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Penalized Projection Estimator for Volatility Density
Author(s) -
COMTE F.,
GECATALOT V.
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00519.x
Subject(s) - mathematics , estimator , stochastic volatility , volatility (finance) , rate of convergence , mixing (physics) , econometrics , combinatorics , statistics , computer science , physics , channel (broadcasting) , computer network , quantum mechanics
. In this paper, we consider a stochastic volatility model ( Y t , V t ), where the volatility (V t ) is a positive stationary Markov process. We assume that ( ln V t ) admits a stationary density f that we want to estimate. Only the price process Y t is observed at n discrete times with regular sampling interval Δ . We propose a non‐parametric estimator for f obtained by a penalized projection method. Under mixing assumptions on ( V t ), we derive bounds for the quadratic risk of the estimator. Assuming that Δ=Δ n tends to 0 while the number of observations and the length of the observation time tend to infinity, we discuss the rate of convergence of the risk. Examples of models included in this framework are given.