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When Do Jumps Matter for Portfolio Optimization?

SAFE Working Paper No. 16

39 Pages Posted: 4 May 2013 Last revised: 28 Nov 2015

Marius Ascheberg

Goethe University Frankfurt

Nicole Branger

University of Muenster - Finance Center Muenster

Holger Kraft

Goethe University Frankfurt

Frank Thomas Seifried

University of Trier

Multiple version iconThere are 2 versions of this paper

Date Written: November 25, 2015

Abstract

We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on quantities known only in the true model. We apply our method to a calibrated affine model. Our findings are threefold: Jumps matter more, i.e. our approximation is less accurate, if (i) the expected jump size or (ii) the jump intensity is large. Fixing the average impact of jumps, we find that (iii) rare, but severe jumps matter more than frequent, but small jumps.

Keywords: Optimal investment, jumps, stochastic volatility, welfare loss

JEL Classification: G11, C63

Suggested Citation

Ascheberg, Marius and Branger, Nicole and Kraft, Holger and Seifried, Frank Thomas, When Do Jumps Matter for Portfolio Optimization? (November 25, 2015). SAFE Working Paper No. 16. Available at SSRN: https://ssrn.com/abstract=2259630 or http://dx.doi.org/10.2139/ssrn.2259630

Marius Ascheberg

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Gr├╝neburgplatz 1
Frankfurt am Main, 60323
Germany

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

Holger Kraft (Contact Author)

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universit├Ątsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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