Modeling the volatility of stock returns in periods of Financial market stress

Research output: Working paper

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DateIn preparation - 2012
Original languageEnglish

Abstract

In this paper we evaluate the statistical properties of daily US stock index returns over more
than three decades. The relationship between volatility of the stock return process and its
fourth moments is shown to be time-varying over that horizon, which we model by identi-
fying three subperiods with more stable properties. We nd that subperiod-specic models
of stochastic volatility oer superior performance to a single model t to the entire period.
During periods of high kurtosis, we propose a new model for stock returns pricing that can
hold even in the event of severe nancial market stress. For instance, implied volatility of the
S&P500 index during 1987 was characterized by very sharp movements in both directions.
Unlike existing models which only allow for dramatic increases in volatility, the proposed
model allows the stock return volatility to wander about its path without any restrictions.
This allows the volatility to either rise or fall violently while the entire process remains pos-
itive. The Efficient Method of Moments is used to estimate the parameters of the stock
index returns process and its corresponding volatility. Improved modeling of volatility has
important implications for option pricing.

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