Implied risk-neutral probability density functions from option prices: theory and application

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Abstract
Due to their forward-looking nature, derivative markets provide monetary authorities with a rich source of information for gauging market sentiment. For example, a futures price gives a widely used measure of the market's views about the future value of an asset, namely its mean or expected value at the maturity date of the futures contract. Moreover, the information available from futures prices can be extended by using option prices to estimate the market's entire probability distribution of the future value of an asset. This paper develops various techniques for estimating the market's probability distribution of the future value of an underlying asset from the prices of options on that asset. It discusses the relative merits and drawbacks of each approach, and shows how our preferred approach can be applied to estimate ex ante probability distributions using LIFFE equity and interest rate options, and Philadelphia Stock Exchange currency options. The paper then illustrates the potential value of this type of information to the policy-maker in assessing monetary conditions and conducting monetary operations. Finally, the paper looks at the limitations in data availability and highlights some areas for future research.
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