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SESSION VIII-2 : EMPIRICAL METHODS (21/12/2007 à 16h30)

Christophe Pérignon (HEC Paris)

Testing For Jumps In A Discretely Observed Process

Auteurs : AIT-SAHALIA Yacine (Princeton University) and JACOD Jean (University of Paris 6) Email :

Intervenants : AIT-SAHALIA Yacine (Princeton University)

Rapporteurs : LE COURTOIS Olivier (EM Lyon)

We propose a new test to determine whether jumps are present in asset returns
or other discretelly sampled processses. As the sampling interval tends to 0, our test
statistic converges to 1 if there are jumps, and to another deterministic and known
value (such as 2) if there are no jumps. The test is valid for all Itô semimartingales,
depends neither on the law of the process nor on the coefficients of the equation which
it solves, does not require a preliminary estimation of these coefficients, and when there
are jumps the test is applicable whether jumps have finite or infinite activity and for an
arbitrary Blumenthal-Getoor index. We finally implement the test on simulations and
asset returns data.

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Assessing the power and the size of the event study method through the decades

Auteurs : AKTAS Nihat (Univ.Catholique Louvain Core & IAG), COUSIN Jean-Gabriel and DE BODT E.(Univ. Lille2 and Groupe Esc Lille)

Intervenants : COUSIN Jean-Gabriel (University of Lille2 and Groupe Esc Lille)

Rapporteurs : WANG Zaizhi (Cerna, Ecole des Mines de Paris)

The idiosyncratic risk is a key input of the standard event study method. The recent
literature has suggested that the idiosyncratic risk is not stable through time, and it has
increased significantly in the nineties. This paper investigates to what extent the event
study method is affected by this economic phenomenon. Using both simulation and real
dataset analyses, we show that the classical event study methods suffer from a significant
loss of power due to increasing idiosyncratic risk, as the intuition suggests it.
A (and maybe the only) solution to alleviate the impact of increasing idiosyncratic risk
consists in increasing the sample size by a factor corresponding to the ratio of average
idiosyncratic variances between the analyzed periods.

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”Effective” parameters for stochastic volatility models

Auteurs : WANG Zaizhi (Cerna, Ecole des Mines de Paris) Email :

Intervenants : WANG Zaizhi (Cerna, Ecole des Mines de Paris)

Rapporteurs : Pierre CLAUSS (ENSAI Rennes)

This paper tackles the issue of approximated formula for stochastic model with time dependent
model parameters, using an averaging principle. The idea lies in finding a similar model but
with constant parameters that is the closest to our initial process, along the same lines as
results proven by Gyöngy (1986) for general stochastic processes. We extend previous
results found by Piterbarg (2005) for the particular case of SABR model (Hagan (2002)).
The resulting formula can be evaluated very quickly solving the implied Riccati equations.
We compare the approximation with exact solution of the corresponding partial differential
equation using an ADI method. Numerical results show that the approximation works well
for short term maturities.

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