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Figueroa-López, José E.; Luo, Yankeng; Ouyang, Cheng

Small-time expansions for local jump-diffusion models with infinite jump activity. (English) Zbl 1304.60083

Bernoulli 20, No. 3, 1165-1209 (2014).
Authors’ abstract: We consider a Markov process \(X\), which is the solution of a stochastic differential equation driven by a Lévy process \(Z\) and an independent Wiener process \(W\). Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of \( Z \) outside any neighborhood of the origin, we obtain a small-time second-order polynomial expansion for the tail distribution and the transition density of the process \(X\). Our method of proof combines a recent regularizing technique for deriving the analog small-time expansions for a Lévy process with some new tail and density estimates for jump-diffusion processes with small jumps based on the theory of Malliavin calculus, flow of diffeomorphisms for SDEs, and time-reversibility. As an application, the leading term for out-of-the-money option prices in short maturity under a local jump-diffusion model is also derived.
Reviewer: Marius Iosifescu (Bucureşti)

Cited in 4 Documents

MSC:

60J60 Diffusion processes
60J75 Jump processes (MSC2010)

Keywords:

local jump-diffusion model; option pricing; small-time asymptotic expansion; transition densities; transition distributions
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Full Text: DOI arXiv Euclid

References:

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