Strike-Adjusted Spread: A New Metric for Estimating the Value of Equity Options

Posted: 6 Aug 1999

See all articles by Joseph Zou

Joseph Zou

Goldman Sachs Group, Inc.

Emanuel Derman

Columbia University


Investors in equity options experience two problems that compound each other. In contrast to fixed-income and currency markets, there are thousands of underlyers and tens of thousands of options, and each underlyer can have a potentially large volatility skew. How can an options investor gauge which option provides the best relative value?

In this paper, we propose a method for estimating the fair volatility smile of any equity underlyer from information embedded in the time series of that underlyer's historical returns. We can then compute the relative richness or cheapness of any particular strike and expiration by examining the option's Strike-Adjusted Spread, or SAS, the difference between its market implied volatility and its estimated historically-fair volatility.

Our method obtains fair volatility smiles by estimating the appropriate risk-neutral distribution for valuing options on any equity underlyer from that underlyer's historical returns. The distribution includes the effect of both past price jumps and past shifts in realized volatility. Using this distribution, we can estimate the fair volatility skews for illiquid or thinly-traded single-stock and basket options. We can also forecast changes in the skew from changes in a single options price.

JEL Classification: C61, G12, G13

Suggested Citation

Zou, Joseph Zhou and Derman, Emanuel, Strike-Adjusted Spread: A New Metric for Estimating the Value of Equity Options. Available at SSRN:

Joseph Zhou Zou (Contact Author)

Goldman Sachs Group, Inc. ( email )

85 Broad Street
Quantitative Strategies Group, 46 Floor
New York, NY 10004
United States
212 902 9794 (Phone)
212 902 7550 (Fax)

Emanuel Derman

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States
212 854 9883 (Phone)


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