When Do Jumps Matter for Portfolio Optimization?
SAFE Working Paper No. 16
39 Pages Posted: 4 May 2013 Last revised: 28 Nov 2015
Date Written: November 25, 2015
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: Suggested Citation