Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

By Leif Andersen, J. Andreasen. 2000

353 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/c1a26a6279355edc7e8c34dc6c7d71a275039938

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Citations in the corpus

Maximum likelihood estimation of the double exponential jump-diffusion process (2007, background): “Andersen and Andreasen (2000) combined a deterministic volatility structure with log-normally distributed Poisson jumps.”
On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View (2010, neutral): “[4, 19]), based on wavelet methods ([37]), or Fourier transform based methods ([30, 36]).”
On American Options Under the Variance Gamma Process (2007, methodology): “We accompany the method by a stability analysis, similar in spirit to the Von Neumann stability analysis given in [4] for the jump-diffusion case.”
Wavelet Galerkin pricing of American options on Lévy driven assets (2005, methodology): “From the results of [10] it follows in particular that for the family of CGMY Lévy processes, the principle of smooth fit may fail if Y ∈ (0, 1), but also that the smooth fit condition always holds for Y ∈ [1, 2).”
Robust numerical methods for contingent claims under jump diffusion processes (2005, methodology): “Andersen and Andreasen (2000) used an operator splitting type of approach combined with a fast Fourier transform (FFT) evaluation of a convolution integral to price European options with jump diffusion, where the diffusion terms involved non-constant local volatilities.”
Efficient numerical methods for pricing American options under stochastic volatility (2008, background): “Examples of these are value and time dependent volatility functions [15], jump processes for the value [11], [30], their combinations [2], stochastic volatility models [18], [20], and stochastic volatility models with jumps [14].”
Numerical solution of two asset jump diffusion models for option valuation (2008, background): “Andersen and Andreasen [4] developed an operator splitting approach for European options which was unconditionally stable and second order in time.”
From local volatility to local Lévy models (2004, neutral): “For extensions of this approach to a jump diffusion context we cite Andersen (2000) and Andersen and Andreasen (1999). The local uncertainty of a local volatility model is Gaussian with zero skewness and kurtosis equal to 3.”
ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS (2012, neutral): “Mathematical Finance, Vol. 22, No. 4 (October 2012), 591–620”
Calibration and hedging under jump diffusion (2007, methodology): “While such an approach has not been subjected to extensive empirical tests (as far as we are aware), Andersen and Andreasen (2000) report preliminary evidence indicating that this approach shows some promise in terms of capturing observed behavior of implied volatilities.”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, neutral): “, [94], [39], [59], [14], [4], [76] among others.”
Pricing methods and hedging strategies for volatility derivatives (2006, background): “These parameters are approximately the values reported in [1], which the authors found were implied in a certain set of S&P options market prices.”
Numerical valuation of options with jumps in the underlying (2005, neutral): “Keywords:Option pricing; Jump-diffusion processes; Finite differences; Finite elements; Fast Fourier transform; Integro-differential equations”
The effect of modelling parameters on the value of GMWB guarantees (2008, methodology): “As in Andersen and Andreasen (2000), we calibrate the parameters of equation (8) to traded prices of options.”
Extended Libor Market Models with Stochastic Volatility (2001, neutral): “For Case I and Case II, the “Exact” numbers are computed by a known closed-form result (see e.g. Andersen and Andreasen (2000)); for Case III the “Exact” numbers are computed in a Crank-Nicholson finite difference grid with 150 time steps and 250 spatial steps.”
Robustly Hedging Variable Annuities with Guarantees under Jump and Volatility Risks (2007, background): “, a jump diffusion model with a local volatility function [2], it is difficult to accurately model the implied volatility evolution for a long time horizon based on market calibration.”
Option Pricing: Valuation Models and Applications (2004, neutral): “An extension to SV is given in Andersen and Brotherton-Ratcliffe (2001). Empirical evidence supporting SV and jumps in interest rates is given in Collin-Dufresne and Goldstein (2002) and Johannes (2004).”