Lévy Processes in Finance: Theory, Numerics, and Empirical Facts

By Sebastian Raible. 2000

318 citations recorded by the source corpus.

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Citations in the corpus

Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “Now, letĉ denotes the Laplace transform of the payoff functionc of an option, i.e. ĉ(z) = ∫ ∞ −∞ e−zxc(x)dx, see Raible (2000) for explicit forms.”
An introduction to Lévy processes with applications in finance (2008, methodology): “3 in Raible (2000) are satisfied and we can invert this Laplace transform to recover the option value.”
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions (2008, methodology): “The difference with the Carr-Madan approach is that the transform is with respect to the log-spot price in the CONV method instead of the log-strike price (something which [17] and [23] also consider).”
Numerical valuation of options with jumps in the underlying (2005, unknown): “(5) Letting ζ̃ = ζ − E[Y ], the reduced Lévy triplet results in( σ 2, r − λζ̃ − σ 2/2, λF ).”
On a new approach to calculating expectations for option pricing (2002, methodology): “This method was also described by Raible [7].”
A Didactic Note on Affine Stochastic Volatility Models (2006, background): “A large class of arbitrary payoffs can be represented explicitly as a linear combination or, more precisely, integral of such “simple” claims (cf. e.g. Carr & Madan (1999), Raible (2000)).”
PRICING DISCRETELY MONITORED BARRIER OPTIONS AND DEFAULTABLE BONDS IN LÉVY PROCESS MODELS: A FAST HILBERT TRANSFORM APPROACH (2008, unknown): “This defines an equivalent probability measure P(α) (Esscher transform or exponential tilting of the original probability measure) such that under P(α) the process X is a Lévy process with the characteristic exponent (4.3) (e.g., Raible 2000, proposition 1.8; Jeanblanc et al. 2006).”
Static Hedging of Asian Options under Lévy Models (2005, unknown): “For more examples and applications of Levy processes in finance see [5, 13, 14, 21, 29, 36].”
Analysis of Fourier Transform Valuation Formulas and Applications (2008, methodology): “Since the seminal work of Carr and Madan (1999) and Raible (2000) on the valuation of options with Fourier transform methods, there have been several articles dealing with extensions and analysis of these valuation formulas.”
Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type (2003, methodology): “Hence, formula (4.2) can be computed numerically for any θ ∈ (1, θ+) using adaptive integration software packages or more sophisticated algorithms as described in Carr and Madan (1999), Raible (2000), and Lewis (2001).”