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- José Enrique Figueroa-López, Christian Houdré, +6 authors Hamed Marrofi
- 2003

ACKNOWLEDGEMENTS There have been many individuals in my life without whom the completion of this work would not have been possible. It is my intension to briefly recognize their contribution to my personal and professional life. I would like to thank my advisor, Dr. Christian Houdré, for his support and orientation through all my studies at Georgia Tech. In… (More)

Given a Lévy process X with Lévy measure ν, conditions ensuring that limt→0 1t E f(Xt) = ∫ f(x)ν(dx) are given. The moment functions f considered here can be unbounded as well as satisfy simpler regularity conditions than those considered in some previous works. Also, the rate of convergence is determined when f vanishes in a neighborhood of the origin and… (More)

- José E. Figueroa-López, Martin Forde
- SIAM J. Financial Math.
- 2012

We derive a small-time expansion for out-of-the-money call options under an exponential Lévy model, using the small-time expansion for the distribution function given in Figueroa-López&Houdré[FLH09], combined with a change of numéraire via the Esscher transform. In particular, we find that the effect of a non-zero volatility σ of the Gaussian component of… (More)

A Lévy model combines a Brownian motion with drift and a purejump homogeneous process such as a compound Poisson process. The estimation of the Lévy density, the infinite-dimensional parameter controlling the jump dynamics of the process, is studied under a discrete-sampling scheme. In that case, the jumps are latent variables whose statistical properties… (More)

Let X = (Xt)t≥0 be a Lévy process with absolutely continuous Lévy measure ν. Small time expansions of arbitrary polynomial order in t are obtained for the tails P (Xt ≥ y), y > 0, of the process, assuming smoothness conditions on the Lévy density away from the origin. By imposing additional regularity conditions on the transition density pt of Xt, an… (More)

Estimation methods for the Lévy density of a Lévy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good estimator, from an approximating (finite-dimensional) linear model S for the true Lévy density. The second is a data-driven… (More)

We consider a stochastic volatility model with Lévy jumps for a log-return process Z = (Zt)t≥0 of the form Z = U+X, where U = (Ut)t≥0 is a classical stochastic volatility process and X = (Xt)t≥0 is an independent Lévy process with absolutely continuous Lévy measure ν. Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the… (More)

A Lévy process combines a Brownian motion and a pure-jump homogeneous process, such as a compound Poisson process. The estimation of the Lévy density, the infinite-dimensional parameter controlling the jump dynamics of the process, is considered under a discrete-sampling scheme. In that case, the jumps are latent variables which statistical properties can… (More)

We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time… (More)

Let {Zt}t≥0 be a Lévy process with Lévy measure ν and let τ(t) = ∫ t 0 r(u)du where {r(t)}t≥0 is a positive ergodic diffusion independent from Z. Based upon discrete observations of the time-changed Lévy process Xt := Zτt during a time interval [0, T ], we study the asymptotic properties of certain estimators of the parameters β(φ) := ∫ φ(x)ν(dx), which in… (More)