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Volatility and Time Series EconometricsEssays in Honor of Robert Engle$
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Tim Bollerslev, Jeffrey Russell, and Mark Watson

Print publication date: 2010

Print ISBN-13: 9780199549498

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199549498.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 September 2021

Estimating the Implied Risk‐Neutral Density for the US Market Portfolio *

Estimating the Implied Risk‐Neutral Density for the US Market Portfolio *

(p.323) 15 Estimating the Implied Risk‐Neutral Density for the US Market Portfolio*
Volatility and Time Series Econometrics

Stephen Figlewski

Oxford University Press

This chapter presents a new methodology for extracting complete well-behaved risk-neutral density (RND) functions from options market prices, and illustrates the potential of this tool for understanding how expectations and risk preferences are incorporated into prices in the US stock market. It reviews a variety of techniques for obtaining smooth densities from a set of observed options prices and selects one that offers good performance. This procedure is then modified to incorporate the market's bid-ask spread into the estimation. The chapter shows how the tails of the RND obtained from the options market may be extended and completed by appending tails from a generalized extreme value (GEV) distribution. The procedure is employed in order to estimate RNDs for the S&P 500 stock index from 1996-2008, and develops several interesting results.

Keywords:   risk-neutral density functions, options market prices, US stock market, S&P 500 stock index

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