No abstract

No abstract

No abstract

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. JEL: G12, G13 AbstractWe 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.

It is often difficult to distinguish among different option pricing models that consider stochastic volatility and/or jumps based on a cross-section of European option prices. This can result in model misspecification. We analyze the hedging error induced by model misspecification and show that it can be economically significant in the cases of a delta hedge, a minimum-variance hedge, and a delta-vega hedge. Furthermore, we explain the surprisingly good performance of a simple ad-hoc Black-Scholes hedge. We compare realized hedging errors (an incorrect hedge model is applied) and anticipated hedging errors (the hedge model is the true one) and find that there are substantial differences between the two distributions, particularly depending on whether stochastic volatility is included in the hedge model. Therefore, hedging errors can be useful for identifying model misspecification. Furthermore, model risk has severe implications for risk measurement and can lead to a significant misestimation, specifically underestimation, of the risk to which a hedged position is exposed.