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Nonparametric estimation for Lévy processes from lowfrequency observations
 Bernoulli 15, 223–248. J.M. BARDET AND D. SURGAILIS
, 2009
"... We suppose that a Lévy process is observed at discrete time points. A rather general construction of minimumdistance estimators is shown to give consistent estimators of the LévyKhinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a ..."
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We suppose that a Lévy process is observed at discrete time points. A rather general construction of minimumdistance estimators is shown to give consistent estimators of the LévyKhinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a specific C 2criterion this estimator is rateoptimal. The connection with deconvolution and inverse problems is explained. A key step in the proof is a uniform control on the deviations of the empirical characteristic function on the whole real line. 2000 Mathematics Subject Classification. Primary 62G15; secondary 62M15. Keywords and Phrases. LévyKhinchine characteristics, density estimation, minimum distance estimator, deconvolution. Short title. Nonparametric estimation for Lévy processes. 1 1.
A jumpdiffusion Libor model and its robust calibration
 Preprint 1113, Weierstraß Institute (WIAS
, 2006
"... In this paper we propose a jumpdiffusion Libor model with jumps in a highdimensional space (R m) and test a stable nonparametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the ..."
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Cited by 6 (5 self)
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In this paper we propose a jumpdiffusion Libor model with jumps in a highdimensional space (R m) and test a stable nonparametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to implement, and yields good results, particularly in view of the severe illposedness of the underlying inverse problem. 1
Hedging with options in models with jumps
 in "Proceedings of the II Abel Symposium 2005 on Stochastic analysis and applications
, 2005
"... in honor of Kiyosi Ito’s 90th birthday. We consider the problem of hedging a contingent claim, in a market where prices of traded assets can undergo jumps, by trading in the underlying asset and a set of traded options. We give a general expression for the hedging strategy which minimizes the varian ..."
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Cited by 6 (3 self)
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in honor of Kiyosi Ito’s 90th birthday. We consider the problem of hedging a contingent claim, in a market where prices of traded assets can undergo jumps, by trading in the underlying asset and a set of traded options. We give a general expression for the hedging strategy which minimizes the variance of the hedging error, in terms of integral representations of the options involved. This formula is then applied to compute hedge ratios for common options in various models with jumps, leading to easily computable expressions. The performance of these hedging strategies is assessed through numerical experiments.
A Bayesian Approach to Financial Model Calibration, Uncertainty Measures and Optimal Hedging
"... Michaelmas 2009This thesis is dedicated to the late ..."
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Michaelmas 2009This thesis is dedicated to the late
Nonparametric inference for discretely sampled
, 2009
"... Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, we study the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X. Our estimator of ρ is based on a suitable inversion of the LévyKhintchine formula and a plugin devi ..."
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Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, we study the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X. Our estimator of ρ is based on a suitable inversion of the LévyKhintchine formula and a plugin device. The main result of the paper deals with an upper bound on the mean square error of the estimator of ρ at a fixed point x. We also show that the estimator attains the minimax convergence rate over a suitable class of Lévy densities.