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Encyclopedia of Financial Models, 3 Volume Set by Frank J. Fabozzi

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Extracting Risk-Neutral Density Information from Options Market Prices

ARTURO LECCADITO, PhD

Business Administration Department, Università della Calabria

RADU TUNARU, PhD

Professor of Quantitative Finance, Business School, University of Kent

Abstract: Information on risk-neutral density is valuable in financial markets for a wide range of participants. This density can be used to mark-to-market exotic options that are not very liquid on the market, for anticipation of effects determined by new policy or possible extreme events such as crashes, and even for designing new trading strategies. There are many models that have been proposed in the past for estimating the risk-neutral density, each with their pros and cons.

The concept of risk-neutral density (RND) plays an important theoretical role in asset pricing as outlined in Cox and Ross (1976), published very shortly after the publication of the Black-Scholes model. Since then, the estimation of RND has become an essential tool for central banks in monitoring the stability of the financial system and for measuring the impact of new policies. Investment banks also rely on the RND calibrated from liquid European vanilla options to determine the price of more exotic positions on their balance sheet that are not very liquid. Moreover, the first moments of the RND, such as implied volatility and skewness, can be used to design trading strategies.

One may argue that the information contained in option prices is redundant to the ...

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