The Role of Volatility Shocks and Rare Events in Long-Run Risk Models

59 Pages Posted: 14 Mar 2012

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Paulo Rodrigues

Maastricht University

Christian Schlag

Goethe University Frankfurt - Research Center SAFE

Date Written: November 18, 2011

Abstract

We study a long-run risk model with a stochastic consumption growth rate, a stochastic volatility, a stochastic jump intensity, and a stochastic mean reversion level for the latter two processes. First, using a square-root specification instead of the Ornstein-Uhlenbeck process suggested by Drechsler and Yaron (2010) for the long-run mean reversion level of uncertainty has far-reaching economic consequences: the equity risk premium is increasing not only with short-run but also with long-run uncertainty, and the predictive power of the current price-dividend ratio for future excess returns increases and comes closer to empirically observed values. Second, we distinguish between two sources of a time-varying uncertainty of cash-flows, stochastic diffusive variance and stochastic jump intensity. We find that for most effects caused by time-varying uncertainty, time-variation in the jump intensity is much more important than time-variation in diffusive volatility risk. Third, the empirically observed low correlation between changes in the level and changes in the slope of the implied volatility smile for the S&P 500 index can only be matched with a model where jump intensity and conditional variance are locally uncorrelated.

Keywords: Epstein-Zin preferences, variance risk premium, jump risk, stochastic volatility, level and slope of implied volatility smile

JEL Classification: G12

Suggested Citation

Branger, Nicole and Rodrigues, Paulo and Schlag, Christian, The Role of Volatility Shocks and Rare Events in Long-Run Risk Models (November 18, 2011). Available at SSRN: https://ssrn.com/abstract=2021070 or http://dx.doi.org/10.2139/ssrn.2021070

Nicole Branger

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Paulo Rodrigues

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200MD
Netherlands

Christian Schlag (Contact Author)

Goethe University Frankfurt - Research Center SAFE ( email )

(http://www.safe-frankfurt.de)
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany
+49 69 798 33699 (Phone)

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