UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 42.1 41.2 41.1 40.2 40.1
39.2 39.1 38.2 38.1 37.2 37.1 36.2
36.1 35.2 35.1 34.2 34.1 33.2 33.1
32.2 32.1 31.2 31.1 30.2 30.1 29.2
29.1 28.2 28.1 27.2 27.1 26.2 26.1
25.2 25.1 24.2 24.1 23.2 23.1 22.2
22.1 21.2 21.1 20.2 20.1 19.2 19.1
18.2 18.1 17.2 17.1 16.2 16.1 15
14.2 14.1 13.2 13.1 12.2 12.1 11.2
11.1 10.2 10.1 9.2 9.1 8 7.2
7.1 6.2 6.1 5.2 5.1 4.2 4.1
3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 28, Fasc. 1,
pages 1 - 19
 

STOCHASTIC VOLATILITY: APPROXIMATION AND GOODNESS-OF-FIT TEST

Mihai Gradinaru
Ivan Nourdin

Abstract: Let $X$ be the unique solution started from $x_0$ of the stochastic differential equation

$dX_t=\theta (t,X_t)dB_t+b(t,X_t)dt$
with $B$ a standard Brownian motion. We consider an approximation of the volatility $\theta (t,X_t)$, the drift being considered as a nuisance parameter. The approximation is based on a discrete time observation of $X$ and we study its rate of convergence as a process. A goodness-of-fit test is also constructed.

2000 AMS Mathematics Subject Classification: Primary: 62M05; Secondary: 62M02, 62L20, 60H10, 60F15, 60F05.

Key words and phrases: Non-parametric estimation, goodness-of-fit test, stochastic volatility, discrete time observation.

Download:    Abstract    Full text   Abstract + References