TY - JOUR

T1 - Do option markets correctly price the probabilities of movement of the underlying asset?

AU - Aït-Sahalia, Yacine

AU - Wang, Yubo

AU - Yared, Francis

N1 - Funding Information:
We are grateful to David Bates, George Constantinides, Robert Engle and Robert MacDonald for useful discussions. Seminar participants also provided helpful comments. This research was conducted in part during the first author's tenure as an Alfred P. Sloan Research Fellow. Financial support from the NSF (Grant SBR-9996023) and the University of Chicago's Center for Research in Security Prices is gratefully acknowledged.

PY - 2001/5

Y1 - 2001/5

N2 - 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 different 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 unadjusted density from index returns. Our only maintained hypothesis is a one-factor structure for the S&P 500 returns. We propose a new method, based on an empirical Girsanov's change of measure, to identify the risk-neutral density from the observed unadjusted index returns. We design four different tests of the null hypothesis that the S&P 500 options are efficiently priced given the S&P 500 index dynamics, and reject it. By adding a jump component to the index dynamics, we are able to partly reconcile the differences between the index and option-implied risk-neutral densities, and propose a peso-problem interpretation of this evidence.

AB - 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 different 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 unadjusted density from index returns. Our only maintained hypothesis is a one-factor structure for the S&P 500 returns. We propose a new method, based on an empirical Girsanov's change of measure, to identify the risk-neutral density from the observed unadjusted index returns. We design four different tests of the null hypothesis that the S&P 500 options are efficiently priced given the S&P 500 index dynamics, and reject it. By adding a jump component to the index dynamics, we are able to partly reconcile the differences between the index and option-implied risk-neutral densities, and propose a peso-problem interpretation of this evidence.

KW - Arbitrage relationships

KW - Density comparison

KW - Girsanov's theorem

KW - Implied volatility smile

KW - Jump risk

KW - Peso problem

KW - Risk-neutral densities

KW - State-price densities

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U2 - 10.1016/S0304-4076(00)00091-9

DO - 10.1016/S0304-4076(00)00091-9

M3 - Article

AN - SCOPUS:18044400024

SN - 0304-4076

VL - 102

SP - 67

EP - 110

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

ER -