Risk Models with Jumps and Time-Varying Second Moments

31 Pages Posted: 23 Apr 2011 Last revised: 14 Jun 2011

See all articles by Rob van den Goorbergh

Rob van den Goorbergh

APG Asset Management

Roderick Molenaar

Robeco Asset Management

Onno W. Steenbeek

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); APG All Pensions Group

Peter Vlaar

Algemene Pensioen Groep (APG)

Date Written: June 10, 2011

Abstract

In this paper, we propose a new risk model to better address events like the recent credit crisis. First, the possible start of a crisis is modeled by including a low-probability jump process. Second, the risk characteristics of the crisis are captured by allowing for time-varying volatilities and correlations. Time variation in correlations is due to the changing importance of two sources: monetary shocks leading to a positive stock-bond correlation, and risk aversion (or “flight to safety”) shocks leading to a negative stock-bond correlation. The model stays within the essentially affine class, thereby allowing for closed-form solutions for arbitrage-free nominal and real bond prices of all maturities. Moreover, equity options and swaption prices are included in the estimation procedure to enhance the proper modeling of the volatility on the equity and interest rate markets. The model captures a large part of the time variation in financial risks for pension funds due to both changing volatilities and correlations.

Keywords: essentially affine macro-finance term structure model, time-varying volatilities and correlations, jumps, options, swaptions

JEL Classification: E43, G13, G17

Suggested Citation

van den Goorbergh, Rob and Molenaar, Roderick and Steenbeek, Onno W. and Vlaar, Peter, Risk Models with Jumps and Time-Varying Second Moments (June 10, 2011). Netspar Discussion Paper No. 03/2011-034. Available at SSRN: https://ssrn.com/abstract=1816371 or http://dx.doi.org/10.2139/ssrn.1816371

Rob Van den Goorbergh

APG Asset Management ( email )

P.O. Box 75283
1070 AG Amsterdam
Netherlands

HOME PAGE: http://www.apg.nl/apgsite/pages/english/

Roderick Molenaar

Robeco Asset Management ( email )

Weena 850
Rotterdam, 3014 DA
Netherlands

Onno W. Steenbeek

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

Dept. of Finance, H14-1
P.O. Box 1738
3000 DR Rotterdam, 3000DR
Netherlands
+31-10-4081400 (Phone)
+31-10-4089165 (Fax)

HOME PAGE: http://people.few.eur.nl/steenbeek/

APG All Pensions Group ( email )

Gustav Mahlerplein 3
P.O. Box 75283
1070 AG Amsterdam
Netherlands
+31-20-6049122 (Phone)
+31-20-4059176 (Fax)

HOME PAGE: http://www.apg.nl

Peter Vlaar (Contact Author)

Algemene Pensioen Groep (APG) ( email )

P.O. Box 75283
Amsterdam, 1070 AG
Netherlands

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