Optimal Portfolios when Volatility can Jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and (possibly correlated) jumps in both, the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. One main finding is that the demand for jump risk now also includes a hedging component, which is not present in models without jumps in volatility. Second, we show in a partial equilibrium framework that the introduction of nonlinear derivative contracts can have a substantial economic value. Third, we analyze the distribution of terminal wealth for an investor who uses the wrong model when making portfolio choices, either by ignoring volatility jumps or by falsely including such jumps although they are not present in the true model. In both cases the terminal wealth distribution exhibits fatter tails than under the correctly specified model, as well as significant default risk. Volatility jumps are thus an important risk factor in portfolio planning.