Performance of utility-based strategies for hedging basis risk

Abstract

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, correlated with 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 formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of 2 = 1􀀀 2. The terms in the price expansion are found to be proportional to the central moments of the claim payo under a measure equivalent to the physical measure. The resulting fast computation capability is used to carry out a simulation based test of the optimal hedging program, computing the terminal hedg- ing 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 nd that the the optimal pol- icy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative pro t. The frequency of pro ts over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies.