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Nonparametric Risk-Neutral Return and Volatility Distributions

Mark-Jan Boes

VU University Amsterdam

Feike C. Drost

Tilburg University - Center for Economic Research (CentER)

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)


AFA 2006 Boston Meetings Paper

Using a no-arbitrage condition we develop a nonparametric technique to extract the risk-neutral distribution of both asset returns and instantaneous volatilities from plain vanilla option prices. Our technique extends existing approaches that lead to risk-neutral return distributions only. In order to estimate the risk-neutral volatility distribution, we do not need to that derivatives on volatility are traded. More generally, as our method yields a nonparametric estimate of the joint risk-neutral return/volatility distribution, we can also estimate conditional distributions of returns given future volatility levels. This opens the possibility to answer several important questions on risk-neutral volatility distributions and, thus, volatility risk premiums. Using S&P-500 data, we confirm negative volatility risk premiums and a right-shift in the future volatility distribution for higher initial volatility levels, but find additionally positive risk-neutral volatility skewness. Moreover, volatility skewness is more pronounced in low volatility periods. This is consistent with a large aversion towards unexpected positive volatility shocks. With respect to the risk-neutral return distribution, we confirm overall negative skewness, but find that conditionally on decreasing volatility levels, the negative return skewness disappears. Concerning the risk-neutral dependence between return and volatility, we confirm that this dependence is negative. Compared to parametric models, we find that risk-neutral volatility of volatility is much smaller than predicted by the popular Heston (1993) model. This indicates the necessity of a jump component in the risk-neutral return process. Furthermore, the risk-neutral volatility of volatility cannot be described by a single diffusion risk-neutral volatility process.

Number of Pages in PDF File: 22

Keywords: Derivative pricing, Skewness, State-price-density, Stochastic volatility

JEL Classification: G12, G13

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Date posted: March 24, 2005  

Suggested Citation

Boes, Mark-Jan and Drost, Feike C. and Werker, Bas J. M., Nonparametric Risk-Neutral Return and Volatility Distributions (04-15-2005). AFA 2006 Boston Meetings Paper. Available at SSRN: https://ssrn.com/abstract=685943 or http://dx.doi.org/10.2139/ssrn.685943

Contact Information

Mark-Jan Boes (Contact Author)
VU University Amsterdam ( email )
De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Feike C. Drost
Tilburg University - Center for Economic Research (CentER) ( email )
Econometrics and Finance Group
P.O. Box 90153
5000 LE Tilburg
+31 13 466 3038 (Phone)
Bas J.M. Werker
Tilburg University - Center for Economic Research (CentER) ( email )
Econometrics and Finance Group
5000 LE Tilburg
Feedback to SSRN

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