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Journal of Financial Economics 74 (2004) 487528 Disentangling diffusion from jumps$

Summary: Journal of Financial Economics 74 (2004) 487528
Disentangling diffusion from jumps$
Yacine A.it-Sahalia*
Bendheim Center for Finance, Princeton University, Princeton, NJ 08540-5296, USA
Received 7 August 2003; accepted 22 September 2003
Available online 20 July 2004
Realistic models for financial asset prices used in portfolio choice, option pricing or risk
management include both a continuous Brownian and a jump components. This paper studies
our ability to distinguish one from the other. I find that, surprisingly, it is possible to perfectly
disentangle Brownian noise from jumps. This is true even if, unlike the usual Poisson jumps,
the jump process exhibits an infinite number of small jumps in any finite time interval, which
ought to be harder to distinguish from Brownian noise, itself made up of many small moves.
r 2004 Elsevier B.V. All rights reserved.
JEL classification: G12; C22
Keywords: Poisson jumps; Cauchy jumps; L!evy process; Diffusion; Maximum likelihood
1. Introduction
From an asset pricing perspective, being able to decompose the total amount of
noise into a continuous Brownian part and a discontinuous jump part is useful in a
number of contexts. For instance, in option pricing, the two types of noise have


Source: At-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University


Collections: Mathematics