Summary: * Corresponding author. Tel.: #1-609-258-4015; fax: #1-609-258-0719.
E-mail address: firstname.lastname@example.org (Y. AmKt-Sahalia).
Journal of Econometrics 102 (2001) 67}110
Do option markets correctly price the
probabilities of movement of
the underlying asset?
Yacine AmKt-Sahalia *, Yubo Wang , Francis Yared
Department of Economics, Princeton University, Princeton, NJ 08544-1021, USA
Fixed Income Research, J.P. Morgan Securities Inc., New York, NY 10017, USA
Lehman Brothers International (Europe), London EC 2M7HA, UK
Received 4 January 1999; received in revised form 21 August 2000; accepted 2 October 2000
We answer this question by comparing te risk-neutral density estimated in complete
markets from cross-section of S&P 500 option prices to the risk-neutral density inferred
from the time series density of the S&P 500 index. If investors are risk-averse, the latter
density is di!erent from the actual density that could be inferred from the time series of
S&P 500 returns. Naturally, the observed asset returns do not follow the risk-neutral
dynamics, which are therefore not directly observable. In contrast to the existing
literature, we avoid making any assumptions on investors' preferences, by comparing two
risk-adjusted densities, rather than a risk-adjusted density from option prices to an