Extracting Risk-Neutral Density and its Moments from American Option Prices

Posted: 5 Aug 2011

See all articles by Yisong S. Tian

Yisong S. Tian

York University - Schulich School of Business

Date Written: November 24, 2010


There has been a surge in the use of option-implied moments (e.g., volatility, skewness and kurtosis) in various empirical applications such as volatility forecasting, variance risk premium, empirical asset pricing, and portfolio selection. One potential obstacle in such applications is the requirement of European option prices in the estimation of these moments. In this paper, we develop a simple, accurate method for extracting risk-neutral density and its moments from American option prices. A key advantage of our approach is that a single implied binomial tree is constructed to fit all American option prices, utilizing the full information set in the entire options market. Since American options are more commonly traded than European options, our methodology expands the scope of research on option-implied density and moments to a much wider class of underlying assets (e.g., equity and futures options).

Keywords: Risk-neutral distribution, risk-neutral moments, model-free implied volatility, skewness, kurtosis, American options

JEL Classification: G13, G14

Suggested Citation

Tian, Yisong Sam, Extracting Risk-Neutral Density and its Moments from American Option Prices (November 24, 2010). Journal of Derivatives, Vol. 18, No. 3, 2011, https://doi.org/10.3905/jod.2011.18.3.017. Available at SSRN: https://ssrn.com/abstract=1905555

Yisong Sam Tian (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
416-736-2100, ext 77943 (Phone)
416-736-5687 (Fax)

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