ u, t) 2/ } (t−u)/ √ 2 ((t −u)/ ) ( (z∗u, t) 2 2 +2…”
Spread Option Valuation and the Fast Fourier Transform (2002, methodology): “This includes the Variance Gamma (VG) model [15], the inverse Gaussian model [3] and numerous stochastic volatility and stochastic interest rates models in the general affine jump-diffusion family [1, 4, 6, 14, 21].”
A multivariate jump-driven financial asset model (2006, unknown): “In [22], it was shown that the VG-process may also be expressed as the difference of two independent Gamma processes.”