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 max-imization framework, using exponential utility. A traded asset, correlatedwith that underlying the claim, is used for hedging, with the correlation typically close to 1. Using a distortion method [30, 31] we derive a non-linear expectation representation for the claim's ask price and a formulafor the optimal hedging strategy. We generate a perturbation expansionfor the price and hedging strategy in powers of 2 = 1 2. The terms inthe price expansion are found to be proportional to the central momentsof the claim payo under a measure equivalent to the physical measure.The resulting fast computation capability is used to carry out a simulationbased test of the optimal hedging program, computing the terminal hedg-ing error over many asset price paths. These errors are compared withthose from a naive strategy which uses the traded asset as a proxy for thenon-traded one. The distribution of the hedging error acts as a suitablemetric to analyze hedging performance. We nd that the the optimal pol-icy improves hedging performance, in that the hedging error distributionis more sharply peaked around a non-negative pro t. The frequency ofpro ts over losses is increased, and this is measured by the median of thedistribution, which is always increased by the optimal strategies.