Edgeworth expansion for functionals of continuous diffusion processes
نویسندگان
چکیده
منابع مشابه
Edgeworth expansion for functionals of continuous diffusion processes
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the second order Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central...
متن کاملParametric first-order Edgeworth expansion for Markov additive functionals. Application to M-estimations
We give a spectral approach to prove a parametric rst-order Edgeworth expansion for bivariate additive functionals of strongly ergodic Markov chains. In particular, given any V geometrically ergodic Markov chain (Xn)n∈IN whose distribution depends on a parameter θ, we prove that {ξp(Xn−1, Xn); p ∈ P, n ≥ 1} satis es a uniform (in (θ, p)) rst-order Edgeworth expansion provided that {ξp(·, ·); p ...
متن کاملAsymptotic Analysis for Stochastic Volatility: Edgeworth expansion
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff functions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean re...
متن کاملModerate Deviations Type Evaluation for Integral Functionals of Diffusion Processes
where Ψ and g are smooth functions, ξε t is a “fast” ergodic diffusion whileXε t is a “slow” diffusion type process, κ ∈ (0, 1/2). Under the assumption that g has zero barycenter with respect to the invariant distribution of the fast diffusion, we derive the main result from the moderate deviation principle for the family (ε−κ ∫ t 0 g(ξ ε s)ds)t≥0, ε ↘ 0 which has an independent interest as wel...
متن کاملExponential functionals of Brownian motion, II: Some related diffusion processes
This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2016
ISSN: 1050-5164
DOI: 10.1214/16-aap1179