Performance of utility based strategies for hedging basis risk

The performance of optimal strategies for hedging a claim on a non-traded asset is analyzed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation $\rho$ typically close to 1. Using a distortion method (Zariphopoulou 2001, Finance and Stochastics 5, 61-82) we derive a nonlinear expectation representation for the claim's ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of $\epsilon^{2}=1-\rho^{2}$. The terms in the price expansion are proportional to the central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyze hedging performance. We find that the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies. An empirical example illustrates the application ofthe method to the hedging of a stock basket using index futures