Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations

DOI10.1002/cpa.21478zbMath1300.60093arXiv1111.2462OpenAlexW2963784336MaRDI QIDQ5746482

Jean-Dominique Deuschel, S. Violante, Peter K. Friz, Antoine Jacquier

Publication date: 18 February 2014

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2462

zbMATH Keywords

control problemdensity expansionhypoelliptic diffusionHörmander conditionHamiltonian ODEshort-timenot-in-cut-locus conditionsmall-noise

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Ordinary differential equations and systems with randomness (34F05) Diffusion processes and stochastic analysis on manifolds (58J65) Hypoelliptic equations (35H10)

Related Items (29)

SHORT TIME FULL ASYMPTOTIC EXPANSION OF HYPOELLIPTIC HEAT KERNEL AT THE CUT LOCUS ⋮ ASYMPTOTICS OF THE TIME-DISCRETIZED LOG-NORMAL SABR MODEL: THE IMPLIED VOLATILITY SURFACE ⋮ Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation ⋮ Black-Scholes in a CEV random environment ⋮ General Asymptotics of Wiener Functionals and Application to Implied Volatilities ⋮ Small-Time Asymptotics for the At-the-Money Implied Volatility in a Multi-dimensional Local Volatility Model ⋮ Asymptotics for $$d$$ -Dimensional Lévy-Type Processes ⋮ Asymptotic Expansion Approach in Finance ⋮ On the Probability Density Function of Baskets ⋮ On Small-Noise Equations with Degenerate Limiting System Arising from Volatility Models ⋮ Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators ⋮ Local Volatility, Conditioned Diffusions, and Varadhan's Formula ⋮ Option pricing in the moderate deviations regime ⋮ Reconstructing volatility: Pricing of index options under rough volatility ⋮ Symmetries and zero modes in sample path large deviations ⋮ Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems ⋮ Extreme-strike asymptotics for general Gaussian stochastic volatility models ⋮ SUPPORT THEOREM FOR PINNED DIFFUSION PROCESSES ⋮ Small-Time Asymptotics under Local-Stochastic Volatility with a Jump-to-Default: Curvature and the Heat Kernel Expansion ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Pathwise large deviations for the rough Bergomi model ⋮ FUNCTIONAL ANALYTIC (IR-)REGULARITY PROPERTIES OF SABR-TYPE PROCESSES ⋮ Precise asymptotics: robust stochastic volatility models ⋮ Distance to the line in the Heston model ⋮ Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications ⋮ Large-maturity regimes of the Heston forward smile ⋮ Asymptotic behaviour of randomised fractional volatility models ⋮ Short-time near-the-money skew in rough fractional volatility models ⋮ Small-time asymptotics for Gaussian self-similar stochastic volatility models

Cites Work

• Unnamed Item
• Unnamed Item
• Polynomial control systems
• Décroissance exponentielle du noyau de la chaleur sur la diagonale. I. (Exponential decay of the heat kernel over the diagonal. I)
• Exponential decay of the heat kernel over the diagonal. II
• A remark on the asymptotic expansion of density function of Wiener functionals
• Mimicking the one-dimensional marginal distributions of processes having an Ito differential
• Precise asymptotics of certain Wiener functionals
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Asymptotic behavior of the stock price distribution density and implied volatility in stochastic volatility models
• A generalized Fernique theorem and applications
• Computing the implied volatility in stochastic volatility models
• Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus
• Methods de laplace et de la phase stationnaire sur l'espace de wiener
• On the Asymptotics of the Transition Density of Processes with Small Diffusion
• ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS
• On refined volatility smile expansion in the Heston model
• Diffusion processes in a small time interval
• Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications

This page was built for publication: Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations