Density estimates and short-time asymptotics for a hypoelliptic diffusion process

Paolo Pigato

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 117-142

Abstract: We study a system of n differential equations, each in dimension d. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak Hörmander condition, the noise propagates to the whole system. We prove upper bounds for the transition density (heat kernel) and its derivatives of any order. Then we give precise short-time asymptotics of the density at a suitable central limit time scale. Both these results account for the different non-diffusive scales of propagation in the various components. Finally, we provide a valuation formula for short-maturity at-the-money Asian basket options under correlated local volatility dynamics.

Keywords: Heat kernel estimates; Density derivatives estimates; Short-time asymptotics; Hörmander condition; Asian basket option; Correlated local volatility (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:145:y:2022:i:c:p:117-142

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DOI: 10.1016/j.spa.2021.11.012

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